Name __________________

Chemical Kinetics Unit 5 (sev e n c l ass per io ds )

Unit 51 Collision Theory amp Potential Energy Diagrams

1) Collision theory -- Reactions only occur if reactants collide with enough

energy amp in the correct orientation

a) Reactions that produce products are known as fruitful collision

b) The energy they need to have when they collide is known as the

activation energy It an amount of energy needed to overcome

their intramolecular attraction to convert shift those attractions to

another atom or groups of atoms

2) The rate of fruitful can be seen if we graph the concentration of each species of a reaction

a) The rate of a reaction is how quickly the molarity (119898119900119897119871frasl ) of reactants or

products changes over time Therefore its units are 119872 119904119890119888frasl or 119898119900119897

119871lowast119904119890119888

b) The rate of a reaction can only be determined experimentally and in second year

chemistry (AP Chemistry) we will do just that For now just know that it is

possible to change the rate of a reaction a couple of ways

3) How to speed up a chemical reaction

a) Increase the concentration of the particles ndash the more particles you have in the reaction container the more

likely they are to collide with sufficient energy and in the correct orientation to produce a product

b) Increase the amount of particles ndash the more particles you have in the reaction container the more likely they

are to collide with sufficient energy and in the correct orientation to produce a product

c) Speed up the particles of the reaction ndash by increasing the speed of the particles you increase the number of

them that have sufficient energy when they collide to overcome their activation energy

i) Heat lsquoem up speed lsquoem up

ii) Generally every 10oC increase in temperature doubles the rate of the reactions

d) Break up clumps to increase surface area ndash when particles are clumped together they insulate particles on the

inside from colliding By breaking solids up you allow more locations for collisions to occur

e) Add a catalyst ndash catalysts lower the activation energy of a reaction thus allowing more collisions to overcome

this obstacle

4) Enthalpy (H)

a) The potential energy stored in a substances bonds we sometimes refer to it as heat

b) However it is always a massive number therefore we focus on the change in this value

c) For a reaction to occur the bonds holding the reactants together must

be broken before the bonds of a product can form

i) When bonds break energy must be absorbed

ii) When bonds are formed energy is released

d) The change in enthalpy between your reactants and products is known

as the heat or enthalpy of the reaction

e) When energy is absorbed the reaction is said to be endothermic

f) When energy is released the reaction is said to be exothermic

Products Because they are appearing

Reactants Because they are being used up

5) Potential energy diagrams

a) Graphical representation of the enthalpy of a reaction as it proceeds

b) Shows the enthalpy of the reaction (Hrxn) and can be calculated as products ndash reactants

c) Reactants are always on the left and products are always on the left

d) A catalyst lowers the activation energy by either providing an additional lower energy pathway or by orienting

the reactants

6) Maxwell-Boltzmann Distributions

a) You can mark the position of activation energy Ea on a Maxwell-

Boltzmann distribution to get a diagram like the one shown right If

the temperature is increased the molecules speed up and collide

more frequently with more energetic collisions

b) Only those particles represented by the area to the right of the

activation energy mark will react when they collide The great

majority dont have enough energy and will simply bounce apart

c) If we increase the temperature from T1 to T2 more molecules are

energetic enough to achieve the Ea thus more molecules react and

the overall reaction rate increases Notice how many more molecules

are to the right of the activation energy and thus will react when they

collide

d) A general rule of thumb is that reaction rate doubles for each 10 1048689C rise in temperature

7) Chemical Reaction Rates

a) The speed of a reaction is expressed in terms of its ldquoraterdquo which is equal to some measurable quantity that is

changing with time

b) The rate of a chemical reaction is measured by the decrease in concentration of a reactant or an increase in

concentration of a product in a unit of time

c) Concentration can be abbreviated as [x] where x is the substance in question

119929119938119957119942 = minus∆[119955119951119957]

∆119957 119952119955

∆[119953119955119952119941]

∆119957

d) Rate is not constant it changes

with time Graphing the data of an

experiment will show an average

rate of reaction

e) Calculating the rate of a reaction

can be done a number of ways

i) Instanteous rate law ndash the rate

at a given moment

ii) Relative reaction rate ndash the rate of one species vs another

iii) Differential rate law ndash experimentally determined rate based on the

rate at the instant of mixing

iv) Integrated rate law ndash experimentally determined rate based on

mathematical manipulation of concentrations of

ONE substance over the course of time

8) Instataneous Reaction Rate

a) The rate at a given time

b) The slope (y=mx+b) of the tangent line is the reaction

rate

i) (+) for reactants

ii) (-) for products

9) Relative Reaction Rate

a) Rate relate to each other in the context of a given chemical system based on their stoichiometric values

Consider the reaction 2 1198731198742(119892) rarr 2 119873119874(119892) + 1 1198742(119892)

b) reveals that oxygen gas can appear only half as rapidly as the nitrogen dioxide gas disappears while NO gas

appears twice as fast as oxygen appears

c) The simplest way to obtain relative rate expressions

i) place a one over each coefficient in the balanced equation

ii) make reactants negative (-) as they will be used up

iii) make products positive (+) as they will be produced

Exercise 1 Determine the rate of the species at the given

time

Reactant

10s

20s

Product

10s

20s

Co

mm

on

mu

ltip

le

cho

ice

que

stio

ns

Co

mm

on

FR

Q

qu

est

ion

s

d) You will OFTEN be asked to express this as a ratio To do that Simply multiply ALL the terms by the same factor

to eliminate the fractions

For 2 1198731198742(119892) rarr 2 119873119874(119892) + 1 1198742(119892) the ratio would be -121

52 Rate Law Expression

1 Most reactions are reversible meaning that products can combine to form reactants In unit 7 we will look at

what exactly that means but for now it means we will need to look at the rate of reactions at the moment of

mixing

2 The rate of the reaction is determined experimentally (I will give you data which you have to analyze) This data

is obtained by

a Count number of bubbles of gas produce (capture volume by water displacement)

b Mass of precipitate formed

c spectrophotometry

3 we will look only at reactants since at the moment of mixing there shouldnrsquot be any products Common sense

tells us that ratereaction [reactants] mathematically a proportion () can be replaced with ldquo= krdquo where k is

some constant This is how we got all those gas laws in unit 3 thus a rate expressions general format is

k = rate constant [A] = concentration of reactant A [B] = concentration of reactant B m = order of reaction for reactant A n = order of reaction for reactant B

Exercise 2 What is the relative reaction rate for the reaction below What is the whole number ratio

4 1198751198673 rarr 1198754 + 6 1198672

Exercise 3 Write the relative rates of change in concentration of the products and reactant in the decomposition of

nitrosyl chloride NOCl

2 119873119874119862119897 rarr 2 119873119874 + 1198621198972

119886119860 + 119887119861 rarr 119909119883

Rate Law written as

119929119938119957119942 = 119948[119912]119950[119913]119951

Can be zero whole numbers or fractions CAN ONLY BE DETERMINED BY EXPERIMENTATION

a Rate constant (k)

i A lower case k we will use the upper case for another constant later

ii Varies wildly with temperature

iii Units are required so that rate is measured in concentration for each unit of time (119898119900119897

119871 119905119894119898119890 or

119872

119905119894119898119890)

b Orders of reaction with respect for each reagent

i Zero order ndash changing the concentration of this reactant has no effect on the rate Say ldquoThe

reaction is zero order with respect to Ardquo

ii First order ndash doubling the concentration doubles the rate of the reaction (all nuclear decay is 1st order)

Say ldquoThe reaction is 1st order with respect to Ardquo

iii Second order ndash doubling the concentration quadruples the rate of the reaction Say ldquoThe

reaction is 2nd order with respect to Ardquo

THE OVER ALL ORDER IS THE SUM OF ALL THE REACTION ORDERS

4 Differential Rate law

a Examining Concentration vs rate data Allows you to determine the rate expression

b Two methods

i Table logic

1 look at the data find two experiments where one reactant is static and the other makes

a measureable change see how the rate reacts Which order is that

2 Pros Fast Good for MC

3 Cons requires you recognize the math on FRQs requires exact explanations

YOU MUST explain it as ldquoIn experiments ltXgt amp ltYgt reactant ltAgt is constant while

reactant ltBgt ltmakes changegt and the rate ltmakes changegt This shows the

reaction is ltordergt with respect to ltBgtrdquo

ii Dirty quick math

1 Since any value divided by itself is 1 we could set two

experimental data sets us a fraction and they should

cancel out

I suggest you put the experiment with the larger values as the numerator

2 Pros never fails is its own explaination you only need to say ldquoreaction is ltordergt with

respect to ltBgtrdquo

3 Cons MUCH slower

c Determining K

i Value ndash simply plug any experiment into the rate law you determined and solve for k

ii Units

1 Since rate MUST be 119898119900119897

119871 119905119894119898119890 k must have units that cancel out the concentrations and

provides that time unit

2 Therefore the units of k are always 1M to the -OAO (overall order of the reaction)-1

119871(119874119860119874minus1)

119898119900119897(119874119860119874minus1) 119905119894119898119890 or

1

119872(119874119860119874minus1) 119905119894119898119890

On the next two pages please take notes on BOTH ways to do the same problem

1199031198861199051198902 = 1198962[119860]2119898[119861]2

119899

1199031198861199051198901 = 1198961[119860]1119898[119861]1

119899

Exercise 4a Table logic

a) What is the order of the reaction with respect to A

b) What is the order of the reaction with respect to B

c) What is the value of the rate constant including units

Exercise 4b dirty math

a) What is the order of the reaction with respect to A

b) What is the order of the reaction with respect to B

c) What is the value of the rate constant including units

Exercise 5

Exercise 6

5) Reaction mechanisms

a) the sequence of bond-making and bond-breaking steps that occurs during the conversion of reactants to

products

i) Must be experimentally determined

ii) Must agree with the overall stoichiometry

iii) Must agree with the experimentally determined rate law

b) The vocabulary of mechanisms involves elementary steps amp molecularity which describes the number of

molecules that participate in an atomic rearrangement Add these terms into your explanations

i) unimolecular involves one reactant molecule that collides with a solvent or background molecule thereby

becoming collisionally activated In this state the reactant molecule is thermodynamically favorable for

converting into product

ii) bimolecular involves a collision between two reactant molecules

iii) termolecular simultaneous collision between three reactant molecules [very rare]

c) the rate expression cannot be predicted from overall stoichiometry The rate expression of an elementary step is

predicted from the stoichiometry of the elementary step as per the table below

d) Catalysts ndash species that are reactants in an elementary step but in subsequent steps is a product They LOWER

the activation energy amp donrsquot change H

i) Homogeneous catalyst ndash exist in the same phase as the reactants

ii) Heterogeneous catalyst ndash exist in a different phase than the reactants

e) Intermediaries ndashspecies that are products in an elementary step but in subsequent steps are reactants amp

consumed

i) Neither catalysts or intermediaries appear in the overall reaction or rate law

Exercise 7

Label the intermediaries amp catalysts

f) the slowest step is the rate determining step -- the rate of the overall reaction is limited by and is exactly equal

to the combined rates of all elementary steps up to and including the slowest step in the mechanism

Exercise 8

Exercise 9

In the reaction 2X+Y rarr Z

For a particular reaction the rate is found to be rate=k[Y]

Which of the below purposed mechanisms is a valid mechanism for this reaction

53 Rate Law Expression pt 2

1 Differential rate law

a Concentration vs rate data

b Use table logic or ugly algebra to find rate law amp value of K

2 Integrated rate law

a Concentration vs time data

b Must choose the straightest line graph and know what it means

c ONLY one reactant

d Done to determine how long a reaction must run to reach a certain concentration of reactant

e The value of the rate constant k is equal to the absolute value of the slope of the best fit line which is

decided by examining 3 linear regressions and analyzing the regression correlation coefficient (r)

i Graphs WILL be provided (except for the lab)

ii Time is ALWAYS X

iii The Y axi are

1 concentration of the reactant

2 natural log of the concentration (ln[A] NOT log[A])

3 reciprocal of the concentration on the y-axis of the third graph

iv If you remember them in this order with the y-axes being ldquoconcentrationrdquo ldquonatural log of

concentrationrdquo and ldquoreciprocal concentrationrdquo the alphabetical order of the y-axis variable

leads to 0 1 2 orders respectively for that reactant

REMEMBER what each variable is

Exercise 10

y = -00002x + 00831Rsup2 = 08871

-005

0

005

01

015

0 200 400 600

[N2O5]

y = -00069x - 23026Rsup2 = 1

-6

-4

-2

0

0 200 400 600

Ln [N2O5] y = 03535x - 78441

Rsup2 = 08841

-100

0

100

200

0 200 400 600

1[N2O5]

Unit 54 Kinetics Clean up

1 Half Life

a the time required for one half of one of the

reactants to disappear

b focus on the half-life for first order reactions only

i Discuss order (what order is it NOT)

ii Determine half life

iii What is the concentration after a set

number of half lives

iv What time would a set concentration be

found

2 In lab we will determine the order of a reaction by ldquoswampingrdquo We maximize one reactants concentration so

that ANY change is negligible

Exercise 11

a) What order is it NOT

b) Determine half life

c) What is the concentration after the second half life

d) When would 75 of the sample have decayed

For the generic reaction A + B C

1 The reaction below was studied at 25frac14C and the following data was obtained

NH4+ + NO2

N2 + 2H2O(L)

a What is the rate law

b What is the rate constant Be sure and include units

2 The reaction below was studied at 10frac14C and the following data was obtained

2NO(g) + Cl2(g) 2NOCl(g)

a What is the rate law

b What is the rate constant Be sure and include units

3 The reaction below was studied and the following data were obtained

2ClO2 + 2OH ClO3 + ClO2

+ H2O

a What is the rate law

b What is the rate constant Be sure and include units

4 The reaction below was studied and the following data were obtained

I + OCl IO + Cl

a What is the rate law

b What is the rate constant Be sure and include units

5 The reaction below was studied and the following data were obtained

BrO3 + 5 Br + 6 H+ 3 Br2 + 3 H2O

a What is the rate law

b What is the rate constant Be sure and include units

P E1 (pg 1 of 3) Using Initial Rates to Determine Order Name_____________________Per___

[NO]0

(molL)[Cl2]0

(molL)Initial Rate

(moleL min)

010 010 018

010 020 035

020 020 145

[I]0

(molL)[OCl]0

(molL)Initial Rate

(molL s)

012 018 791 102

006 018 395 102

003 009 988 103

024 009 791 102

[ClO2]0

(molL)[OH]0

(molL)Initial Rate

(molL s)

0050 0100 0057

0100 0100 023

0100 0050 0115

[NH4+]0

(molL)[NO2

]0

(molL)Initial Rate(moleL sec)

0100 0005 135 107

0100 0010 270 107

0200 0010 540 107

[BrO3]0

(molL)[Br]0

(molL)[H+]0

(molL)Initial Rate

(molL s)

0100 0100 0100 80 104

0200 0100 0100 16 103

0200 0200 0100 32 103

0100 0100 0200 32 103

trial[A]0

(molL)[B]0

(molL)Initial Rate

(moleL hour)

1 4 6 20

2 4 3 10

3 2 6 5

rate1

rate2=k

k

[A]ox

[A]ox

[B]oy

[B]oy

20

10=k

k

[4]ox

[4]ox

[6]oy

[3]oy

2 = [2]y

y = 1

20

5=k

k

[4]o

x

[2]o

x

[6]o

1

[6]o

1

4 = [2]x

x = 2 rate = k[A]2[B]

While it is most likely that any rate laws on the AP exam will only be first or second order it is possible that other orders will show up and are indeed possible When the order is not so obvious it is useful to know a useful log rule

RateRatio = [ConcRatio]x

log[RateRatio] = x log[ConcRatio] thus it is quite simple to solve for the order x log[RateRatio]

log[ConcRatio]= x

6 Given the hypothetical data below determine the order of the reaction A + B + C D + E

[A] (M) [B] (M) [C] (M) Rate (Msec)

10 10 10 00076

20 10 10 00304

10 10 20 00107

10 20 10 00152

7 Given the hypothetical data below determine the order of the reaction H + I + J K

[H] (M) [I] (M) [J] (M) Rate (Msec)

10 10 10 17

23 10 10 391

10 10 40 27

10 18 20 694

8 Given the hypothetical data below determine the order of the reaction P + Q + R S + T

[P] (M) [Q] (M) [R] (M) Rate (Msec)

10 10 10 00365

10 635 10 147

10 10 075 00274

19 47 23 185

9 Given the hypothetical data below determine the order of the reaction V + W + X Y + Z

[V] (M) [W] (M) [X] (M) Rate (Msec)

001 001 001 280 106

001 004 001 448 105

001 002 006 672 105

005 0025 0036 141 104

P E1 (pg 2 of 3) Using Initial Rates to Determine Order

Nitrogen dioxide will decompose into nitrogen oxide and oxygen gas as indicated in the equation below

2 NO2(g) 2 NO(g) + O2(g)

A graph of the concentration of each constituent at various times during the course of the reaction at 300frac14C is presented below Use this graph to understand that the loss of reactant and formation of products is stoichiometrically related

Decomposition of nitrogen dioxide

0

0002

0004

0006

0008

001

0012

0 100 200 300 400 500

time

co

nc

Next you can use the concentration of the reactant vs time data presented in the data table above and manipulate the concentration

values to ln[NO2] and 1

[NO2]

and then graph ln[NO2] vs time and also graph 1

[NO2]

vs time You can use these two graphs to

look for which of the graphs presented will give a straight line in order to determine the order of the reaction These two graphs are shown below

The r2 value which is the coefficient of determination you will learn more about r and r2 when you take a statistics course but for now you can think of it as a Ogravegoodness-of-fitOacute indicator The closer the r2 is to 1 the better the data fits to a straight line Thus

you can see that the r2 value is best for 1

[NO2]

vs time indicating this reaction is second order

P E2 (pg 1 of 6) Rate Laws Using data amp graphs Name_____________________Per____

Decomposition of Nitrogen Dioxide

time (sec) [NO2] [NO] [O2]

0 001 0 0

50 00079 00021 00011

100 00065 00035 00018

150 00055 00045 00023

200 00048 00052 00026

250 00043 00057 00029

300 00038 00062 00031

350 00034 00066 00033

400 00031 00069 00035

$amp()$amp+-

amp++

$-amp

$0amp(

$0amp-

$0amp

$0amp

$0amp

$amp(

$amp-

0 1 10 0 2 20 0

$$

amp(

)$$+amp(

$ampamp()+$-$+++-amp

amp$$$

($$$$

(amp$$$

-$$$$

-amp$$$

0$$$$

0amp$$$

$ amp$ ($$ (amp$ -$$ -amp$ 0$$ 0amp$ $$

$amp

()amp

$+amp-amp()amp

1 The dimerization of butadiene is studied at 500 K and the following reaction and experimental data is presented below

2 C4H6(g) C8H12(g)

a Determine the rate law for this reaction

b Determine the rate constant

c Calculate the half-life for this reaction (If it is not 1st order calculate the half-life at the initial concentration)

P E2 (pg 2 of 6) Rate Law for Dimerization of Butadiene

Time (s) [C4H6(g)] (M)

0 00167

195 00160

604 00150

1246 00130

2180 00110

6210 00068

$

$

amp$

amp$

amp($

amp$

amp$

$ amp$ $ )$ ($ $ $ +$

$

amp$

()$+$amp$

$amp($)amp)+

-amp0+

$0amp+

$0amp

$)amp

$)amp1

$)amp)

$)amp+

$)amp

+ ) 0 1 2

$$

amp(

)$$+amp(

$$amp()+(-

$+

0$$$

1$$$

2$$$

$$$

amp$$$$

ampamp$$$

amp($$$

amp-$$$

amp$$$

amp+$$$

$ amp$$$ ($$$ -$$$ $$$ +$$$ 0$$$ 1$$$

$amp

()amp

$+amp-amp()amp

2 Dinitrogen pentoxide can be decomposed according to the reaction below

2 N2O5(soln) 4 NO2(soln) + O2(g) All Trials are performed at 45frac14C

Data for this reaction can be collected in different ways It is presented in two different ways below instantaneous rates for various concentrations and concentration at various time The concentration vs time data is graphed

Concentration and Initial Rates

a What are a few methods by which you could determine the reaction order

b What are several different methods by which you could determine the rate constant k

c What are a few different methods by which you could determine the half-life

P E2 (pg 3 of 6) Decomposition of Dinitrogen Pentoxide

[N2O5(solOtilden)] (molesL)

Instantaneous rate Msec

10 000060

050 000030

025 000015

Concentration vs Time DataConcentration vs Time Data

Time (s)[N2O5(solOtilden)] (molesL)

0 100

200 088

400 078

600 069

800 061

1000 054

1200 048

1400 043

1600 038

1800 034

2000 030

$amp($amp)

+amp)))-

$amp

$amp

$amp-

$amp

$amp0

$amp

amp

1 1

$$

amp(

)$$+amp(

$$$ampamp($))

+$-$

$0$

amp$$

amp0$

$$

0$

1$$

10$

$ 0$$ amp$$$ amp0$$ $$$

$amp

()amp

$+amp-amp()amp

$

$

amp$

$

($

)$

$

+$

$

$

$ $ amp$ ($ $ $ $ amp$ ($ $ $

$

amp$

()$+$amp$

3 The decomposition of hydrogen peroxide was studied at a particular temperature and experimental data is presented in the table to the right

2 H2O2(g) 2H2O(g) + O2(g)

a What are the two methods that you could use to determine the rate law for this reaction with the data that has been given

b Write out the rate law for this decomposition reaction

c What are the three methods that you could use to determine the rate constant

i Use the easiest of these two methods to determine a value for k

ii What are the units on k

d Now that you know the order of the reaction calculate the half-life for this reaction (if it is not 1st order calculate the half-life at the initial concentration)

yen Show how the conc vs time graph confirms the value that you calculated

P E3 (pg 4 of 6) Decomposition of H2O2

Time (s) [H2O2(g)] (moleL)

0 10

120 091

300 078

600 059

1200 037

1800 022

2400 013

3000 0082

3600 0050

$$$amp()$amp+

-$++

)$$

$$$

$$

amp$$

$$

$$

$$$

$$

amp$$

$$

$$

$$$

$$

$ 0$$ $$$ 0$$ $$$ 0$$ 1$$$ 10$$ amp$$$

$amp

()amp

$+amp-amp()amp

$amp($amp)

+amp-

$amp

$amp

$0amp

$0amp

$1amp

$1amp

$amp

amp

1 1 0 0 )

$$

amp(

)$$+amp(

$

$

amp$

$

($

)$

$

+$

$

$

$ $ amp$ ($ $ $ $ amp$ ($ $ $

$

amp$

()$+$amp$

Please work in PENCIL Please put some work on the page that indicates HOW you did the problem

1 If a 84 g sample of thorium decays with a 10 minute half life how much would the sample weigh in a half hour

2 A sample of radioactive iodine (half life = 3 days) originally weighed 10 g but now weighs 0625 g How old is this sample

You can estimate the half life quickly and easily but youOtildell need a calculator to use the integrated rate equation and half life equations

3 A sample of radioactive calcium originally weighed 24 g and in 12 hours it weighs 125 g What is the half-life

4 If a 500 g sample of barium decays with a 45 day half life how much would the sample weigh in a 18 days

5 A sample of an ancient grass mat containing radioactive carbon (half life = 5730 years) seems to be emitting on 625 of the radiation that a sample of a grass mat woven last year would have How old is this ancient grass mat

6 A sample of radioactive calcium originally weighed 32 kg and in 2 days it weighs 05 kg What is the half-life in hours

7 If a 96 g sample of tin decays with a 25 minute half life how much would the sample weigh in 15 minutes

8 A sample of radioactive magnesium (half life = 183 days) originally weighed 80 g but now weighs 25 g How many years old is this sample

9 A sample of radioactive radium originally weighed 56 g and in three days it weighs just less than a gram What is the half life in hours

P E3 (pg 1 of 2) Half Life ETH The Rate of Radioactive Decay Name________________________Per____

5) Potential energy diagrams

a) Graphical representation of the enthalpy of a reaction as it proceeds

b) Shows the enthalpy of the reaction (Hrxn) and can be calculated as products ndash reactants

c) Reactants are always on the left and products are always on the left

d) A catalyst lowers the activation energy by either providing an additional lower energy pathway or by orienting

the reactants

6) Maxwell-Boltzmann Distributions

a) You can mark the position of activation energy Ea on a Maxwell-

Boltzmann distribution to get a diagram like the one shown right If

the temperature is increased the molecules speed up and collide

more frequently with more energetic collisions

b) Only those particles represented by the area to the right of the

activation energy mark will react when they collide The great

majority dont have enough energy and will simply bounce apart

c) If we increase the temperature from T1 to T2 more molecules are

energetic enough to achieve the Ea thus more molecules react and

the overall reaction rate increases Notice how many more molecules

are to the right of the activation energy and thus will react when they

collide

d) A general rule of thumb is that reaction rate doubles for each 10 1048689C rise in temperature

7) Chemical Reaction Rates

a) The speed of a reaction is expressed in terms of its ldquoraterdquo which is equal to some measurable quantity that is

changing with time

b) The rate of a chemical reaction is measured by the decrease in concentration of a reactant or an increase in

concentration of a product in a unit of time

c) Concentration can be abbreviated as [x] where x is the substance in question

119929119938119957119942 = minus∆[119955119951119957]

∆119957 119952119955

∆[119953119955119952119941]

∆119957

d) Rate is not constant it changes

with time Graphing the data of an

experiment will show an average

rate of reaction

e) Calculating the rate of a reaction

can be done a number of ways

i) Instanteous rate law ndash the rate

at a given moment

ii) Relative reaction rate ndash the rate of one species vs another

iii) Differential rate law ndash experimentally determined rate based on the

rate at the instant of mixing

iv) Integrated rate law ndash experimentally determined rate based on

mathematical manipulation of concentrations of

ONE substance over the course of time

8) Instataneous Reaction Rate

a) The rate at a given time

b) The slope (y=mx+b) of the tangent line is the reaction

rate

i) (+) for reactants

ii) (-) for products

9) Relative Reaction Rate

a) Rate relate to each other in the context of a given chemical system based on their stoichiometric values

Consider the reaction 2 1198731198742(119892) rarr 2 119873119874(119892) + 1 1198742(119892)

b) reveals that oxygen gas can appear only half as rapidly as the nitrogen dioxide gas disappears while NO gas

appears twice as fast as oxygen appears

c) The simplest way to obtain relative rate expressions

i) place a one over each coefficient in the balanced equation

ii) make reactants negative (-) as they will be used up

iii) make products positive (+) as they will be produced

Exercise 1 Determine the rate of the species at the given

time

Reactant

10s

20s

Product

10s

20s

Co

mm

on

mu

ltip

le

cho

ice

que

stio

ns

Co

mm

on

FR

Q

qu

est

ion

s

d) You will OFTEN be asked to express this as a ratio To do that Simply multiply ALL the terms by the same factor

to eliminate the fractions

For 2 1198731198742(119892) rarr 2 119873119874(119892) + 1 1198742(119892) the ratio would be -121

52 Rate Law Expression

1 Most reactions are reversible meaning that products can combine to form reactants In unit 7 we will look at

what exactly that means but for now it means we will need to look at the rate of reactions at the moment of

mixing

2 The rate of the reaction is determined experimentally (I will give you data which you have to analyze) This data

is obtained by

a Count number of bubbles of gas produce (capture volume by water displacement)

b Mass of precipitate formed

c spectrophotometry

3 we will look only at reactants since at the moment of mixing there shouldnrsquot be any products Common sense

tells us that ratereaction [reactants] mathematically a proportion () can be replaced with ldquo= krdquo where k is

some constant This is how we got all those gas laws in unit 3 thus a rate expressions general format is

k = rate constant [A] = concentration of reactant A [B] = concentration of reactant B m = order of reaction for reactant A n = order of reaction for reactant B

Exercise 2 What is the relative reaction rate for the reaction below What is the whole number ratio

4 1198751198673 rarr 1198754 + 6 1198672

Exercise 3 Write the relative rates of change in concentration of the products and reactant in the decomposition of

nitrosyl chloride NOCl

2 119873119874119862119897 rarr 2 119873119874 + 1198621198972

119886119860 + 119887119861 rarr 119909119883

Rate Law written as

119929119938119957119942 = 119948[119912]119950[119913]119951

Can be zero whole numbers or fractions CAN ONLY BE DETERMINED BY EXPERIMENTATION

a Rate constant (k)

i A lower case k we will use the upper case for another constant later

ii Varies wildly with temperature

iii Units are required so that rate is measured in concentration for each unit of time (119898119900119897

119871 119905119894119898119890 or

119872

119905119894119898119890)

b Orders of reaction with respect for each reagent

i Zero order ndash changing the concentration of this reactant has no effect on the rate Say ldquoThe

reaction is zero order with respect to Ardquo

ii First order ndash doubling the concentration doubles the rate of the reaction (all nuclear decay is 1st order)

Say ldquoThe reaction is 1st order with respect to Ardquo

iii Second order ndash doubling the concentration quadruples the rate of the reaction Say ldquoThe

reaction is 2nd order with respect to Ardquo

THE OVER ALL ORDER IS THE SUM OF ALL THE REACTION ORDERS

4 Differential Rate law

a Examining Concentration vs rate data Allows you to determine the rate expression

b Two methods

i Table logic

1 look at the data find two experiments where one reactant is static and the other makes

a measureable change see how the rate reacts Which order is that

2 Pros Fast Good for MC

3 Cons requires you recognize the math on FRQs requires exact explanations

YOU MUST explain it as ldquoIn experiments ltXgt amp ltYgt reactant ltAgt is constant while

reactant ltBgt ltmakes changegt and the rate ltmakes changegt This shows the

reaction is ltordergt with respect to ltBgtrdquo

ii Dirty quick math

1 Since any value divided by itself is 1 we could set two

experimental data sets us a fraction and they should

cancel out

I suggest you put the experiment with the larger values as the numerator

2 Pros never fails is its own explaination you only need to say ldquoreaction is ltordergt with

respect to ltBgtrdquo

3 Cons MUCH slower

c Determining K

i Value ndash simply plug any experiment into the rate law you determined and solve for k

ii Units

1 Since rate MUST be 119898119900119897

119871 119905119894119898119890 k must have units that cancel out the concentrations and

provides that time unit

2 Therefore the units of k are always 1M to the -OAO (overall order of the reaction)-1

119871(119874119860119874minus1)

119898119900119897(119874119860119874minus1) 119905119894119898119890 or

1

119872(119874119860119874minus1) 119905119894119898119890

On the next two pages please take notes on BOTH ways to do the same problem

1199031198861199051198902 = 1198962[119860]2119898[119861]2

119899

1199031198861199051198901 = 1198961[119860]1119898[119861]1

119899

Exercise 4a Table logic

a) What is the order of the reaction with respect to A

b) What is the order of the reaction with respect to B

c) What is the value of the rate constant including units

Exercise 4b dirty math

a) What is the order of the reaction with respect to A

b) What is the order of the reaction with respect to B

c) What is the value of the rate constant including units

Exercise 5

Exercise 6

5) Reaction mechanisms

a) the sequence of bond-making and bond-breaking steps that occurs during the conversion of reactants to

products

i) Must be experimentally determined

ii) Must agree with the overall stoichiometry

iii) Must agree with the experimentally determined rate law

b) The vocabulary of mechanisms involves elementary steps amp molecularity which describes the number of

molecules that participate in an atomic rearrangement Add these terms into your explanations

i) unimolecular involves one reactant molecule that collides with a solvent or background molecule thereby

becoming collisionally activated In this state the reactant molecule is thermodynamically favorable for

converting into product

ii) bimolecular involves a collision between two reactant molecules

iii) termolecular simultaneous collision between three reactant molecules [very rare]

c) the rate expression cannot be predicted from overall stoichiometry The rate expression of an elementary step is

predicted from the stoichiometry of the elementary step as per the table below

d) Catalysts ndash species that are reactants in an elementary step but in subsequent steps is a product They LOWER

the activation energy amp donrsquot change H

i) Homogeneous catalyst ndash exist in the same phase as the reactants

ii) Heterogeneous catalyst ndash exist in a different phase than the reactants

e) Intermediaries ndashspecies that are products in an elementary step but in subsequent steps are reactants amp

consumed

i) Neither catalysts or intermediaries appear in the overall reaction or rate law

Exercise 7

Label the intermediaries amp catalysts

f) the slowest step is the rate determining step -- the rate of the overall reaction is limited by and is exactly equal

to the combined rates of all elementary steps up to and including the slowest step in the mechanism

Exercise 8

Exercise 9

In the reaction 2X+Y rarr Z

For a particular reaction the rate is found to be rate=k[Y]

Which of the below purposed mechanisms is a valid mechanism for this reaction

53 Rate Law Expression pt 2

1 Differential rate law

a Concentration vs rate data

b Use table logic or ugly algebra to find rate law amp value of K

2 Integrated rate law

a Concentration vs time data

b Must choose the straightest line graph and know what it means

c ONLY one reactant

d Done to determine how long a reaction must run to reach a certain concentration of reactant

e The value of the rate constant k is equal to the absolute value of the slope of the best fit line which is

decided by examining 3 linear regressions and analyzing the regression correlation coefficient (r)

i Graphs WILL be provided (except for the lab)

ii Time is ALWAYS X

iii The Y axi are

1 concentration of the reactant

2 natural log of the concentration (ln[A] NOT log[A])

3 reciprocal of the concentration on the y-axis of the third graph

iv If you remember them in this order with the y-axes being ldquoconcentrationrdquo ldquonatural log of

concentrationrdquo and ldquoreciprocal concentrationrdquo the alphabetical order of the y-axis variable

leads to 0 1 2 orders respectively for that reactant

REMEMBER what each variable is

Exercise 10

y = -00002x + 00831Rsup2 = 08871

-005

0

005

01

015

0 200 400 600

[N2O5]

y = -00069x - 23026Rsup2 = 1

-6

-4

-2

0

0 200 400 600

Ln [N2O5] y = 03535x - 78441

Rsup2 = 08841

-100

0

100

200

0 200 400 600

1[N2O5]

Unit 54 Kinetics Clean up

1 Half Life

a the time required for one half of one of the

reactants to disappear

b focus on the half-life for first order reactions only

i Discuss order (what order is it NOT)

ii Determine half life

iii What is the concentration after a set

number of half lives

iv What time would a set concentration be

found

2 In lab we will determine the order of a reaction by ldquoswampingrdquo We maximize one reactants concentration so

that ANY change is negligible

Exercise 11

a) What order is it NOT

b) Determine half life

c) What is the concentration after the second half life

d) When would 75 of the sample have decayed

For the generic reaction A + B C

1 The reaction below was studied at 25frac14C and the following data was obtained

NH4+ + NO2

N2 + 2H2O(L)

a What is the rate law

b What is the rate constant Be sure and include units

2 The reaction below was studied at 10frac14C and the following data was obtained

2NO(g) + Cl2(g) 2NOCl(g)

a What is the rate law

b What is the rate constant Be sure and include units

3 The reaction below was studied and the following data were obtained

2ClO2 + 2OH ClO3 + ClO2

+ H2O

a What is the rate law

b What is the rate constant Be sure and include units

4 The reaction below was studied and the following data were obtained

I + OCl IO + Cl

a What is the rate law

b What is the rate constant Be sure and include units

5 The reaction below was studied and the following data were obtained

BrO3 + 5 Br + 6 H+ 3 Br2 + 3 H2O

a What is the rate law

b What is the rate constant Be sure and include units

P E1 (pg 1 of 3) Using Initial Rates to Determine Order Name_____________________Per___

[NO]0

(molL)[Cl2]0

(molL)Initial Rate

(moleL min)

010 010 018

010 020 035

020 020 145

[I]0

(molL)[OCl]0

(molL)Initial Rate

(molL s)

012 018 791 102

006 018 395 102

003 009 988 103

024 009 791 102

[ClO2]0

(molL)[OH]0

(molL)Initial Rate

(molL s)

0050 0100 0057

0100 0100 023

0100 0050 0115

[NH4+]0

(molL)[NO2

]0

(molL)Initial Rate(moleL sec)

0100 0005 135 107

0100 0010 270 107

0200 0010 540 107

[BrO3]0

(molL)[Br]0

(molL)[H+]0

(molL)Initial Rate

(molL s)

0100 0100 0100 80 104

0200 0100 0100 16 103

0200 0200 0100 32 103

0100 0100 0200 32 103

trial[A]0

(molL)[B]0

(molL)Initial Rate

(moleL hour)

1 4 6 20

2 4 3 10

3 2 6 5

rate1

rate2=k

k

[A]ox

[A]ox

[B]oy

[B]oy

20

10=k

k

[4]ox

[4]ox

[6]oy

[3]oy

2 = [2]y

y = 1

20

5=k

k

[4]o

x

[2]o

x

[6]o

1

[6]o

1

4 = [2]x

x = 2 rate = k[A]2[B]

While it is most likely that any rate laws on the AP exam will only be first or second order it is possible that other orders will show up and are indeed possible When the order is not so obvious it is useful to know a useful log rule

RateRatio = [ConcRatio]x

log[RateRatio] = x log[ConcRatio] thus it is quite simple to solve for the order x log[RateRatio]

log[ConcRatio]= x

6 Given the hypothetical data below determine the order of the reaction A + B + C D + E

[A] (M) [B] (M) [C] (M) Rate (Msec)

10 10 10 00076

20 10 10 00304

10 10 20 00107

10 20 10 00152

7 Given the hypothetical data below determine the order of the reaction H + I + J K

[H] (M) [I] (M) [J] (M) Rate (Msec)

10 10 10 17

23 10 10 391

10 10 40 27

10 18 20 694

8 Given the hypothetical data below determine the order of the reaction P + Q + R S + T

[P] (M) [Q] (M) [R] (M) Rate (Msec)

10 10 10 00365

10 635 10 147

10 10 075 00274

19 47 23 185

9 Given the hypothetical data below determine the order of the reaction V + W + X Y + Z

[V] (M) [W] (M) [X] (M) Rate (Msec)

001 001 001 280 106

001 004 001 448 105

001 002 006 672 105

005 0025 0036 141 104

P E1 (pg 2 of 3) Using Initial Rates to Determine Order

Nitrogen dioxide will decompose into nitrogen oxide and oxygen gas as indicated in the equation below

2 NO2(g) 2 NO(g) + O2(g)

A graph of the concentration of each constituent at various times during the course of the reaction at 300frac14C is presented below Use this graph to understand that the loss of reactant and formation of products is stoichiometrically related

Decomposition of nitrogen dioxide

0

0002

0004

0006

0008

001

0012

0 100 200 300 400 500

time

co

nc

Next you can use the concentration of the reactant vs time data presented in the data table above and manipulate the concentration

values to ln[NO2] and 1

[NO2]

and then graph ln[NO2] vs time and also graph 1

[NO2]

vs time You can use these two graphs to

look for which of the graphs presented will give a straight line in order to determine the order of the reaction These two graphs are shown below

The r2 value which is the coefficient of determination you will learn more about r and r2 when you take a statistics course but for now you can think of it as a Ogravegoodness-of-fitOacute indicator The closer the r2 is to 1 the better the data fits to a straight line Thus

you can see that the r2 value is best for 1

[NO2]

vs time indicating this reaction is second order

P E2 (pg 1 of 6) Rate Laws Using data amp graphs Name_____________________Per____

Decomposition of Nitrogen Dioxide

time (sec) [NO2] [NO] [O2]

0 001 0 0

50 00079 00021 00011

100 00065 00035 00018

150 00055 00045 00023

200 00048 00052 00026

250 00043 00057 00029

300 00038 00062 00031

350 00034 00066 00033

400 00031 00069 00035

$amp()$amp+-

amp++

$-amp

$0amp(

$0amp-

$0amp

$0amp

$0amp

$amp(

$amp-

0 1 10 0 2 20 0

$$

amp(

)$$+amp(

$ampamp()+$-$+++-amp

amp$$$

($$$$

(amp$$$

-$$$$

-amp$$$

0$$$$

0amp$$$

$ amp$ ($$ (amp$ -$$ -amp$ 0$$ 0amp$ $$

$amp

()amp

$+amp-amp()amp

1 The dimerization of butadiene is studied at 500 K and the following reaction and experimental data is presented below

2 C4H6(g) C8H12(g)

a Determine the rate law for this reaction

b Determine the rate constant

c Calculate the half-life for this reaction (If it is not 1st order calculate the half-life at the initial concentration)

P E2 (pg 2 of 6) Rate Law for Dimerization of Butadiene

Time (s) [C4H6(g)] (M)

0 00167

195 00160

604 00150

1246 00130

2180 00110

6210 00068

$

$

amp$

amp$

amp($

amp$

amp$

$ amp$ $ )$ ($ $ $ +$

$

amp$

()$+$amp$

$amp($)amp)+

-amp0+

$0amp+

$0amp

$)amp

$)amp1

$)amp)

$)amp+

$)amp

+ ) 0 1 2

$$

amp(

)$$+amp(

$$amp()+(-

$+

0$$$

1$$$

2$$$

$$$

amp$$$$

ampamp$$$

amp($$$

amp-$$$

amp$$$

amp+$$$

$ amp$$$ ($$$ -$$$ $$$ +$$$ 0$$$ 1$$$

$amp

()amp

$+amp-amp()amp

2 Dinitrogen pentoxide can be decomposed according to the reaction below

2 N2O5(soln) 4 NO2(soln) + O2(g) All Trials are performed at 45frac14C

Data for this reaction can be collected in different ways It is presented in two different ways below instantaneous rates for various concentrations and concentration at various time The concentration vs time data is graphed

Concentration and Initial Rates

a What are a few methods by which you could determine the reaction order

b What are several different methods by which you could determine the rate constant k

c What are a few different methods by which you could determine the half-life

P E2 (pg 3 of 6) Decomposition of Dinitrogen Pentoxide

[N2O5(solOtilden)] (molesL)

Instantaneous rate Msec

10 000060

050 000030

025 000015

Concentration vs Time DataConcentration vs Time Data

Time (s)[N2O5(solOtilden)] (molesL)

0 100

200 088

400 078

600 069

800 061

1000 054

1200 048

1400 043

1600 038

1800 034

2000 030

$amp($amp)

+amp)))-

$amp

$amp

$amp-

$amp

$amp0

$amp

amp

1 1

$$

amp(

)$$+amp(

$$$ampamp($))

+$-$

$0$

amp$$

amp0$

$$

0$

1$$

10$

$ 0$$ amp$$$ amp0$$ $$$

$amp

()amp

$+amp-amp()amp

$

$

amp$

$

($

)$

$

+$

$

$

$ $ amp$ ($ $ $ $ amp$ ($ $ $

$

amp$

()$+$amp$

3 The decomposition of hydrogen peroxide was studied at a particular temperature and experimental data is presented in the table to the right

2 H2O2(g) 2H2O(g) + O2(g)

a What are the two methods that you could use to determine the rate law for this reaction with the data that has been given

b Write out the rate law for this decomposition reaction

c What are the three methods that you could use to determine the rate constant

i Use the easiest of these two methods to determine a value for k

ii What are the units on k

d Now that you know the order of the reaction calculate the half-life for this reaction (if it is not 1st order calculate the half-life at the initial concentration)

yen Show how the conc vs time graph confirms the value that you calculated

P E3 (pg 4 of 6) Decomposition of H2O2

Time (s) [H2O2(g)] (moleL)

0 10

120 091

300 078

600 059

1200 037

1800 022

2400 013

3000 0082

3600 0050

$$$amp()$amp+

-$++

)$$

$$$

$$

amp$$

$$

$$

$$$

$$

amp$$

$$

$$

$$$

$$

$ 0$$ $$$ 0$$ $$$ 0$$ 1$$$ 10$$ amp$$$

$amp

()amp

$+amp-amp()amp

$amp($amp)

+amp-

$amp

$amp

$0amp

$0amp

$1amp

$1amp

$amp

amp

1 1 0 0 )

$$

amp(

)$$+amp(

$

$

amp$

$

($

)$

$

+$

$

$

$ $ amp$ ($ $ $ $ amp$ ($ $ $

$

amp$

()$+$amp$

Please work in PENCIL Please put some work on the page that indicates HOW you did the problem

1 If a 84 g sample of thorium decays with a 10 minute half life how much would the sample weigh in a half hour

2 A sample of radioactive iodine (half life = 3 days) originally weighed 10 g but now weighs 0625 g How old is this sample

You can estimate the half life quickly and easily but youOtildell need a calculator to use the integrated rate equation and half life equations

3 A sample of radioactive calcium originally weighed 24 g and in 12 hours it weighs 125 g What is the half-life

4 If a 500 g sample of barium decays with a 45 day half life how much would the sample weigh in a 18 days

5 A sample of an ancient grass mat containing radioactive carbon (half life = 5730 years) seems to be emitting on 625 of the radiation that a sample of a grass mat woven last year would have How old is this ancient grass mat

6 A sample of radioactive calcium originally weighed 32 kg and in 2 days it weighs 05 kg What is the half-life in hours

7 If a 96 g sample of tin decays with a 25 minute half life how much would the sample weigh in 15 minutes

8 A sample of radioactive magnesium (half life = 183 days) originally weighed 80 g but now weighs 25 g How many years old is this sample

9 A sample of radioactive radium originally weighed 56 g and in three days it weighs just less than a gram What is the half life in hours

P E3 (pg 1 of 2) Half Life ETH The Rate of Radioactive Decay Name________________________Per____

d) Rate is not constant it changes

with time Graphing the data of an

experiment will show an average

rate of reaction

e) Calculating the rate of a reaction

can be done a number of ways

i) Instanteous rate law ndash the rate

at a given moment

ii) Relative reaction rate ndash the rate of one species vs another

iii) Differential rate law ndash experimentally determined rate based on the

rate at the instant of mixing

iv) Integrated rate law ndash experimentally determined rate based on

mathematical manipulation of concentrations of

ONE substance over the course of time

8) Instataneous Reaction Rate

a) The rate at a given time

b) The slope (y=mx+b) of the tangent line is the reaction

rate

i) (+) for reactants

ii) (-) for products

9) Relative Reaction Rate

a) Rate relate to each other in the context of a given chemical system based on their stoichiometric values

Consider the reaction 2 1198731198742(119892) rarr 2 119873119874(119892) + 1 1198742(119892)

b) reveals that oxygen gas can appear only half as rapidly as the nitrogen dioxide gas disappears while NO gas

appears twice as fast as oxygen appears

c) The simplest way to obtain relative rate expressions

i) place a one over each coefficient in the balanced equation

ii) make reactants negative (-) as they will be used up

iii) make products positive (+) as they will be produced

Exercise 1 Determine the rate of the species at the given

time

Reactant

10s

20s

Product

10s

20s

Co

mm

on

mu

ltip

le

cho

ice

que

stio

ns

Co

mm

on

FR

Q

qu

est

ion

s

d) You will OFTEN be asked to express this as a ratio To do that Simply multiply ALL the terms by the same factor

to eliminate the fractions

For 2 1198731198742(119892) rarr 2 119873119874(119892) + 1 1198742(119892) the ratio would be -121

52 Rate Law Expression

1 Most reactions are reversible meaning that products can combine to form reactants In unit 7 we will look at

what exactly that means but for now it means we will need to look at the rate of reactions at the moment of

mixing

2 The rate of the reaction is determined experimentally (I will give you data which you have to analyze) This data

is obtained by

a Count number of bubbles of gas produce (capture volume by water displacement)

b Mass of precipitate formed

c spectrophotometry

3 we will look only at reactants since at the moment of mixing there shouldnrsquot be any products Common sense

tells us that ratereaction [reactants] mathematically a proportion () can be replaced with ldquo= krdquo where k is

some constant This is how we got all those gas laws in unit 3 thus a rate expressions general format is

k = rate constant [A] = concentration of reactant A [B] = concentration of reactant B m = order of reaction for reactant A n = order of reaction for reactant B

Exercise 2 What is the relative reaction rate for the reaction below What is the whole number ratio

4 1198751198673 rarr 1198754 + 6 1198672

Exercise 3 Write the relative rates of change in concentration of the products and reactant in the decomposition of

nitrosyl chloride NOCl

2 119873119874119862119897 rarr 2 119873119874 + 1198621198972

119886119860 + 119887119861 rarr 119909119883

Rate Law written as

119929119938119957119942 = 119948[119912]119950[119913]119951

Can be zero whole numbers or fractions CAN ONLY BE DETERMINED BY EXPERIMENTATION

a Rate constant (k)

i A lower case k we will use the upper case for another constant later

ii Varies wildly with temperature

iii Units are required so that rate is measured in concentration for each unit of time (119898119900119897

119871 119905119894119898119890 or

119872

119905119894119898119890)

b Orders of reaction with respect for each reagent

i Zero order ndash changing the concentration of this reactant has no effect on the rate Say ldquoThe

reaction is zero order with respect to Ardquo

ii First order ndash doubling the concentration doubles the rate of the reaction (all nuclear decay is 1st order)

Say ldquoThe reaction is 1st order with respect to Ardquo

iii Second order ndash doubling the concentration quadruples the rate of the reaction Say ldquoThe

reaction is 2nd order with respect to Ardquo

THE OVER ALL ORDER IS THE SUM OF ALL THE REACTION ORDERS

4 Differential Rate law

a Examining Concentration vs rate data Allows you to determine the rate expression

b Two methods

i Table logic

1 look at the data find two experiments where one reactant is static and the other makes

a measureable change see how the rate reacts Which order is that

2 Pros Fast Good for MC

3 Cons requires you recognize the math on FRQs requires exact explanations

YOU MUST explain it as ldquoIn experiments ltXgt amp ltYgt reactant ltAgt is constant while

reactant ltBgt ltmakes changegt and the rate ltmakes changegt This shows the

reaction is ltordergt with respect to ltBgtrdquo

ii Dirty quick math

1 Since any value divided by itself is 1 we could set two

experimental data sets us a fraction and they should

cancel out

I suggest you put the experiment with the larger values as the numerator

2 Pros never fails is its own explaination you only need to say ldquoreaction is ltordergt with

respect to ltBgtrdquo

3 Cons MUCH slower

c Determining K

i Value ndash simply plug any experiment into the rate law you determined and solve for k

ii Units

1 Since rate MUST be 119898119900119897

119871 119905119894119898119890 k must have units that cancel out the concentrations and

provides that time unit

2 Therefore the units of k are always 1M to the -OAO (overall order of the reaction)-1

119871(119874119860119874minus1)

119898119900119897(119874119860119874minus1) 119905119894119898119890 or

1

119872(119874119860119874minus1) 119905119894119898119890

On the next two pages please take notes on BOTH ways to do the same problem

1199031198861199051198902 = 1198962[119860]2119898[119861]2

119899

1199031198861199051198901 = 1198961[119860]1119898[119861]1

119899

Exercise 4a Table logic

a) What is the order of the reaction with respect to A

b) What is the order of the reaction with respect to B

c) What is the value of the rate constant including units

Exercise 4b dirty math

a) What is the order of the reaction with respect to A

b) What is the order of the reaction with respect to B

c) What is the value of the rate constant including units

Exercise 5

Exercise 6

5) Reaction mechanisms

a) the sequence of bond-making and bond-breaking steps that occurs during the conversion of reactants to

products

i) Must be experimentally determined

ii) Must agree with the overall stoichiometry

iii) Must agree with the experimentally determined rate law

b) The vocabulary of mechanisms involves elementary steps amp molecularity which describes the number of

molecules that participate in an atomic rearrangement Add these terms into your explanations

i) unimolecular involves one reactant molecule that collides with a solvent or background molecule thereby

becoming collisionally activated In this state the reactant molecule is thermodynamically favorable for

converting into product

ii) bimolecular involves a collision between two reactant molecules

iii) termolecular simultaneous collision between three reactant molecules [very rare]

c) the rate expression cannot be predicted from overall stoichiometry The rate expression of an elementary step is

predicted from the stoichiometry of the elementary step as per the table below

d) Catalysts ndash species that are reactants in an elementary step but in subsequent steps is a product They LOWER

the activation energy amp donrsquot change H

i) Homogeneous catalyst ndash exist in the same phase as the reactants

ii) Heterogeneous catalyst ndash exist in a different phase than the reactants

e) Intermediaries ndashspecies that are products in an elementary step but in subsequent steps are reactants amp

consumed

i) Neither catalysts or intermediaries appear in the overall reaction or rate law

Exercise 7

Label the intermediaries amp catalysts

f) the slowest step is the rate determining step -- the rate of the overall reaction is limited by and is exactly equal

to the combined rates of all elementary steps up to and including the slowest step in the mechanism

Exercise 8

Exercise 9

In the reaction 2X+Y rarr Z

For a particular reaction the rate is found to be rate=k[Y]

Which of the below purposed mechanisms is a valid mechanism for this reaction

53 Rate Law Expression pt 2

1 Differential rate law

a Concentration vs rate data

b Use table logic or ugly algebra to find rate law amp value of K

2 Integrated rate law

a Concentration vs time data

b Must choose the straightest line graph and know what it means

c ONLY one reactant

d Done to determine how long a reaction must run to reach a certain concentration of reactant

e The value of the rate constant k is equal to the absolute value of the slope of the best fit line which is

decided by examining 3 linear regressions and analyzing the regression correlation coefficient (r)

i Graphs WILL be provided (except for the lab)

ii Time is ALWAYS X

iii The Y axi are

1 concentration of the reactant

2 natural log of the concentration (ln[A] NOT log[A])

3 reciprocal of the concentration on the y-axis of the third graph

iv If you remember them in this order with the y-axes being ldquoconcentrationrdquo ldquonatural log of

concentrationrdquo and ldquoreciprocal concentrationrdquo the alphabetical order of the y-axis variable

leads to 0 1 2 orders respectively for that reactant

REMEMBER what each variable is

Exercise 10

y = -00002x + 00831Rsup2 = 08871

-005

0

005

01

015

0 200 400 600

[N2O5]

y = -00069x - 23026Rsup2 = 1

-6

-4

-2

0

0 200 400 600

Ln [N2O5] y = 03535x - 78441

Rsup2 = 08841

-100

0

100

200

0 200 400 600

1[N2O5]

Unit 54 Kinetics Clean up

1 Half Life

a the time required for one half of one of the

reactants to disappear

b focus on the half-life for first order reactions only

i Discuss order (what order is it NOT)

ii Determine half life

iii What is the concentration after a set

number of half lives

iv What time would a set concentration be

found

2 In lab we will determine the order of a reaction by ldquoswampingrdquo We maximize one reactants concentration so

that ANY change is negligible

Exercise 11

a) What order is it NOT

b) Determine half life

c) What is the concentration after the second half life

d) When would 75 of the sample have decayed

For the generic reaction A + B C

1 The reaction below was studied at 25frac14C and the following data was obtained

NH4+ + NO2

N2 + 2H2O(L)

a What is the rate law

b What is the rate constant Be sure and include units

2 The reaction below was studied at 10frac14C and the following data was obtained

2NO(g) + Cl2(g) 2NOCl(g)

a What is the rate law

b What is the rate constant Be sure and include units

3 The reaction below was studied and the following data were obtained

2ClO2 + 2OH ClO3 + ClO2

+ H2O

a What is the rate law

b What is the rate constant Be sure and include units

4 The reaction below was studied and the following data were obtained

I + OCl IO + Cl

a What is the rate law

b What is the rate constant Be sure and include units

5 The reaction below was studied and the following data were obtained

BrO3 + 5 Br + 6 H+ 3 Br2 + 3 H2O

a What is the rate law

b What is the rate constant Be sure and include units

P E1 (pg 1 of 3) Using Initial Rates to Determine Order Name_____________________Per___

[NO]0

(molL)[Cl2]0

(molL)Initial Rate

(moleL min)

010 010 018

010 020 035

020 020 145

[I]0

(molL)[OCl]0

(molL)Initial Rate

(molL s)

012 018 791 102

006 018 395 102

003 009 988 103

024 009 791 102

[ClO2]0

(molL)[OH]0

(molL)Initial Rate

(molL s)

0050 0100 0057

0100 0100 023

0100 0050 0115

[NH4+]0

(molL)[NO2

]0

(molL)Initial Rate(moleL sec)

0100 0005 135 107

0100 0010 270 107

0200 0010 540 107

[BrO3]0

(molL)[Br]0

(molL)[H+]0

(molL)Initial Rate

(molL s)

0100 0100 0100 80 104

0200 0100 0100 16 103

0200 0200 0100 32 103

0100 0100 0200 32 103

trial[A]0

(molL)[B]0

(molL)Initial Rate

(moleL hour)

1 4 6 20

2 4 3 10

3 2 6 5

rate1

rate2=k

k

[A]ox

[A]ox

[B]oy

[B]oy

20

10=k

k

[4]ox

[4]ox

[6]oy

[3]oy

2 = [2]y

y = 1

20

5=k

k

[4]o

x

[2]o

x

[6]o

1

[6]o

1

4 = [2]x

x = 2 rate = k[A]2[B]

While it is most likely that any rate laws on the AP exam will only be first or second order it is possible that other orders will show up and are indeed possible When the order is not so obvious it is useful to know a useful log rule

RateRatio = [ConcRatio]x

log[RateRatio] = x log[ConcRatio] thus it is quite simple to solve for the order x log[RateRatio]

log[ConcRatio]= x

6 Given the hypothetical data below determine the order of the reaction A + B + C D + E

[A] (M) [B] (M) [C] (M) Rate (Msec)

10 10 10 00076

20 10 10 00304

10 10 20 00107

10 20 10 00152

7 Given the hypothetical data below determine the order of the reaction H + I + J K

[H] (M) [I] (M) [J] (M) Rate (Msec)

10 10 10 17

23 10 10 391

10 10 40 27

10 18 20 694

8 Given the hypothetical data below determine the order of the reaction P + Q + R S + T

[P] (M) [Q] (M) [R] (M) Rate (Msec)

10 10 10 00365

10 635 10 147

10 10 075 00274

19 47 23 185

9 Given the hypothetical data below determine the order of the reaction V + W + X Y + Z

[V] (M) [W] (M) [X] (M) Rate (Msec)

001 001 001 280 106

001 004 001 448 105

001 002 006 672 105

005 0025 0036 141 104

P E1 (pg 2 of 3) Using Initial Rates to Determine Order

Nitrogen dioxide will decompose into nitrogen oxide and oxygen gas as indicated in the equation below

2 NO2(g) 2 NO(g) + O2(g)

A graph of the concentration of each constituent at various times during the course of the reaction at 300frac14C is presented below Use this graph to understand that the loss of reactant and formation of products is stoichiometrically related

Decomposition of nitrogen dioxide

0

0002

0004

0006

0008

001

0012

0 100 200 300 400 500

time

co

nc

Next you can use the concentration of the reactant vs time data presented in the data table above and manipulate the concentration

values to ln[NO2] and 1

[NO2]

and then graph ln[NO2] vs time and also graph 1

[NO2]

vs time You can use these two graphs to

look for which of the graphs presented will give a straight line in order to determine the order of the reaction These two graphs are shown below

The r2 value which is the coefficient of determination you will learn more about r and r2 when you take a statistics course but for now you can think of it as a Ogravegoodness-of-fitOacute indicator The closer the r2 is to 1 the better the data fits to a straight line Thus

you can see that the r2 value is best for 1

[NO2]

vs time indicating this reaction is second order

P E2 (pg 1 of 6) Rate Laws Using data amp graphs Name_____________________Per____

Decomposition of Nitrogen Dioxide

time (sec) [NO2] [NO] [O2]

0 001 0 0

50 00079 00021 00011

100 00065 00035 00018

150 00055 00045 00023

200 00048 00052 00026

250 00043 00057 00029

300 00038 00062 00031

350 00034 00066 00033

400 00031 00069 00035

$amp()$amp+-

amp++

$-amp

$0amp(

$0amp-

$0amp

$0amp

$0amp

$amp(

$amp-

0 1 10 0 2 20 0

$$

amp(

)$$+amp(

$ampamp()+$-$+++-amp

amp$$$

($$$$

(amp$$$

-$$$$

-amp$$$

0$$$$

0amp$$$

$ amp$ ($$ (amp$ -$$ -amp$ 0$$ 0amp$ $$

$amp

()amp

$+amp-amp()amp

1 The dimerization of butadiene is studied at 500 K and the following reaction and experimental data is presented below

2 C4H6(g) C8H12(g)

a Determine the rate law for this reaction

b Determine the rate constant

c Calculate the half-life for this reaction (If it is not 1st order calculate the half-life at the initial concentration)

P E2 (pg 2 of 6) Rate Law for Dimerization of Butadiene

Time (s) [C4H6(g)] (M)

0 00167

195 00160

604 00150

1246 00130

2180 00110

6210 00068

$

$

amp$

amp$

amp($

amp$

amp$

$ amp$ $ )$ ($ $ $ +$

$

amp$

()$+$amp$

$amp($)amp)+

-amp0+

$0amp+

$0amp

$)amp

$)amp1

$)amp)

$)amp+

$)amp

+ ) 0 1 2

$$

amp(

)$$+amp(

$$amp()+(-

$+

0$$$

1$$$

2$$$

$$$

amp$$$$

ampamp$$$

amp($$$

amp-$$$

amp$$$

amp+$$$

$ amp$$$ ($$$ -$$$ $$$ +$$$ 0$$$ 1$$$

$amp

()amp

$+amp-amp()amp

2 Dinitrogen pentoxide can be decomposed according to the reaction below

2 N2O5(soln) 4 NO2(soln) + O2(g) All Trials are performed at 45frac14C

Data for this reaction can be collected in different ways It is presented in two different ways below instantaneous rates for various concentrations and concentration at various time The concentration vs time data is graphed

Concentration and Initial Rates

a What are a few methods by which you could determine the reaction order

b What are several different methods by which you could determine the rate constant k

c What are a few different methods by which you could determine the half-life

P E2 (pg 3 of 6) Decomposition of Dinitrogen Pentoxide

[N2O5(solOtilden)] (molesL)

Instantaneous rate Msec

10 000060

050 000030

025 000015

Concentration vs Time DataConcentration vs Time Data

Time (s)[N2O5(solOtilden)] (molesL)

0 100

200 088

400 078

600 069

800 061

1000 054

1200 048

1400 043

1600 038

1800 034

2000 030

$amp($amp)

+amp)))-

$amp

$amp

$amp-

$amp

$amp0

$amp

amp

1 1

$$

amp(

)$$+amp(

$$$ampamp($))

+$-$

$0$

amp$$

amp0$

$$

0$

1$$

10$

$ 0$$ amp$$$ amp0$$ $$$

$amp

()amp

$+amp-amp()amp

$

$

amp$

$

($

)$

$

+$

$

$

$ $ amp$ ($ $ $ $ amp$ ($ $ $

$

amp$

()$+$amp$

3 The decomposition of hydrogen peroxide was studied at a particular temperature and experimental data is presented in the table to the right

2 H2O2(g) 2H2O(g) + O2(g)

a What are the two methods that you could use to determine the rate law for this reaction with the data that has been given

b Write out the rate law for this decomposition reaction

c What are the three methods that you could use to determine the rate constant

i Use the easiest of these two methods to determine a value for k

ii What are the units on k

d Now that you know the order of the reaction calculate the half-life for this reaction (if it is not 1st order calculate the half-life at the initial concentration)

yen Show how the conc vs time graph confirms the value that you calculated

P E3 (pg 4 of 6) Decomposition of H2O2

Time (s) [H2O2(g)] (moleL)

0 10

120 091

300 078

600 059

1200 037

1800 022

2400 013

3000 0082

3600 0050

$$$amp()$amp+

-$++

)$$

$$$

$$

amp$$

$$

$$

$$$

$$

amp$$

$$

$$

$$$

$$

$ 0$$ $$$ 0$$ $$$ 0$$ 1$$$ 10$$ amp$$$

$amp

()amp

$+amp-amp()amp

$amp($amp)

+amp-

$amp

$amp

$0amp

$0amp

$1amp

$1amp

$amp

amp

1 1 0 0 )

$$

amp(

)$$+amp(

$

$

amp$

$

($

)$

$

+$

$

$

$ $ amp$ ($ $ $ $ amp$ ($ $ $

$

amp$

()$+$amp$

Please work in PENCIL Please put some work on the page that indicates HOW you did the problem

1 If a 84 g sample of thorium decays with a 10 minute half life how much would the sample weigh in a half hour

2 A sample of radioactive iodine (half life = 3 days) originally weighed 10 g but now weighs 0625 g How old is this sample

You can estimate the half life quickly and easily but youOtildell need a calculator to use the integrated rate equation and half life equations

3 A sample of radioactive calcium originally weighed 24 g and in 12 hours it weighs 125 g What is the half-life

4 If a 500 g sample of barium decays with a 45 day half life how much would the sample weigh in a 18 days

5 A sample of an ancient grass mat containing radioactive carbon (half life = 5730 years) seems to be emitting on 625 of the radiation that a sample of a grass mat woven last year would have How old is this ancient grass mat

6 A sample of radioactive calcium originally weighed 32 kg and in 2 days it weighs 05 kg What is the half-life in hours

7 If a 96 g sample of tin decays with a 25 minute half life how much would the sample weigh in 15 minutes

8 A sample of radioactive magnesium (half life = 183 days) originally weighed 80 g but now weighs 25 g How many years old is this sample

9 A sample of radioactive radium originally weighed 56 g and in three days it weighs just less than a gram What is the half life in hours

P E3 (pg 1 of 2) Half Life ETH The Rate of Radioactive Decay Name________________________Per____

d) You will OFTEN be asked to express this as a ratio To do that Simply multiply ALL the terms by the same factor

to eliminate the fractions

For 2 1198731198742(119892) rarr 2 119873119874(119892) + 1 1198742(119892) the ratio would be -121

52 Rate Law Expression

1 Most reactions are reversible meaning that products can combine to form reactants In unit 7 we will look at

what exactly that means but for now it means we will need to look at the rate of reactions at the moment of

mixing

2 The rate of the reaction is determined experimentally (I will give you data which you have to analyze) This data

is obtained by

a Count number of bubbles of gas produce (capture volume by water displacement)

b Mass of precipitate formed

c spectrophotometry

3 we will look only at reactants since at the moment of mixing there shouldnrsquot be any products Common sense

tells us that ratereaction [reactants] mathematically a proportion () can be replaced with ldquo= krdquo where k is

some constant This is how we got all those gas laws in unit 3 thus a rate expressions general format is

k = rate constant [A] = concentration of reactant A [B] = concentration of reactant B m = order of reaction for reactant A n = order of reaction for reactant B

Exercise 2 What is the relative reaction rate for the reaction below What is the whole number ratio

4 1198751198673 rarr 1198754 + 6 1198672

Exercise 3 Write the relative rates of change in concentration of the products and reactant in the decomposition of

nitrosyl chloride NOCl

2 119873119874119862119897 rarr 2 119873119874 + 1198621198972

119886119860 + 119887119861 rarr 119909119883

Rate Law written as

119929119938119957119942 = 119948[119912]119950[119913]119951

Can be zero whole numbers or fractions CAN ONLY BE DETERMINED BY EXPERIMENTATION

a Rate constant (k)

i A lower case k we will use the upper case for another constant later

ii Varies wildly with temperature

iii Units are required so that rate is measured in concentration for each unit of time (119898119900119897

119871 119905119894119898119890 or

119872

119905119894119898119890)

b Orders of reaction with respect for each reagent

i Zero order ndash changing the concentration of this reactant has no effect on the rate Say ldquoThe

reaction is zero order with respect to Ardquo

ii First order ndash doubling the concentration doubles the rate of the reaction (all nuclear decay is 1st order)

Say ldquoThe reaction is 1st order with respect to Ardquo

iii Second order ndash doubling the concentration quadruples the rate of the reaction Say ldquoThe

reaction is 2nd order with respect to Ardquo

THE OVER ALL ORDER IS THE SUM OF ALL THE REACTION ORDERS

4 Differential Rate law

a Examining Concentration vs rate data Allows you to determine the rate expression

b Two methods

i Table logic

1 look at the data find two experiments where one reactant is static and the other makes

a measureable change see how the rate reacts Which order is that

2 Pros Fast Good for MC

3 Cons requires you recognize the math on FRQs requires exact explanations

YOU MUST explain it as ldquoIn experiments ltXgt amp ltYgt reactant ltAgt is constant while

reactant ltBgt ltmakes changegt and the rate ltmakes changegt This shows the

reaction is ltordergt with respect to ltBgtrdquo

ii Dirty quick math

1 Since any value divided by itself is 1 we could set two

experimental data sets us a fraction and they should

cancel out

I suggest you put the experiment with the larger values as the numerator

2 Pros never fails is its own explaination you only need to say ldquoreaction is ltordergt with

respect to ltBgtrdquo

3 Cons MUCH slower

c Determining K

i Value ndash simply plug any experiment into the rate law you determined and solve for k

ii Units

1 Since rate MUST be 119898119900119897

119871 119905119894119898119890 k must have units that cancel out the concentrations and

provides that time unit

2 Therefore the units of k are always 1M to the -OAO (overall order of the reaction)-1

119871(119874119860119874minus1)

119898119900119897(119874119860119874minus1) 119905119894119898119890 or

1

119872(119874119860119874minus1) 119905119894119898119890

On the next two pages please take notes on BOTH ways to do the same problem

1199031198861199051198902 = 1198962[119860]2119898[119861]2

119899

1199031198861199051198901 = 1198961[119860]1119898[119861]1

119899

Exercise 4a Table logic

a) What is the order of the reaction with respect to A

b) What is the order of the reaction with respect to B

c) What is the value of the rate constant including units

Exercise 4b dirty math

a) What is the order of the reaction with respect to A

b) What is the order of the reaction with respect to B

c) What is the value of the rate constant including units

Exercise 5

Exercise 6

5) Reaction mechanisms

a) the sequence of bond-making and bond-breaking steps that occurs during the conversion of reactants to

products

i) Must be experimentally determined

ii) Must agree with the overall stoichiometry

iii) Must agree with the experimentally determined rate law

b) The vocabulary of mechanisms involves elementary steps amp molecularity which describes the number of

molecules that participate in an atomic rearrangement Add these terms into your explanations

i) unimolecular involves one reactant molecule that collides with a solvent or background molecule thereby

becoming collisionally activated In this state the reactant molecule is thermodynamically favorable for

converting into product

ii) bimolecular involves a collision between two reactant molecules

iii) termolecular simultaneous collision between three reactant molecules [very rare]

c) the rate expression cannot be predicted from overall stoichiometry The rate expression of an elementary step is

predicted from the stoichiometry of the elementary step as per the table below

d) Catalysts ndash species that are reactants in an elementary step but in subsequent steps is a product They LOWER

the activation energy amp donrsquot change H

i) Homogeneous catalyst ndash exist in the same phase as the reactants

ii) Heterogeneous catalyst ndash exist in a different phase than the reactants

e) Intermediaries ndashspecies that are products in an elementary step but in subsequent steps are reactants amp

consumed

i) Neither catalysts or intermediaries appear in the overall reaction or rate law

Exercise 7

Label the intermediaries amp catalysts

f) the slowest step is the rate determining step -- the rate of the overall reaction is limited by and is exactly equal

to the combined rates of all elementary steps up to and including the slowest step in the mechanism

Exercise 8

Exercise 9

In the reaction 2X+Y rarr Z

For a particular reaction the rate is found to be rate=k[Y]

Which of the below purposed mechanisms is a valid mechanism for this reaction

53 Rate Law Expression pt 2

1 Differential rate law

a Concentration vs rate data

b Use table logic or ugly algebra to find rate law amp value of K

2 Integrated rate law

a Concentration vs time data

b Must choose the straightest line graph and know what it means

c ONLY one reactant

d Done to determine how long a reaction must run to reach a certain concentration of reactant

e The value of the rate constant k is equal to the absolute value of the slope of the best fit line which is

decided by examining 3 linear regressions and analyzing the regression correlation coefficient (r)

i Graphs WILL be provided (except for the lab)

ii Time is ALWAYS X

iii The Y axi are

1 concentration of the reactant

2 natural log of the concentration (ln[A] NOT log[A])

3 reciprocal of the concentration on the y-axis of the third graph

iv If you remember them in this order with the y-axes being ldquoconcentrationrdquo ldquonatural log of

concentrationrdquo and ldquoreciprocal concentrationrdquo the alphabetical order of the y-axis variable

leads to 0 1 2 orders respectively for that reactant

REMEMBER what each variable is

Exercise 10

y = -00002x + 00831Rsup2 = 08871

-005

0

005

01

015

0 200 400 600

[N2O5]

y = -00069x - 23026Rsup2 = 1

-6

-4

-2

0

0 200 400 600

Ln [N2O5] y = 03535x - 78441

Rsup2 = 08841

-100

0

100

200

0 200 400 600

1[N2O5]

Unit 54 Kinetics Clean up

1 Half Life

a the time required for one half of one of the

reactants to disappear

b focus on the half-life for first order reactions only

i Discuss order (what order is it NOT)

ii Determine half life

iii What is the concentration after a set

number of half lives

iv What time would a set concentration be

found

2 In lab we will determine the order of a reaction by ldquoswampingrdquo We maximize one reactants concentration so

that ANY change is negligible

Exercise 11

a) What order is it NOT

b) Determine half life

c) What is the concentration after the second half life

d) When would 75 of the sample have decayed

For the generic reaction A + B C

1 The reaction below was studied at 25frac14C and the following data was obtained

NH4+ + NO2

N2 + 2H2O(L)

a What is the rate law

b What is the rate constant Be sure and include units

2 The reaction below was studied at 10frac14C and the following data was obtained

2NO(g) + Cl2(g) 2NOCl(g)

a What is the rate law

b What is the rate constant Be sure and include units

3 The reaction below was studied and the following data were obtained

2ClO2 + 2OH ClO3 + ClO2

+ H2O

a What is the rate law

b What is the rate constant Be sure and include units

4 The reaction below was studied and the following data were obtained

I + OCl IO + Cl

a What is the rate law

b What is the rate constant Be sure and include units

5 The reaction below was studied and the following data were obtained

BrO3 + 5 Br + 6 H+ 3 Br2 + 3 H2O

a What is the rate law

b What is the rate constant Be sure and include units

P E1 (pg 1 of 3) Using Initial Rates to Determine Order Name_____________________Per___

[NO]0

(molL)[Cl2]0

(molL)Initial Rate

(moleL min)

010 010 018

010 020 035

020 020 145

[I]0

(molL)[OCl]0

(molL)Initial Rate

(molL s)

012 018 791 102

006 018 395 102

003 009 988 103

024 009 791 102

[ClO2]0

(molL)[OH]0

(molL)Initial Rate

(molL s)

0050 0100 0057

0100 0100 023

0100 0050 0115

[NH4+]0

(molL)[NO2

]0

(molL)Initial Rate(moleL sec)

0100 0005 135 107

0100 0010 270 107

0200 0010 540 107

[BrO3]0

(molL)[Br]0

(molL)[H+]0

(molL)Initial Rate

(molL s)

0100 0100 0100 80 104

0200 0100 0100 16 103

0200 0200 0100 32 103

0100 0100 0200 32 103

trial[A]0

(molL)[B]0

(molL)Initial Rate

(moleL hour)

1 4 6 20

2 4 3 10

3 2 6 5

rate1

rate2=k

k

[A]ox

[A]ox

[B]oy

[B]oy

20

10=k

k

[4]ox

[4]ox

[6]oy

[3]oy

2 = [2]y

y = 1

20

5=k

k

[4]o

x

[2]o

x

[6]o

1

[6]o

1

4 = [2]x

x = 2 rate = k[A]2[B]

While it is most likely that any rate laws on the AP exam will only be first or second order it is possible that other orders will show up and are indeed possible When the order is not so obvious it is useful to know a useful log rule

RateRatio = [ConcRatio]x

log[RateRatio] = x log[ConcRatio] thus it is quite simple to solve for the order x log[RateRatio]

log[ConcRatio]= x

6 Given the hypothetical data below determine the order of the reaction A + B + C D + E

[A] (M) [B] (M) [C] (M) Rate (Msec)

10 10 10 00076

20 10 10 00304

10 10 20 00107

10 20 10 00152

7 Given the hypothetical data below determine the order of the reaction H + I + J K

[H] (M) [I] (M) [J] (M) Rate (Msec)

10 10 10 17

23 10 10 391

10 10 40 27

10 18 20 694

8 Given the hypothetical data below determine the order of the reaction P + Q + R S + T

[P] (M) [Q] (M) [R] (M) Rate (Msec)

10 10 10 00365

10 635 10 147

10 10 075 00274

19 47 23 185

9 Given the hypothetical data below determine the order of the reaction V + W + X Y + Z

[V] (M) [W] (M) [X] (M) Rate (Msec)

001 001 001 280 106

001 004 001 448 105

001 002 006 672 105

005 0025 0036 141 104

P E1 (pg 2 of 3) Using Initial Rates to Determine Order

Nitrogen dioxide will decompose into nitrogen oxide and oxygen gas as indicated in the equation below

2 NO2(g) 2 NO(g) + O2(g)

A graph of the concentration of each constituent at various times during the course of the reaction at 300frac14C is presented below Use this graph to understand that the loss of reactant and formation of products is stoichiometrically related

Decomposition of nitrogen dioxide

0

0002

0004

0006

0008

001

0012

0 100 200 300 400 500

time

co

nc

Next you can use the concentration of the reactant vs time data presented in the data table above and manipulate the concentration

values to ln[NO2] and 1

[NO2]

and then graph ln[NO2] vs time and also graph 1

[NO2]

vs time You can use these two graphs to

look for which of the graphs presented will give a straight line in order to determine the order of the reaction These two graphs are shown below

The r2 value which is the coefficient of determination you will learn more about r and r2 when you take a statistics course but for now you can think of it as a Ogravegoodness-of-fitOacute indicator The closer the r2 is to 1 the better the data fits to a straight line Thus

you can see that the r2 value is best for 1

[NO2]

vs time indicating this reaction is second order

P E2 (pg 1 of 6) Rate Laws Using data amp graphs Name_____________________Per____

Decomposition of Nitrogen Dioxide

time (sec) [NO2] [NO] [O2]

0 001 0 0

50 00079 00021 00011

100 00065 00035 00018

150 00055 00045 00023

200 00048 00052 00026

250 00043 00057 00029

300 00038 00062 00031

350 00034 00066 00033

400 00031 00069 00035

$amp()$amp+-

amp++

$-amp

$0amp(

$0amp-

$0amp

$0amp

$0amp

$amp(

$amp-

0 1 10 0 2 20 0

$$

amp(

)$$+amp(

$ampamp()+$-$+++-amp

amp$$$

($$$$

(amp$$$

-$$$$

-amp$$$

0$$$$

0amp$$$

$ amp$ ($$ (amp$ -$$ -amp$ 0$$ 0amp$ $$

$amp

()amp

$+amp-amp()amp

1 The dimerization of butadiene is studied at 500 K and the following reaction and experimental data is presented below

2 C4H6(g) C8H12(g)

a Determine the rate law for this reaction

b Determine the rate constant

c Calculate the half-life for this reaction (If it is not 1st order calculate the half-life at the initial concentration)

P E2 (pg 2 of 6) Rate Law for Dimerization of Butadiene

Time (s) [C4H6(g)] (M)

0 00167

195 00160

604 00150

1246 00130

2180 00110

6210 00068

$

$

amp$

amp$

amp($

amp$

amp$

$ amp$ $ )$ ($ $ $ +$

$

amp$

()$+$amp$

$amp($)amp)+

-amp0+

$0amp+

$0amp

$)amp

$)amp1

$)amp)

$)amp+

$)amp

+ ) 0 1 2

$$

amp(

)$$+amp(

$$amp()+(-

$+

0$$$

1$$$

2$$$

$$$

amp$$$$

ampamp$$$

amp($$$

amp-$$$

amp$$$

amp+$$$

$ amp$$$ ($$$ -$$$ $$$ +$$$ 0$$$ 1$$$

$amp

()amp

$+amp-amp()amp

2 Dinitrogen pentoxide can be decomposed according to the reaction below

2 N2O5(soln) 4 NO2(soln) + O2(g) All Trials are performed at 45frac14C

Data for this reaction can be collected in different ways It is presented in two different ways below instantaneous rates for various concentrations and concentration at various time The concentration vs time data is graphed

Concentration and Initial Rates

a What are a few methods by which you could determine the reaction order

b What are several different methods by which you could determine the rate constant k

c What are a few different methods by which you could determine the half-life

P E2 (pg 3 of 6) Decomposition of Dinitrogen Pentoxide

[N2O5(solOtilden)] (molesL)

Instantaneous rate Msec

10 000060

050 000030

025 000015

Concentration vs Time DataConcentration vs Time Data

Time (s)[N2O5(solOtilden)] (molesL)

0 100

200 088

400 078

600 069

800 061

1000 054

1200 048

1400 043

1600 038

1800 034

2000 030

$amp($amp)

+amp)))-

$amp

$amp

$amp-

$amp

$amp0

$amp

amp

1 1

$$

amp(

)$$+amp(

$$$ampamp($))

+$-$

$0$

amp$$

amp0$

$$

0$

1$$

10$

$ 0$$ amp$$$ amp0$$ $$$

$amp

()amp

$+amp-amp()amp

$

$

amp$

$

($

)$

$

+$

$

$

$ $ amp$ ($ $ $ $ amp$ ($ $ $

$

amp$

()$+$amp$

3 The decomposition of hydrogen peroxide was studied at a particular temperature and experimental data is presented in the table to the right

2 H2O2(g) 2H2O(g) + O2(g)

a What are the two methods that you could use to determine the rate law for this reaction with the data that has been given

b Write out the rate law for this decomposition reaction

c What are the three methods that you could use to determine the rate constant

i Use the easiest of these two methods to determine a value for k

ii What are the units on k

d Now that you know the order of the reaction calculate the half-life for this reaction (if it is not 1st order calculate the half-life at the initial concentration)

yen Show how the conc vs time graph confirms the value that you calculated

P E3 (pg 4 of 6) Decomposition of H2O2

Time (s) [H2O2(g)] (moleL)

0 10

120 091

300 078

600 059

1200 037

1800 022

2400 013

3000 0082

3600 0050

$$$amp()$amp+

-$++

)$$

$$$

$$

amp$$

$$

$$

$$$

$$

amp$$

$$

$$

$$$

$$

$ 0$$ $$$ 0$$ $$$ 0$$ 1$$$ 10$$ amp$$$

$amp

()amp

$+amp-amp()amp

$amp($amp)

+amp-

$amp

$amp

$0amp

$0amp

$1amp

$1amp

$amp

amp

1 1 0 0 )

$$

amp(

)$$+amp(

$

$

amp$

$

($

)$

$

+$

$

$

$ $ amp$ ($ $ $ $ amp$ ($ $ $

$

amp$

()$+$amp$

Please work in PENCIL Please put some work on the page that indicates HOW you did the problem

1 If a 84 g sample of thorium decays with a 10 minute half life how much would the sample weigh in a half hour

2 A sample of radioactive iodine (half life = 3 days) originally weighed 10 g but now weighs 0625 g How old is this sample

You can estimate the half life quickly and easily but youOtildell need a calculator to use the integrated rate equation and half life equations

3 A sample of radioactive calcium originally weighed 24 g and in 12 hours it weighs 125 g What is the half-life

4 If a 500 g sample of barium decays with a 45 day half life how much would the sample weigh in a 18 days

5 A sample of an ancient grass mat containing radioactive carbon (half life = 5730 years) seems to be emitting on 625 of the radiation that a sample of a grass mat woven last year would have How old is this ancient grass mat

6 A sample of radioactive calcium originally weighed 32 kg and in 2 days it weighs 05 kg What is the half-life in hours

7 If a 96 g sample of tin decays with a 25 minute half life how much would the sample weigh in 15 minutes

8 A sample of radioactive magnesium (half life = 183 days) originally weighed 80 g but now weighs 25 g How many years old is this sample

9 A sample of radioactive radium originally weighed 56 g and in three days it weighs just less than a gram What is the half life in hours

P E3 (pg 1 of 2) Half Life ETH The Rate of Radioactive Decay Name________________________Per____

a Rate constant (k)

i A lower case k we will use the upper case for another constant later

ii Varies wildly with temperature

iii Units are required so that rate is measured in concentration for each unit of time (119898119900119897

119871 119905119894119898119890 or

119872

119905119894119898119890)

b Orders of reaction with respect for each reagent

i Zero order ndash changing the concentration of this reactant has no effect on the rate Say ldquoThe

reaction is zero order with respect to Ardquo

ii First order ndash doubling the concentration doubles the rate of the reaction (all nuclear decay is 1st order)

Say ldquoThe reaction is 1st order with respect to Ardquo

iii Second order ndash doubling the concentration quadruples the rate of the reaction Say ldquoThe

reaction is 2nd order with respect to Ardquo

THE OVER ALL ORDER IS THE SUM OF ALL THE REACTION ORDERS

4 Differential Rate law

a Examining Concentration vs rate data Allows you to determine the rate expression

b Two methods

i Table logic

1 look at the data find two experiments where one reactant is static and the other makes

a measureable change see how the rate reacts Which order is that

2 Pros Fast Good for MC

3 Cons requires you recognize the math on FRQs requires exact explanations

YOU MUST explain it as ldquoIn experiments ltXgt amp ltYgt reactant ltAgt is constant while

reactant ltBgt ltmakes changegt and the rate ltmakes changegt This shows the

reaction is ltordergt with respect to ltBgtrdquo

ii Dirty quick math

1 Since any value divided by itself is 1 we could set two

experimental data sets us a fraction and they should

cancel out

I suggest you put the experiment with the larger values as the numerator

2 Pros never fails is its own explaination you only need to say ldquoreaction is ltordergt with

respect to ltBgtrdquo

3 Cons MUCH slower

c Determining K

i Value ndash simply plug any experiment into the rate law you determined and solve for k

ii Units

1 Since rate MUST be 119898119900119897

119871 119905119894119898119890 k must have units that cancel out the concentrations and

provides that time unit

2 Therefore the units of k are always 1M to the -OAO (overall order of the reaction)-1

119871(119874119860119874minus1)

119898119900119897(119874119860119874minus1) 119905119894119898119890 or

1

119872(119874119860119874minus1) 119905119894119898119890

On the next two pages please take notes on BOTH ways to do the same problem

1199031198861199051198902 = 1198962[119860]2119898[119861]2

119899

1199031198861199051198901 = 1198961[119860]1119898[119861]1

119899

Exercise 4a Table logic

a) What is the order of the reaction with respect to A

b) What is the order of the reaction with respect to B

c) What is the value of the rate constant including units

Exercise 4b dirty math

a) What is the order of the reaction with respect to A

b) What is the order of the reaction with respect to B

c) What is the value of the rate constant including units

Exercise 5

Exercise 6

5) Reaction mechanisms

a) the sequence of bond-making and bond-breaking steps that occurs during the conversion of reactants to

products

i) Must be experimentally determined

ii) Must agree with the overall stoichiometry

iii) Must agree with the experimentally determined rate law

b) The vocabulary of mechanisms involves elementary steps amp molecularity which describes the number of

molecules that participate in an atomic rearrangement Add these terms into your explanations

i) unimolecular involves one reactant molecule that collides with a solvent or background molecule thereby

becoming collisionally activated In this state the reactant molecule is thermodynamically favorable for

converting into product

ii) bimolecular involves a collision between two reactant molecules

iii) termolecular simultaneous collision between three reactant molecules [very rare]

c) the rate expression cannot be predicted from overall stoichiometry The rate expression of an elementary step is

predicted from the stoichiometry of the elementary step as per the table below

d) Catalysts ndash species that are reactants in an elementary step but in subsequent steps is a product They LOWER

the activation energy amp donrsquot change H

i) Homogeneous catalyst ndash exist in the same phase as the reactants

ii) Heterogeneous catalyst ndash exist in a different phase than the reactants

e) Intermediaries ndashspecies that are products in an elementary step but in subsequent steps are reactants amp

consumed

i) Neither catalysts or intermediaries appear in the overall reaction or rate law

Exercise 7

Label the intermediaries amp catalysts

f) the slowest step is the rate determining step -- the rate of the overall reaction is limited by and is exactly equal

to the combined rates of all elementary steps up to and including the slowest step in the mechanism

Exercise 8

Exercise 9

In the reaction 2X+Y rarr Z

For a particular reaction the rate is found to be rate=k[Y]

Which of the below purposed mechanisms is a valid mechanism for this reaction

53 Rate Law Expression pt 2

1 Differential rate law

a Concentration vs rate data

b Use table logic or ugly algebra to find rate law amp value of K

2 Integrated rate law

a Concentration vs time data

b Must choose the straightest line graph and know what it means

c ONLY one reactant

d Done to determine how long a reaction must run to reach a certain concentration of reactant

e The value of the rate constant k is equal to the absolute value of the slope of the best fit line which is

decided by examining 3 linear regressions and analyzing the regression correlation coefficient (r)

i Graphs WILL be provided (except for the lab)

ii Time is ALWAYS X

iii The Y axi are

1 concentration of the reactant

2 natural log of the concentration (ln[A] NOT log[A])

3 reciprocal of the concentration on the y-axis of the third graph

iv If you remember them in this order with the y-axes being ldquoconcentrationrdquo ldquonatural log of

concentrationrdquo and ldquoreciprocal concentrationrdquo the alphabetical order of the y-axis variable

leads to 0 1 2 orders respectively for that reactant

REMEMBER what each variable is

Exercise 10

y = -00002x + 00831Rsup2 = 08871

-005

0

005

01

015

0 200 400 600

[N2O5]

y = -00069x - 23026Rsup2 = 1

-6

-4

-2

0

0 200 400 600

Ln [N2O5] y = 03535x - 78441

Rsup2 = 08841

-100

0

100

200

0 200 400 600

1[N2O5]

Unit 54 Kinetics Clean up

1 Half Life

a the time required for one half of one of the

reactants to disappear

b focus on the half-life for first order reactions only

i Discuss order (what order is it NOT)

ii Determine half life

iii What is the concentration after a set

number of half lives

iv What time would a set concentration be

found

2 In lab we will determine the order of a reaction by ldquoswampingrdquo We maximize one reactants concentration so

that ANY change is negligible

Exercise 11

a) What order is it NOT

b) Determine half life

c) What is the concentration after the second half life

d) When would 75 of the sample have decayed

For the generic reaction A + B C

1 The reaction below was studied at 25frac14C and the following data was obtained

NH4+ + NO2

N2 + 2H2O(L)

a What is the rate law

b What is the rate constant Be sure and include units

2 The reaction below was studied at 10frac14C and the following data was obtained

2NO(g) + Cl2(g) 2NOCl(g)

a What is the rate law

b What is the rate constant Be sure and include units

3 The reaction below was studied and the following data were obtained

2ClO2 + 2OH ClO3 + ClO2

+ H2O

a What is the rate law

b What is the rate constant Be sure and include units

4 The reaction below was studied and the following data were obtained

I + OCl IO + Cl

a What is the rate law

b What is the rate constant Be sure and include units

5 The reaction below was studied and the following data were obtained

BrO3 + 5 Br + 6 H+ 3 Br2 + 3 H2O

a What is the rate law

b What is the rate constant Be sure and include units

P E1 (pg 1 of 3) Using Initial Rates to Determine Order Name_____________________Per___

[NO]0

(molL)[Cl2]0

(molL)Initial Rate

(moleL min)

010 010 018

010 020 035

020 020 145

[I]0

(molL)[OCl]0

(molL)Initial Rate

(molL s)

012 018 791 102

006 018 395 102

003 009 988 103

024 009 791 102

[ClO2]0

(molL)[OH]0

(molL)Initial Rate

(molL s)

0050 0100 0057

0100 0100 023

0100 0050 0115

[NH4+]0

(molL)[NO2

]0

(molL)Initial Rate(moleL sec)

0100 0005 135 107

0100 0010 270 107

0200 0010 540 107

[BrO3]0

(molL)[Br]0

(molL)[H+]0

(molL)Initial Rate

(molL s)

0100 0100 0100 80 104

0200 0100 0100 16 103

0200 0200 0100 32 103

0100 0100 0200 32 103

trial[A]0

(molL)[B]0

(molL)Initial Rate

(moleL hour)

1 4 6 20

2 4 3 10

3 2 6 5

rate1

rate2=k

k

[A]ox

[A]ox

[B]oy

[B]oy

20

10=k

k

[4]ox

[4]ox

[6]oy

[3]oy

2 = [2]y

y = 1

20

5=k

k

[4]o

x

[2]o

x

[6]o

1

[6]o

1

4 = [2]x

x = 2 rate = k[A]2[B]

While it is most likely that any rate laws on the AP exam will only be first or second order it is possible that other orders will show up and are indeed possible When the order is not so obvious it is useful to know a useful log rule

RateRatio = [ConcRatio]x

log[RateRatio] = x log[ConcRatio] thus it is quite simple to solve for the order x log[RateRatio]

log[ConcRatio]= x

6 Given the hypothetical data below determine the order of the reaction A + B + C D + E

[A] (M) [B] (M) [C] (M) Rate (Msec)

10 10 10 00076

20 10 10 00304

10 10 20 00107

10 20 10 00152

7 Given the hypothetical data below determine the order of the reaction H + I + J K

[H] (M) [I] (M) [J] (M) Rate (Msec)

10 10 10 17

23 10 10 391

10 10 40 27

10 18 20 694

8 Given the hypothetical data below determine the order of the reaction P + Q + R S + T

[P] (M) [Q] (M) [R] (M) Rate (Msec)

10 10 10 00365

10 635 10 147

10 10 075 00274

19 47 23 185

9 Given the hypothetical data below determine the order of the reaction V + W + X Y + Z

[V] (M) [W] (M) [X] (M) Rate (Msec)

001 001 001 280 106

001 004 001 448 105

001 002 006 672 105

005 0025 0036 141 104

P E1 (pg 2 of 3) Using Initial Rates to Determine Order

Nitrogen dioxide will decompose into nitrogen oxide and oxygen gas as indicated in the equation below

2 NO2(g) 2 NO(g) + O2(g)

A graph of the concentration of each constituent at various times during the course of the reaction at 300frac14C is presented below Use this graph to understand that the loss of reactant and formation of products is stoichiometrically related

Decomposition of nitrogen dioxide

0

0002

0004

0006

0008

001

0012

0 100 200 300 400 500

time

co

nc

Next you can use the concentration of the reactant vs time data presented in the data table above and manipulate the concentration

values to ln[NO2] and 1

[NO2]

and then graph ln[NO2] vs time and also graph 1

[NO2]

vs time You can use these two graphs to

look for which of the graphs presented will give a straight line in order to determine the order of the reaction These two graphs are shown below

The r2 value which is the coefficient of determination you will learn more about r and r2 when you take a statistics course but for now you can think of it as a Ogravegoodness-of-fitOacute indicator The closer the r2 is to 1 the better the data fits to a straight line Thus

you can see that the r2 value is best for 1

[NO2]

vs time indicating this reaction is second order

P E2 (pg 1 of 6) Rate Laws Using data amp graphs Name_____________________Per____

Decomposition of Nitrogen Dioxide

time (sec) [NO2] [NO] [O2]

0 001 0 0

50 00079 00021 00011

100 00065 00035 00018

150 00055 00045 00023

200 00048 00052 00026

250 00043 00057 00029

300 00038 00062 00031

350 00034 00066 00033

400 00031 00069 00035

$amp()$amp+-

amp++

$-amp

$0amp(

$0amp-

$0amp

$0amp

$0amp

$amp(

$amp-

0 1 10 0 2 20 0

$$

amp(

)$$+amp(

$ampamp()+$-$+++-amp

amp$$$

($$$$

(amp$$$

-$$$$

-amp$$$

0$$$$

0amp$$$

$ amp$ ($$ (amp$ -$$ -amp$ 0$$ 0amp$ $$

$amp

()amp

$+amp-amp()amp

1 The dimerization of butadiene is studied at 500 K and the following reaction and experimental data is presented below

2 C4H6(g) C8H12(g)

a Determine the rate law for this reaction

b Determine the rate constant

c Calculate the half-life for this reaction (If it is not 1st order calculate the half-life at the initial concentration)

P E2 (pg 2 of 6) Rate Law for Dimerization of Butadiene

Time (s) [C4H6(g)] (M)

0 00167

195 00160

604 00150

1246 00130

2180 00110

6210 00068

$

$

amp$

amp$

amp($

amp$

amp$

$ amp$ $ )$ ($ $ $ +$

$

amp$

()$+$amp$

$amp($)amp)+

-amp0+

$0amp+

$0amp

$)amp

$)amp1

$)amp)

$)amp+

$)amp

+ ) 0 1 2

$$

amp(

)$$+amp(

$$amp()+(-

$+

0$$$

1$$$

2$$$

$$$

amp$$$$

ampamp$$$

amp($$$

amp-$$$

amp$$$

amp+$$$

$ amp$$$ ($$$ -$$$ $$$ +$$$ 0$$$ 1$$$

$amp

()amp

$+amp-amp()amp

2 Dinitrogen pentoxide can be decomposed according to the reaction below

2 N2O5(soln) 4 NO2(soln) + O2(g) All Trials are performed at 45frac14C

Data for this reaction can be collected in different ways It is presented in two different ways below instantaneous rates for various concentrations and concentration at various time The concentration vs time data is graphed

Concentration and Initial Rates

a What are a few methods by which you could determine the reaction order

b What are several different methods by which you could determine the rate constant k

c What are a few different methods by which you could determine the half-life

P E2 (pg 3 of 6) Decomposition of Dinitrogen Pentoxide

[N2O5(solOtilden)] (molesL)

Instantaneous rate Msec

10 000060

050 000030

025 000015

Concentration vs Time DataConcentration vs Time Data

Time (s)[N2O5(solOtilden)] (molesL)

0 100

200 088

400 078

600 069

800 061

1000 054

1200 048

1400 043

1600 038

1800 034

2000 030

$amp($amp)

+amp)))-

$amp

$amp

$amp-

$amp

$amp0

$amp

amp

1 1

$$

amp(

)$$+amp(

$$$ampamp($))

+$-$

$0$

amp$$

amp0$

$$

0$

1$$

10$

$ 0$$ amp$$$ amp0$$ $$$

$amp

()amp

$+amp-amp()amp

$

$

amp$

$

($

)$

$

+$

$

$

$ $ amp$ ($ $ $ $ amp$ ($ $ $

$

amp$

()$+$amp$

3 The decomposition of hydrogen peroxide was studied at a particular temperature and experimental data is presented in the table to the right

2 H2O2(g) 2H2O(g) + O2(g)

a What are the two methods that you could use to determine the rate law for this reaction with the data that has been given

b Write out the rate law for this decomposition reaction

c What are the three methods that you could use to determine the rate constant

i Use the easiest of these two methods to determine a value for k

ii What are the units on k

d Now that you know the order of the reaction calculate the half-life for this reaction (if it is not 1st order calculate the half-life at the initial concentration)

yen Show how the conc vs time graph confirms the value that you calculated

P E3 (pg 4 of 6) Decomposition of H2O2

Time (s) [H2O2(g)] (moleL)

0 10

120 091

300 078

600 059

1200 037

1800 022

2400 013

3000 0082

3600 0050

$$$amp()$amp+

-$++

)$$

$$$

$$

amp$$

$$

$$

$$$

$$

amp$$

$$

$$

$$$

$$

$ 0$$ $$$ 0$$ $$$ 0$$ 1$$$ 10$$ amp$$$

$amp

()amp

$+amp-amp()amp

$amp($amp)

+amp-

$amp

$amp

$0amp

$0amp

$1amp

$1amp

$amp

amp

1 1 0 0 )

$$

amp(

)$$+amp(

$

$

amp$

$

($

)$

$

+$

$

$

$ $ amp$ ($ $ $ $ amp$ ($ $ $

$

amp$

()$+$amp$

Please work in PENCIL Please put some work on the page that indicates HOW you did the problem

1 If a 84 g sample of thorium decays with a 10 minute half life how much would the sample weigh in a half hour

2 A sample of radioactive iodine (half life = 3 days) originally weighed 10 g but now weighs 0625 g How old is this sample

You can estimate the half life quickly and easily but youOtildell need a calculator to use the integrated rate equation and half life equations

3 A sample of radioactive calcium originally weighed 24 g and in 12 hours it weighs 125 g What is the half-life

4 If a 500 g sample of barium decays with a 45 day half life how much would the sample weigh in a 18 days

5 A sample of an ancient grass mat containing radioactive carbon (half life = 5730 years) seems to be emitting on 625 of the radiation that a sample of a grass mat woven last year would have How old is this ancient grass mat

6 A sample of radioactive calcium originally weighed 32 kg and in 2 days it weighs 05 kg What is the half-life in hours

7 If a 96 g sample of tin decays with a 25 minute half life how much would the sample weigh in 15 minutes

8 A sample of radioactive magnesium (half life = 183 days) originally weighed 80 g but now weighs 25 g How many years old is this sample

9 A sample of radioactive radium originally weighed 56 g and in three days it weighs just less than a gram What is the half life in hours

P E3 (pg 1 of 2) Half Life ETH The Rate of Radioactive Decay Name________________________Per____

Exercise 4a Table logic

a) What is the order of the reaction with respect to A

b) What is the order of the reaction with respect to B

c) What is the value of the rate constant including units

Exercise 4b dirty math

a) What is the order of the reaction with respect to A

b) What is the order of the reaction with respect to B

c) What is the value of the rate constant including units

Exercise 5

Exercise 6

5) Reaction mechanisms

a) the sequence of bond-making and bond-breaking steps that occurs during the conversion of reactants to

products

i) Must be experimentally determined

ii) Must agree with the overall stoichiometry

iii) Must agree with the experimentally determined rate law

b) The vocabulary of mechanisms involves elementary steps amp molecularity which describes the number of

molecules that participate in an atomic rearrangement Add these terms into your explanations

i) unimolecular involves one reactant molecule that collides with a solvent or background molecule thereby

becoming collisionally activated In this state the reactant molecule is thermodynamically favorable for

converting into product

ii) bimolecular involves a collision between two reactant molecules

iii) termolecular simultaneous collision between three reactant molecules [very rare]

c) the rate expression cannot be predicted from overall stoichiometry The rate expression of an elementary step is

predicted from the stoichiometry of the elementary step as per the table below

d) Catalysts ndash species that are reactants in an elementary step but in subsequent steps is a product They LOWER

the activation energy amp donrsquot change H

i) Homogeneous catalyst ndash exist in the same phase as the reactants

ii) Heterogeneous catalyst ndash exist in a different phase than the reactants

e) Intermediaries ndashspecies that are products in an elementary step but in subsequent steps are reactants amp

consumed

i) Neither catalysts or intermediaries appear in the overall reaction or rate law

Exercise 7

Label the intermediaries amp catalysts

f) the slowest step is the rate determining step -- the rate of the overall reaction is limited by and is exactly equal

to the combined rates of all elementary steps up to and including the slowest step in the mechanism

Exercise 8

Exercise 9

In the reaction 2X+Y rarr Z

For a particular reaction the rate is found to be rate=k[Y]

Which of the below purposed mechanisms is a valid mechanism for this reaction

53 Rate Law Expression pt 2

1 Differential rate law

a Concentration vs rate data

b Use table logic or ugly algebra to find rate law amp value of K

2 Integrated rate law

a Concentration vs time data

b Must choose the straightest line graph and know what it means

c ONLY one reactant

d Done to determine how long a reaction must run to reach a certain concentration of reactant

e The value of the rate constant k is equal to the absolute value of the slope of the best fit line which is

decided by examining 3 linear regressions and analyzing the regression correlation coefficient (r)

i Graphs WILL be provided (except for the lab)

ii Time is ALWAYS X

iii The Y axi are

1 concentration of the reactant

2 natural log of the concentration (ln[A] NOT log[A])

3 reciprocal of the concentration on the y-axis of the third graph

iv If you remember them in this order with the y-axes being ldquoconcentrationrdquo ldquonatural log of

concentrationrdquo and ldquoreciprocal concentrationrdquo the alphabetical order of the y-axis variable

leads to 0 1 2 orders respectively for that reactant

REMEMBER what each variable is

Exercise 10

y = -00002x + 00831Rsup2 = 08871

-005

0

005

01

015

0 200 400 600

[N2O5]

y = -00069x - 23026Rsup2 = 1

-6

-4

-2

0

0 200 400 600

Ln [N2O5] y = 03535x - 78441

Rsup2 = 08841

-100

0

100

200

0 200 400 600

1[N2O5]

Unit 54 Kinetics Clean up

1 Half Life

a the time required for one half of one of the

reactants to disappear

b focus on the half-life for first order reactions only

i Discuss order (what order is it NOT)

ii Determine half life

iii What is the concentration after a set

number of half lives

iv What time would a set concentration be

found

2 In lab we will determine the order of a reaction by ldquoswampingrdquo We maximize one reactants concentration so

that ANY change is negligible

Exercise 11

a) What order is it NOT

b) Determine half life

c) What is the concentration after the second half life

d) When would 75 of the sample have decayed

For the generic reaction A + B C

1 The reaction below was studied at 25frac14C and the following data was obtained

NH4+ + NO2

N2 + 2H2O(L)

a What is the rate law

b What is the rate constant Be sure and include units

2 The reaction below was studied at 10frac14C and the following data was obtained

2NO(g) + Cl2(g) 2NOCl(g)

a What is the rate law

b What is the rate constant Be sure and include units

3 The reaction below was studied and the following data were obtained

2ClO2 + 2OH ClO3 + ClO2

+ H2O

a What is the rate law

b What is the rate constant Be sure and include units

4 The reaction below was studied and the following data were obtained

I + OCl IO + Cl

a What is the rate law

b What is the rate constant Be sure and include units

5 The reaction below was studied and the following data were obtained

BrO3 + 5 Br + 6 H+ 3 Br2 + 3 H2O

a What is the rate law

b What is the rate constant Be sure and include units

P E1 (pg 1 of 3) Using Initial Rates to Determine Order Name_____________________Per___

[NO]0

(molL)[Cl2]0

(molL)Initial Rate

(moleL min)

010 010 018

010 020 035

020 020 145

[I]0

(molL)[OCl]0

(molL)Initial Rate

(molL s)

012 018 791 102

006 018 395 102

003 009 988 103

024 009 791 102

[ClO2]0

(molL)[OH]0

(molL)Initial Rate

(molL s)

0050 0100 0057

0100 0100 023

0100 0050 0115

[NH4+]0

(molL)[NO2

]0

(molL)Initial Rate(moleL sec)

0100 0005 135 107

0100 0010 270 107

0200 0010 540 107

[BrO3]0

(molL)[Br]0

(molL)[H+]0

(molL)Initial Rate

(molL s)

0100 0100 0100 80 104

0200 0100 0100 16 103

0200 0200 0100 32 103

0100 0100 0200 32 103

trial[A]0

(molL)[B]0

(molL)Initial Rate

(moleL hour)

1 4 6 20

2 4 3 10

3 2 6 5

rate1

rate2=k

k

[A]ox

[A]ox

[B]oy

[B]oy

20

10=k

k

[4]ox

[4]ox

[6]oy

[3]oy

2 = [2]y

y = 1

20

5=k

k

[4]o

x

[2]o

x

[6]o

1

[6]o

1

4 = [2]x

x = 2 rate = k[A]2[B]

While it is most likely that any rate laws on the AP exam will only be first or second order it is possible that other orders will show up and are indeed possible When the order is not so obvious it is useful to know a useful log rule

RateRatio = [ConcRatio]x

log[RateRatio] = x log[ConcRatio] thus it is quite simple to solve for the order x log[RateRatio]

log[ConcRatio]= x

6 Given the hypothetical data below determine the order of the reaction A + B + C D + E

[A] (M) [B] (M) [C] (M) Rate (Msec)

10 10 10 00076

20 10 10 00304

10 10 20 00107

10 20 10 00152

7 Given the hypothetical data below determine the order of the reaction H + I + J K

[H] (M) [I] (M) [J] (M) Rate (Msec)

10 10 10 17

23 10 10 391

10 10 40 27

10 18 20 694

8 Given the hypothetical data below determine the order of the reaction P + Q + R S + T

[P] (M) [Q] (M) [R] (M) Rate (Msec)

10 10 10 00365

10 635 10 147

10 10 075 00274

19 47 23 185

9 Given the hypothetical data below determine the order of the reaction V + W + X Y + Z

[V] (M) [W] (M) [X] (M) Rate (Msec)

001 001 001 280 106

001 004 001 448 105

001 002 006 672 105

005 0025 0036 141 104

P E1 (pg 2 of 3) Using Initial Rates to Determine Order

Nitrogen dioxide will decompose into nitrogen oxide and oxygen gas as indicated in the equation below

2 NO2(g) 2 NO(g) + O2(g)

A graph of the concentration of each constituent at various times during the course of the reaction at 300frac14C is presented below Use this graph to understand that the loss of reactant and formation of products is stoichiometrically related

Decomposition of nitrogen dioxide

0

0002

0004

0006

0008

001

0012

0 100 200 300 400 500

time

co

nc

Next you can use the concentration of the reactant vs time data presented in the data table above and manipulate the concentration

values to ln[NO2] and 1

[NO2]

and then graph ln[NO2] vs time and also graph 1

[NO2]

vs time You can use these two graphs to

look for which of the graphs presented will give a straight line in order to determine the order of the reaction These two graphs are shown below

The r2 value which is the coefficient of determination you will learn more about r and r2 when you take a statistics course but for now you can think of it as a Ogravegoodness-of-fitOacute indicator The closer the r2 is to 1 the better the data fits to a straight line Thus

you can see that the r2 value is best for 1

[NO2]

vs time indicating this reaction is second order

P E2 (pg 1 of 6) Rate Laws Using data amp graphs Name_____________________Per____

Decomposition of Nitrogen Dioxide

time (sec) [NO2] [NO] [O2]

0 001 0 0

50 00079 00021 00011

100 00065 00035 00018

150 00055 00045 00023

200 00048 00052 00026

250 00043 00057 00029

300 00038 00062 00031

350 00034 00066 00033

400 00031 00069 00035

$amp()$amp+-

amp++

$-amp

$0amp(

$0amp-

$0amp

$0amp

$0amp

$amp(

$amp-

0 1 10 0 2 20 0

$$

amp(

)$$+amp(

$ampamp()+$-$+++-amp

amp$$$

($$$$

(amp$$$

-$$$$

-amp$$$

0$$$$

0amp$$$

$ amp$ ($$ (amp$ -$$ -amp$ 0$$ 0amp$ $$

$amp

()amp

$+amp-amp()amp

1 The dimerization of butadiene is studied at 500 K and the following reaction and experimental data is presented below

2 C4H6(g) C8H12(g)

a Determine the rate law for this reaction

b Determine the rate constant

c Calculate the half-life for this reaction (If it is not 1st order calculate the half-life at the initial concentration)

P E2 (pg 2 of 6) Rate Law for Dimerization of Butadiene

Time (s) [C4H6(g)] (M)

0 00167

195 00160

604 00150

1246 00130

2180 00110

6210 00068

$

$

amp$

amp$

amp($

amp$

amp$

$ amp$ $ )$ ($ $ $ +$

$

amp$

()$+$amp$

$amp($)amp)+

-amp0+

$0amp+

$0amp

$)amp

$)amp1

$)amp)

$)amp+

$)amp

+ ) 0 1 2

$$

amp(

)$$+amp(

$$amp()+(-

$+

0$$$

1$$$

2$$$

$$$

amp$$$$

ampamp$$$

amp($$$

amp-$$$

amp$$$

amp+$$$

$ amp$$$ ($$$ -$$$ $$$ +$$$ 0$$$ 1$$$

$amp

()amp

$+amp-amp()amp

2 Dinitrogen pentoxide can be decomposed according to the reaction below

2 N2O5(soln) 4 NO2(soln) + O2(g) All Trials are performed at 45frac14C

Data for this reaction can be collected in different ways It is presented in two different ways below instantaneous rates for various concentrations and concentration at various time The concentration vs time data is graphed

Concentration and Initial Rates

a What are a few methods by which you could determine the reaction order

b What are several different methods by which you could determine the rate constant k

c What are a few different methods by which you could determine the half-life

P E2 (pg 3 of 6) Decomposition of Dinitrogen Pentoxide

[N2O5(solOtilden)] (molesL)

Instantaneous rate Msec

10 000060

050 000030

025 000015

Concentration vs Time DataConcentration vs Time Data

Time (s)[N2O5(solOtilden)] (molesL)

0 100

200 088

400 078

600 069

800 061

1000 054

1200 048

1400 043

1600 038

1800 034

2000 030

$amp($amp)

+amp)))-

$amp

$amp

$amp-

$amp

$amp0

$amp

amp

1 1

$$

amp(

)$$+amp(

$$$ampamp($))

+$-$

$0$

amp$$

amp0$

$$

0$

1$$

10$

$ 0$$ amp$$$ amp0$$ $$$

$amp

()amp

$+amp-amp()amp

$

$

amp$

$

($

)$

$

+$

$

$

$ $ amp$ ($ $ $ $ amp$ ($ $ $

$

amp$

()$+$amp$

3 The decomposition of hydrogen peroxide was studied at a particular temperature and experimental data is presented in the table to the right

2 H2O2(g) 2H2O(g) + O2(g)

a What are the two methods that you could use to determine the rate law for this reaction with the data that has been given

b Write out the rate law for this decomposition reaction

c What are the three methods that you could use to determine the rate constant

i Use the easiest of these two methods to determine a value for k

ii What are the units on k

d Now that you know the order of the reaction calculate the half-life for this reaction (if it is not 1st order calculate the half-life at the initial concentration)

yen Show how the conc vs time graph confirms the value that you calculated

P E3 (pg 4 of 6) Decomposition of H2O2

Time (s) [H2O2(g)] (moleL)

0 10

120 091

300 078

600 059

1200 037

1800 022

2400 013

3000 0082

3600 0050

$$$amp()$amp+

-$++

)$$

$$$

$$

amp$$

$$

$$

$$$

$$

amp$$

$$

$$

$$$

$$

$ 0$$ $$$ 0$$ $$$ 0$$ 1$$$ 10$$ amp$$$

$amp

()amp

$+amp-amp()amp

$amp($amp)

+amp-

$amp

$amp

$0amp

$0amp

$1amp

$1amp

$amp

amp

1 1 0 0 )

$$

amp(

)$$+amp(

$

$

amp$

$

($

)$

$

+$

$

$

$ $ amp$ ($ $ $ $ amp$ ($ $ $

$

amp$

()$+$amp$

Please work in PENCIL Please put some work on the page that indicates HOW you did the problem

1 If a 84 g sample of thorium decays with a 10 minute half life how much would the sample weigh in a half hour

2 A sample of radioactive iodine (half life = 3 days) originally weighed 10 g but now weighs 0625 g How old is this sample

You can estimate the half life quickly and easily but youOtildell need a calculator to use the integrated rate equation and half life equations

3 A sample of radioactive calcium originally weighed 24 g and in 12 hours it weighs 125 g What is the half-life

4 If a 500 g sample of barium decays with a 45 day half life how much would the sample weigh in a 18 days

5 A sample of an ancient grass mat containing radioactive carbon (half life = 5730 years) seems to be emitting on 625 of the radiation that a sample of a grass mat woven last year would have How old is this ancient grass mat

6 A sample of radioactive calcium originally weighed 32 kg and in 2 days it weighs 05 kg What is the half-life in hours

7 If a 96 g sample of tin decays with a 25 minute half life how much would the sample weigh in 15 minutes

8 A sample of radioactive magnesium (half life = 183 days) originally weighed 80 g but now weighs 25 g How many years old is this sample

9 A sample of radioactive radium originally weighed 56 g and in three days it weighs just less than a gram What is the half life in hours

P E3 (pg 1 of 2) Half Life ETH The Rate of Radioactive Decay Name________________________Per____

Exercise 4b dirty math

a) What is the order of the reaction with respect to A

b) What is the order of the reaction with respect to B

c) What is the value of the rate constant including units

Exercise 5

Exercise 6

5) Reaction mechanisms

a) the sequence of bond-making and bond-breaking steps that occurs during the conversion of reactants to

products

i) Must be experimentally determined

ii) Must agree with the overall stoichiometry

iii) Must agree with the experimentally determined rate law

b) The vocabulary of mechanisms involves elementary steps amp molecularity which describes the number of

molecules that participate in an atomic rearrangement Add these terms into your explanations

i) unimolecular involves one reactant molecule that collides with a solvent or background molecule thereby

becoming collisionally activated In this state the reactant molecule is thermodynamically favorable for

converting into product

ii) bimolecular involves a collision between two reactant molecules

iii) termolecular simultaneous collision between three reactant molecules [very rare]

c) the rate expression cannot be predicted from overall stoichiometry The rate expression of an elementary step is

predicted from the stoichiometry of the elementary step as per the table below

d) Catalysts ndash species that are reactants in an elementary step but in subsequent steps is a product They LOWER

the activation energy amp donrsquot change H

i) Homogeneous catalyst ndash exist in the same phase as the reactants

ii) Heterogeneous catalyst ndash exist in a different phase than the reactants

e) Intermediaries ndashspecies that are products in an elementary step but in subsequent steps are reactants amp

consumed

i) Neither catalysts or intermediaries appear in the overall reaction or rate law

Exercise 7

Label the intermediaries amp catalysts

f) the slowest step is the rate determining step -- the rate of the overall reaction is limited by and is exactly equal

to the combined rates of all elementary steps up to and including the slowest step in the mechanism

Exercise 8

Exercise 9

In the reaction 2X+Y rarr Z

For a particular reaction the rate is found to be rate=k[Y]

Which of the below purposed mechanisms is a valid mechanism for this reaction

53 Rate Law Expression pt 2

1 Differential rate law

a Concentration vs rate data

b Use table logic or ugly algebra to find rate law amp value of K

2 Integrated rate law

a Concentration vs time data

b Must choose the straightest line graph and know what it means

c ONLY one reactant

d Done to determine how long a reaction must run to reach a certain concentration of reactant

e The value of the rate constant k is equal to the absolute value of the slope of the best fit line which is

decided by examining 3 linear regressions and analyzing the regression correlation coefficient (r)

i Graphs WILL be provided (except for the lab)

ii Time is ALWAYS X

iii The Y axi are

1 concentration of the reactant

2 natural log of the concentration (ln[A] NOT log[A])

3 reciprocal of the concentration on the y-axis of the third graph

iv If you remember them in this order with the y-axes being ldquoconcentrationrdquo ldquonatural log of

concentrationrdquo and ldquoreciprocal concentrationrdquo the alphabetical order of the y-axis variable

leads to 0 1 2 orders respectively for that reactant

REMEMBER what each variable is

Exercise 10

y = -00002x + 00831Rsup2 = 08871

-005

0

005

01

015

0 200 400 600

[N2O5]

y = -00069x - 23026Rsup2 = 1

-6

-4

-2

0

0 200 400 600

Ln [N2O5] y = 03535x - 78441

Rsup2 = 08841

-100

0

100

200

0 200 400 600

1[N2O5]

Unit 54 Kinetics Clean up

1 Half Life

a the time required for one half of one of the

reactants to disappear

b focus on the half-life for first order reactions only

i Discuss order (what order is it NOT)

ii Determine half life

iii What is the concentration after a set

number of half lives

iv What time would a set concentration be

found

2 In lab we will determine the order of a reaction by ldquoswampingrdquo We maximize one reactants concentration so

that ANY change is negligible

Exercise 11

a) What order is it NOT

b) Determine half life

c) What is the concentration after the second half life

d) When would 75 of the sample have decayed

For the generic reaction A + B C

1 The reaction below was studied at 25frac14C and the following data was obtained

NH4+ + NO2

N2 + 2H2O(L)

a What is the rate law

b What is the rate constant Be sure and include units

2 The reaction below was studied at 10frac14C and the following data was obtained

2NO(g) + Cl2(g) 2NOCl(g)

a What is the rate law

b What is the rate constant Be sure and include units

3 The reaction below was studied and the following data were obtained

2ClO2 + 2OH ClO3 + ClO2

+ H2O

a What is the rate law

b What is the rate constant Be sure and include units

4 The reaction below was studied and the following data were obtained

I + OCl IO + Cl

a What is the rate law

b What is the rate constant Be sure and include units

5 The reaction below was studied and the following data were obtained

BrO3 + 5 Br + 6 H+ 3 Br2 + 3 H2O

a What is the rate law

b What is the rate constant Be sure and include units

P E1 (pg 1 of 3) Using Initial Rates to Determine Order Name_____________________Per___

[NO]0

(molL)[Cl2]0

(molL)Initial Rate

(moleL min)

010 010 018

010 020 035

020 020 145

[I]0

(molL)[OCl]0

(molL)Initial Rate

(molL s)

012 018 791 102

006 018 395 102

003 009 988 103

024 009 791 102

[ClO2]0

(molL)[OH]0

(molL)Initial Rate

(molL s)

0050 0100 0057

0100 0100 023

0100 0050 0115

[NH4+]0

(molL)[NO2

]0

(molL)Initial Rate(moleL sec)

0100 0005 135 107

0100 0010 270 107

0200 0010 540 107

[BrO3]0

(molL)[Br]0

(molL)[H+]0

(molL)Initial Rate

(molL s)

0100 0100 0100 80 104

0200 0100 0100 16 103

0200 0200 0100 32 103

0100 0100 0200 32 103

trial[A]0

(molL)[B]0

(molL)Initial Rate

(moleL hour)

1 4 6 20

2 4 3 10

3 2 6 5

rate1

rate2=k

k

[A]ox

[A]ox

[B]oy

[B]oy

20

10=k

k

[4]ox

[4]ox

[6]oy

[3]oy

2 = [2]y

y = 1

20

5=k

k

[4]o

x

[2]o

x

[6]o

1

[6]o

1

4 = [2]x

x = 2 rate = k[A]2[B]

While it is most likely that any rate laws on the AP exam will only be first or second order it is possible that other orders will show up and are indeed possible When the order is not so obvious it is useful to know a useful log rule

RateRatio = [ConcRatio]x

log[RateRatio] = x log[ConcRatio] thus it is quite simple to solve for the order x log[RateRatio]

log[ConcRatio]= x

6 Given the hypothetical data below determine the order of the reaction A + B + C D + E

[A] (M) [B] (M) [C] (M) Rate (Msec)

10 10 10 00076

20 10 10 00304

10 10 20 00107

10 20 10 00152

7 Given the hypothetical data below determine the order of the reaction H + I + J K

[H] (M) [I] (M) [J] (M) Rate (Msec)

10 10 10 17

23 10 10 391

10 10 40 27

10 18 20 694

8 Given the hypothetical data below determine the order of the reaction P + Q + R S + T

[P] (M) [Q] (M) [R] (M) Rate (Msec)

10 10 10 00365

10 635 10 147

10 10 075 00274

19 47 23 185

9 Given the hypothetical data below determine the order of the reaction V + W + X Y + Z

[V] (M) [W] (M) [X] (M) Rate (Msec)

001 001 001 280 106

001 004 001 448 105

001 002 006 672 105

005 0025 0036 141 104

P E1 (pg 2 of 3) Using Initial Rates to Determine Order

Nitrogen dioxide will decompose into nitrogen oxide and oxygen gas as indicated in the equation below

2 NO2(g) 2 NO(g) + O2(g)

A graph of the concentration of each constituent at various times during the course of the reaction at 300frac14C is presented below Use this graph to understand that the loss of reactant and formation of products is stoichiometrically related

Decomposition of nitrogen dioxide

0

0002

0004

0006

0008

001

0012

0 100 200 300 400 500

time

co

nc

Next you can use the concentration of the reactant vs time data presented in the data table above and manipulate the concentration

values to ln[NO2] and 1

[NO2]

and then graph ln[NO2] vs time and also graph 1

[NO2]

vs time You can use these two graphs to

look for which of the graphs presented will give a straight line in order to determine the order of the reaction These two graphs are shown below

The r2 value which is the coefficient of determination you will learn more about r and r2 when you take a statistics course but for now you can think of it as a Ogravegoodness-of-fitOacute indicator The closer the r2 is to 1 the better the data fits to a straight line Thus

you can see that the r2 value is best for 1

[NO2]

vs time indicating this reaction is second order

P E2 (pg 1 of 6) Rate Laws Using data amp graphs Name_____________________Per____

Decomposition of Nitrogen Dioxide

time (sec) [NO2] [NO] [O2]

0 001 0 0

50 00079 00021 00011

100 00065 00035 00018

150 00055 00045 00023

200 00048 00052 00026

250 00043 00057 00029

300 00038 00062 00031

350 00034 00066 00033

400 00031 00069 00035

$amp()$amp+-

amp++

$-amp

$0amp(

$0amp-

$0amp

$0amp

$0amp

$amp(

$amp-

0 1 10 0 2 20 0

$$

amp(

)$$+amp(

$ampamp()+$-$+++-amp

amp$$$

($$$$

(amp$$$

-$$$$

-amp$$$

0$$$$

0amp$$$

$ amp$ ($$ (amp$ -$$ -amp$ 0$$ 0amp$ $$

$amp

()amp

$+amp-amp()amp

1 The dimerization of butadiene is studied at 500 K and the following reaction and experimental data is presented below

2 C4H6(g) C8H12(g)

a Determine the rate law for this reaction

b Determine the rate constant

c Calculate the half-life for this reaction (If it is not 1st order calculate the half-life at the initial concentration)

P E2 (pg 2 of 6) Rate Law for Dimerization of Butadiene

Time (s) [C4H6(g)] (M)

0 00167

195 00160

604 00150

1246 00130

2180 00110

6210 00068

$

$

amp$

amp$

amp($

amp$

amp$

$ amp$ $ )$ ($ $ $ +$

$

amp$

()$+$amp$

$amp($)amp)+

-amp0+

$0amp+

$0amp

$)amp

$)amp1

$)amp)

$)amp+

$)amp

+ ) 0 1 2

$$

amp(

)$$+amp(

$$amp()+(-

$+

0$$$

1$$$

2$$$

$$$

amp$$$$

ampamp$$$

amp($$$

amp-$$$

amp$$$

amp+$$$

$ amp$$$ ($$$ -$$$ $$$ +$$$ 0$$$ 1$$$

$amp

()amp

$+amp-amp()amp

2 Dinitrogen pentoxide can be decomposed according to the reaction below

2 N2O5(soln) 4 NO2(soln) + O2(g) All Trials are performed at 45frac14C

Data for this reaction can be collected in different ways It is presented in two different ways below instantaneous rates for various concentrations and concentration at various time The concentration vs time data is graphed

Concentration and Initial Rates

a What are a few methods by which you could determine the reaction order

b What are several different methods by which you could determine the rate constant k

c What are a few different methods by which you could determine the half-life

P E2 (pg 3 of 6) Decomposition of Dinitrogen Pentoxide

[N2O5(solOtilden)] (molesL)

Instantaneous rate Msec

10 000060

050 000030

025 000015

Concentration vs Time DataConcentration vs Time Data

Time (s)[N2O5(solOtilden)] (molesL)

0 100

200 088

400 078

600 069

800 061

1000 054

1200 048

1400 043

1600 038

1800 034

2000 030

$amp($amp)

+amp)))-

$amp

$amp

$amp-

$amp

$amp0

$amp

amp

1 1

$$

amp(

)$$+amp(

$$$ampamp($))

+$-$

$0$

amp$$

amp0$

$$

0$

1$$

10$

$ 0$$ amp$$$ amp0$$ $$$

$amp

()amp

$+amp-amp()amp

$

$

amp$

$

($

)$

$

+$

$

$

$ $ amp$ ($ $ $ $ amp$ ($ $ $

$

amp$

()$+$amp$

3 The decomposition of hydrogen peroxide was studied at a particular temperature and experimental data is presented in the table to the right

2 H2O2(g) 2H2O(g) + O2(g)

a What are the two methods that you could use to determine the rate law for this reaction with the data that has been given

b Write out the rate law for this decomposition reaction

c What are the three methods that you could use to determine the rate constant

i Use the easiest of these two methods to determine a value for k

ii What are the units on k

d Now that you know the order of the reaction calculate the half-life for this reaction (if it is not 1st order calculate the half-life at the initial concentration)

yen Show how the conc vs time graph confirms the value that you calculated

P E3 (pg 4 of 6) Decomposition of H2O2

Time (s) [H2O2(g)] (moleL)

0 10

120 091

300 078

600 059

1200 037

1800 022

2400 013

3000 0082

3600 0050

$$$amp()$amp+

-$++

)$$

$$$

$$

amp$$

$$

$$

$$$

$$

amp$$

$$

$$

$$$

$$

$ 0$$ $$$ 0$$ $$$ 0$$ 1$$$ 10$$ amp$$$

$amp

()amp

$+amp-amp()amp

$amp($amp)

+amp-

$amp

$amp

$0amp

$0amp

$1amp

$1amp

$amp

amp

1 1 0 0 )

$$

amp(

)$$+amp(

$

$

amp$

$

($

)$

$

+$

$

$

$ $ amp$ ($ $ $ $ amp$ ($ $ $

$

amp$

()$+$amp$

Please work in PENCIL Please put some work on the page that indicates HOW you did the problem

1 If a 84 g sample of thorium decays with a 10 minute half life how much would the sample weigh in a half hour

2 A sample of radioactive iodine (half life = 3 days) originally weighed 10 g but now weighs 0625 g How old is this sample

You can estimate the half life quickly and easily but youOtildell need a calculator to use the integrated rate equation and half life equations

3 A sample of radioactive calcium originally weighed 24 g and in 12 hours it weighs 125 g What is the half-life

4 If a 500 g sample of barium decays with a 45 day half life how much would the sample weigh in a 18 days

5 A sample of an ancient grass mat containing radioactive carbon (half life = 5730 years) seems to be emitting on 625 of the radiation that a sample of a grass mat woven last year would have How old is this ancient grass mat

6 A sample of radioactive calcium originally weighed 32 kg and in 2 days it weighs 05 kg What is the half-life in hours

7 If a 96 g sample of tin decays with a 25 minute half life how much would the sample weigh in 15 minutes

8 A sample of radioactive magnesium (half life = 183 days) originally weighed 80 g but now weighs 25 g How many years old is this sample

9 A sample of radioactive radium originally weighed 56 g and in three days it weighs just less than a gram What is the half life in hours

P E3 (pg 1 of 2) Half Life ETH The Rate of Radioactive Decay Name________________________Per____

Exercise 5

Exercise 6

5) Reaction mechanisms

a) the sequence of bond-making and bond-breaking steps that occurs during the conversion of reactants to

products

i) Must be experimentally determined

ii) Must agree with the overall stoichiometry

iii) Must agree with the experimentally determined rate law

b) The vocabulary of mechanisms involves elementary steps amp molecularity which describes the number of

molecules that participate in an atomic rearrangement Add these terms into your explanations

i) unimolecular involves one reactant molecule that collides with a solvent or background molecule thereby

becoming collisionally activated In this state the reactant molecule is thermodynamically favorable for

converting into product

ii) bimolecular involves a collision between two reactant molecules

iii) termolecular simultaneous collision between three reactant molecules [very rare]

c) the rate expression cannot be predicted from overall stoichiometry The rate expression of an elementary step is

predicted from the stoichiometry of the elementary step as per the table below

d) Catalysts ndash species that are reactants in an elementary step but in subsequent steps is a product They LOWER

the activation energy amp donrsquot change H

i) Homogeneous catalyst ndash exist in the same phase as the reactants

ii) Heterogeneous catalyst ndash exist in a different phase than the reactants

e) Intermediaries ndashspecies that are products in an elementary step but in subsequent steps are reactants amp

consumed

i) Neither catalysts or intermediaries appear in the overall reaction or rate law

Exercise 7

Label the intermediaries amp catalysts

f) the slowest step is the rate determining step -- the rate of the overall reaction is limited by and is exactly equal

to the combined rates of all elementary steps up to and including the slowest step in the mechanism

Exercise 8

Exercise 9

In the reaction 2X+Y rarr Z

For a particular reaction the rate is found to be rate=k[Y]

Which of the below purposed mechanisms is a valid mechanism for this reaction

53 Rate Law Expression pt 2

1 Differential rate law

a Concentration vs rate data

b Use table logic or ugly algebra to find rate law amp value of K

2 Integrated rate law

a Concentration vs time data

b Must choose the straightest line graph and know what it means

c ONLY one reactant

d Done to determine how long a reaction must run to reach a certain concentration of reactant

e The value of the rate constant k is equal to the absolute value of the slope of the best fit line which is

decided by examining 3 linear regressions and analyzing the regression correlation coefficient (r)

i Graphs WILL be provided (except for the lab)

ii Time is ALWAYS X

iii The Y axi are

1 concentration of the reactant

2 natural log of the concentration (ln[A] NOT log[A])

3 reciprocal of the concentration on the y-axis of the third graph

iv If you remember them in this order with the y-axes being ldquoconcentrationrdquo ldquonatural log of

concentrationrdquo and ldquoreciprocal concentrationrdquo the alphabetical order of the y-axis variable

leads to 0 1 2 orders respectively for that reactant

REMEMBER what each variable is

Exercise 10

y = -00002x + 00831Rsup2 = 08871

-005

0

005

01

015

0 200 400 600

[N2O5]

y = -00069x - 23026Rsup2 = 1

-6

-4

-2

0

0 200 400 600

Ln [N2O5] y = 03535x - 78441

Rsup2 = 08841

-100

0

100

200

0 200 400 600

1[N2O5]

Unit 54 Kinetics Clean up

1 Half Life

a the time required for one half of one of the

reactants to disappear

b focus on the half-life for first order reactions only

i Discuss order (what order is it NOT)

ii Determine half life

iii What is the concentration after a set

number of half lives

iv What time would a set concentration be

found

2 In lab we will determine the order of a reaction by ldquoswampingrdquo We maximize one reactants concentration so

that ANY change is negligible

Exercise 11

a) What order is it NOT

b) Determine half life

c) What is the concentration after the second half life

d) When would 75 of the sample have decayed

For the generic reaction A + B C

1 The reaction below was studied at 25frac14C and the following data was obtained

NH4+ + NO2

N2 + 2H2O(L)

a What is the rate law

b What is the rate constant Be sure and include units

2 The reaction below was studied at 10frac14C and the following data was obtained

2NO(g) + Cl2(g) 2NOCl(g)

a What is the rate law

b What is the rate constant Be sure and include units

3 The reaction below was studied and the following data were obtained

2ClO2 + 2OH ClO3 + ClO2

+ H2O

a What is the rate law

b What is the rate constant Be sure and include units

4 The reaction below was studied and the following data were obtained

I + OCl IO + Cl

a What is the rate law

b What is the rate constant Be sure and include units

5 The reaction below was studied and the following data were obtained

BrO3 + 5 Br + 6 H+ 3 Br2 + 3 H2O

a What is the rate law

b What is the rate constant Be sure and include units

P E1 (pg 1 of 3) Using Initial Rates to Determine Order Name_____________________Per___

[NO]0

(molL)[Cl2]0

(molL)Initial Rate

(moleL min)

010 010 018

010 020 035

020 020 145

[I]0

(molL)[OCl]0

(molL)Initial Rate

(molL s)

012 018 791 102

006 018 395 102

003 009 988 103

024 009 791 102

[ClO2]0

(molL)[OH]0

(molL)Initial Rate

(molL s)

0050 0100 0057

0100 0100 023

0100 0050 0115

[NH4+]0

(molL)[NO2

]0

(molL)Initial Rate(moleL sec)

0100 0005 135 107

0100 0010 270 107

0200 0010 540 107

[BrO3]0

(molL)[Br]0

(molL)[H+]0

(molL)Initial Rate

(molL s)

0100 0100 0100 80 104

0200 0100 0100 16 103

0200 0200 0100 32 103

0100 0100 0200 32 103

trial[A]0

(molL)[B]0

(molL)Initial Rate

(moleL hour)

1 4 6 20

2 4 3 10

3 2 6 5

rate1

rate2=k

k

[A]ox

[A]ox

[B]oy

[B]oy

20

10=k

k

[4]ox

[4]ox

[6]oy

[3]oy

2 = [2]y

y = 1

20

5=k

k

[4]o

x

[2]o

x

[6]o

1

[6]o

1

4 = [2]x

x = 2 rate = k[A]2[B]

While it is most likely that any rate laws on the AP exam will only be first or second order it is possible that other orders will show up and are indeed possible When the order is not so obvious it is useful to know a useful log rule

RateRatio = [ConcRatio]x

log[RateRatio] = x log[ConcRatio] thus it is quite simple to solve for the order x log[RateRatio]

log[ConcRatio]= x

6 Given the hypothetical data below determine the order of the reaction A + B + C D + E

[A] (M) [B] (M) [C] (M) Rate (Msec)

10 10 10 00076

20 10 10 00304

10 10 20 00107

10 20 10 00152

7 Given the hypothetical data below determine the order of the reaction H + I + J K

[H] (M) [I] (M) [J] (M) Rate (Msec)

10 10 10 17

23 10 10 391

10 10 40 27

10 18 20 694

8 Given the hypothetical data below determine the order of the reaction P + Q + R S + T

[P] (M) [Q] (M) [R] (M) Rate (Msec)

10 10 10 00365

10 635 10 147

10 10 075 00274

19 47 23 185

9 Given the hypothetical data below determine the order of the reaction V + W + X Y + Z

[V] (M) [W] (M) [X] (M) Rate (Msec)

001 001 001 280 106

001 004 001 448 105

001 002 006 672 105

005 0025 0036 141 104

P E1 (pg 2 of 3) Using Initial Rates to Determine Order

Nitrogen dioxide will decompose into nitrogen oxide and oxygen gas as indicated in the equation below

2 NO2(g) 2 NO(g) + O2(g)

A graph of the concentration of each constituent at various times during the course of the reaction at 300frac14C is presented below Use this graph to understand that the loss of reactant and formation of products is stoichiometrically related

Decomposition of nitrogen dioxide

0

0002

0004

0006

0008

001

0012

0 100 200 300 400 500

time

co

nc

Next you can use the concentration of the reactant vs time data presented in the data table above and manipulate the concentration

values to ln[NO2] and 1

[NO2]

and then graph ln[NO2] vs time and also graph 1

[NO2]

vs time You can use these two graphs to

look for which of the graphs presented will give a straight line in order to determine the order of the reaction These two graphs are shown below

The r2 value which is the coefficient of determination you will learn more about r and r2 when you take a statistics course but for now you can think of it as a Ogravegoodness-of-fitOacute indicator The closer the r2 is to 1 the better the data fits to a straight line Thus

you can see that the r2 value is best for 1

[NO2]

vs time indicating this reaction is second order

P E2 (pg 1 of 6) Rate Laws Using data amp graphs Name_____________________Per____

Decomposition of Nitrogen Dioxide

time (sec) [NO2] [NO] [O2]

0 001 0 0

50 00079 00021 00011

100 00065 00035 00018

150 00055 00045 00023

200 00048 00052 00026

250 00043 00057 00029

300 00038 00062 00031

350 00034 00066 00033

400 00031 00069 00035

$amp()$amp+-

amp++

$-amp

$0amp(

$0amp-

$0amp

$0amp

$0amp

$amp(

$amp-

0 1 10 0 2 20 0

$$

amp(

)$$+amp(

$ampamp()+$-$+++-amp

amp$$$

($$$$

(amp$$$

-$$$$

-amp$$$

0$$$$

0amp$$$

$ amp$ ($$ (amp$ -$$ -amp$ 0$$ 0amp$ $$

$amp

()amp

$+amp-amp()amp

1 The dimerization of butadiene is studied at 500 K and the following reaction and experimental data is presented below

2 C4H6(g) C8H12(g)

a Determine the rate law for this reaction

b Determine the rate constant

c Calculate the half-life for this reaction (If it is not 1st order calculate the half-life at the initial concentration)

P E2 (pg 2 of 6) Rate Law for Dimerization of Butadiene

Time (s) [C4H6(g)] (M)

0 00167

195 00160

604 00150

1246 00130

2180 00110

6210 00068

$

$

amp$

amp$

amp($

amp$

amp$

$ amp$ $ )$ ($ $ $ +$

$

amp$

()$+$amp$

$amp($)amp)+

-amp0+

$0amp+

$0amp

$)amp

$)amp1

$)amp)

$)amp+

$)amp

+ ) 0 1 2

$$

amp(

)$$+amp(

$$amp()+(-

$+

0$$$

1$$$

2$$$

$$$

amp$$$$

ampamp$$$

amp($$$

amp-$$$

amp$$$

amp+$$$

$ amp$$$ ($$$ -$$$ $$$ +$$$ 0$$$ 1$$$

$amp

()amp

$+amp-amp()amp

2 Dinitrogen pentoxide can be decomposed according to the reaction below

2 N2O5(soln) 4 NO2(soln) + O2(g) All Trials are performed at 45frac14C

Data for this reaction can be collected in different ways It is presented in two different ways below instantaneous rates for various concentrations and concentration at various time The concentration vs time data is graphed

Concentration and Initial Rates

a What are a few methods by which you could determine the reaction order

b What are several different methods by which you could determine the rate constant k

c What are a few different methods by which you could determine the half-life

P E2 (pg 3 of 6) Decomposition of Dinitrogen Pentoxide

[N2O5(solOtilden)] (molesL)

Instantaneous rate Msec

10 000060

050 000030

025 000015

Concentration vs Time DataConcentration vs Time Data

Time (s)[N2O5(solOtilden)] (molesL)

0 100

200 088

400 078

600 069

800 061

1000 054

1200 048

1400 043

1600 038

1800 034

2000 030

$amp($amp)

+amp)))-

$amp

$amp

$amp-

$amp

$amp0

$amp

amp

1 1

$$

amp(

)$$+amp(

$$$ampamp($))

+$-$

$0$

amp$$

amp0$

$$

0$

1$$

10$

$ 0$$ amp$$$ amp0$$ $$$

$amp

()amp

$+amp-amp()amp

$

$

amp$

$

($

)$

$

+$

$

$

$ $ amp$ ($ $ $ $ amp$ ($ $ $

$

amp$

()$+$amp$

3 The decomposition of hydrogen peroxide was studied at a particular temperature and experimental data is presented in the table to the right

2 H2O2(g) 2H2O(g) + O2(g)

a What are the two methods that you could use to determine the rate law for this reaction with the data that has been given

b Write out the rate law for this decomposition reaction

c What are the three methods that you could use to determine the rate constant

i Use the easiest of these two methods to determine a value for k

ii What are the units on k

d Now that you know the order of the reaction calculate the half-life for this reaction (if it is not 1st order calculate the half-life at the initial concentration)

yen Show how the conc vs time graph confirms the value that you calculated

P E3 (pg 4 of 6) Decomposition of H2O2

Time (s) [H2O2(g)] (moleL)

0 10

120 091

300 078

600 059

1200 037

1800 022

2400 013

3000 0082

3600 0050

$$$amp()$amp+

-$++

)$$

$$$

$$

amp$$

$$

$$

$$$

$$

amp$$

$$

$$

$$$

$$

$ 0$$ $$$ 0$$ $$$ 0$$ 1$$$ 10$$ amp$$$

$amp

()amp

$+amp-amp()amp

$amp($amp)

+amp-

$amp

$amp

$0amp

$0amp

$1amp

$1amp

$amp

amp

1 1 0 0 )

$$

amp(

)$$+amp(

$

$

amp$

$

($

)$

$

+$

$

$

$ $ amp$ ($ $ $ $ amp$ ($ $ $

$

amp$

()$+$amp$

Please work in PENCIL Please put some work on the page that indicates HOW you did the problem

1 If a 84 g sample of thorium decays with a 10 minute half life how much would the sample weigh in a half hour

2 A sample of radioactive iodine (half life = 3 days) originally weighed 10 g but now weighs 0625 g How old is this sample

You can estimate the half life quickly and easily but youOtildell need a calculator to use the integrated rate equation and half life equations

3 A sample of radioactive calcium originally weighed 24 g and in 12 hours it weighs 125 g What is the half-life

4 If a 500 g sample of barium decays with a 45 day half life how much would the sample weigh in a 18 days

5 A sample of an ancient grass mat containing radioactive carbon (half life = 5730 years) seems to be emitting on 625 of the radiation that a sample of a grass mat woven last year would have How old is this ancient grass mat

6 A sample of radioactive calcium originally weighed 32 kg and in 2 days it weighs 05 kg What is the half-life in hours

7 If a 96 g sample of tin decays with a 25 minute half life how much would the sample weigh in 15 minutes

8 A sample of radioactive magnesium (half life = 183 days) originally weighed 80 g but now weighs 25 g How many years old is this sample

9 A sample of radioactive radium originally weighed 56 g and in three days it weighs just less than a gram What is the half life in hours

P E3 (pg 1 of 2) Half Life ETH The Rate of Radioactive Decay Name________________________Per____

5) Reaction mechanisms

a) the sequence of bond-making and bond-breaking steps that occurs during the conversion of reactants to

products

i) Must be experimentally determined

ii) Must agree with the overall stoichiometry

iii) Must agree with the experimentally determined rate law

b) The vocabulary of mechanisms involves elementary steps amp molecularity which describes the number of

molecules that participate in an atomic rearrangement Add these terms into your explanations

i) unimolecular involves one reactant molecule that collides with a solvent or background molecule thereby

becoming collisionally activated In this state the reactant molecule is thermodynamically favorable for

converting into product

ii) bimolecular involves a collision between two reactant molecules

iii) termolecular simultaneous collision between three reactant molecules [very rare]

c) the rate expression cannot be predicted from overall stoichiometry The rate expression of an elementary step is

predicted from the stoichiometry of the elementary step as per the table below

d) Catalysts ndash species that are reactants in an elementary step but in subsequent steps is a product They LOWER

the activation energy amp donrsquot change H

i) Homogeneous catalyst ndash exist in the same phase as the reactants

ii) Heterogeneous catalyst ndash exist in a different phase than the reactants

e) Intermediaries ndashspecies that are products in an elementary step but in subsequent steps are reactants amp

consumed

i) Neither catalysts or intermediaries appear in the overall reaction or rate law

Exercise 7

Label the intermediaries amp catalysts

f) the slowest step is the rate determining step -- the rate of the overall reaction is limited by and is exactly equal

to the combined rates of all elementary steps up to and including the slowest step in the mechanism

Exercise 8

Exercise 9

In the reaction 2X+Y rarr Z

For a particular reaction the rate is found to be rate=k[Y]

Which of the below purposed mechanisms is a valid mechanism for this reaction

53 Rate Law Expression pt 2

1 Differential rate law

a Concentration vs rate data

b Use table logic or ugly algebra to find rate law amp value of K

2 Integrated rate law

a Concentration vs time data

b Must choose the straightest line graph and know what it means

c ONLY one reactant

d Done to determine how long a reaction must run to reach a certain concentration of reactant

e The value of the rate constant k is equal to the absolute value of the slope of the best fit line which is

decided by examining 3 linear regressions and analyzing the regression correlation coefficient (r)

i Graphs WILL be provided (except for the lab)

ii Time is ALWAYS X

iii The Y axi are

1 concentration of the reactant

2 natural log of the concentration (ln[A] NOT log[A])

3 reciprocal of the concentration on the y-axis of the third graph

iv If you remember them in this order with the y-axes being ldquoconcentrationrdquo ldquonatural log of

concentrationrdquo and ldquoreciprocal concentrationrdquo the alphabetical order of the y-axis variable

leads to 0 1 2 orders respectively for that reactant

REMEMBER what each variable is

Exercise 10

y = -00002x + 00831Rsup2 = 08871

-005

0

005

01

015

0 200 400 600

[N2O5]

y = -00069x - 23026Rsup2 = 1

-6

-4

-2

0

0 200 400 600

Ln [N2O5] y = 03535x - 78441

Rsup2 = 08841

-100

0

100

200

0 200 400 600

1[N2O5]

Unit 54 Kinetics Clean up

1 Half Life

a the time required for one half of one of the

reactants to disappear

b focus on the half-life for first order reactions only

i Discuss order (what order is it NOT)

ii Determine half life

iii What is the concentration after a set

number of half lives

iv What time would a set concentration be

found

2 In lab we will determine the order of a reaction by ldquoswampingrdquo We maximize one reactants concentration so

that ANY change is negligible

Exercise 11

a) What order is it NOT

b) Determine half life

c) What is the concentration after the second half life

d) When would 75 of the sample have decayed

For the generic reaction A + B C

1 The reaction below was studied at 25frac14C and the following data was obtained

NH4+ + NO2

N2 + 2H2O(L)

a What is the rate law

b What is the rate constant Be sure and include units

2 The reaction below was studied at 10frac14C and the following data was obtained

2NO(g) + Cl2(g) 2NOCl(g)

a What is the rate law

b What is the rate constant Be sure and include units

3 The reaction below was studied and the following data were obtained

2ClO2 + 2OH ClO3 + ClO2

+ H2O

a What is the rate law

b What is the rate constant Be sure and include units

4 The reaction below was studied and the following data were obtained

I + OCl IO + Cl

a What is the rate law

b What is the rate constant Be sure and include units

5 The reaction below was studied and the following data were obtained

BrO3 + 5 Br + 6 H+ 3 Br2 + 3 H2O

a What is the rate law

b What is the rate constant Be sure and include units

P E1 (pg 1 of 3) Using Initial Rates to Determine Order Name_____________________Per___

[NO]0

(molL)[Cl2]0

(molL)Initial Rate

(moleL min)

010 010 018

010 020 035

020 020 145

[I]0

(molL)[OCl]0

(molL)Initial Rate

(molL s)

012 018 791 102

006 018 395 102

003 009 988 103

024 009 791 102

[ClO2]0

(molL)[OH]0

(molL)Initial Rate

(molL s)

0050 0100 0057

0100 0100 023

0100 0050 0115

[NH4+]0

(molL)[NO2

]0

(molL)Initial Rate(moleL sec)

0100 0005 135 107

0100 0010 270 107

0200 0010 540 107

[BrO3]0

(molL)[Br]0

(molL)[H+]0

(molL)Initial Rate

(molL s)

0100 0100 0100 80 104

0200 0100 0100 16 103

0200 0200 0100 32 103

0100 0100 0200 32 103

trial[A]0

(molL)[B]0

(molL)Initial Rate

(moleL hour)

1 4 6 20

2 4 3 10

3 2 6 5

rate1

rate2=k

k

[A]ox

[A]ox

[B]oy

[B]oy

20

10=k

k

[4]ox

[4]ox

[6]oy

[3]oy

2 = [2]y

y = 1

20

5=k

k

[4]o

x

[2]o

x

[6]o

1

[6]o

1

4 = [2]x

x = 2 rate = k[A]2[B]

While it is most likely that any rate laws on the AP exam will only be first or second order it is possible that other orders will show up and are indeed possible When the order is not so obvious it is useful to know a useful log rule

RateRatio = [ConcRatio]x

log[RateRatio] = x log[ConcRatio] thus it is quite simple to solve for the order x log[RateRatio]

log[ConcRatio]= x

6 Given the hypothetical data below determine the order of the reaction A + B + C D + E

[A] (M) [B] (M) [C] (M) Rate (Msec)

10 10 10 00076

20 10 10 00304

10 10 20 00107

10 20 10 00152

7 Given the hypothetical data below determine the order of the reaction H + I + J K

[H] (M) [I] (M) [J] (M) Rate (Msec)

10 10 10 17

23 10 10 391

10 10 40 27

10 18 20 694

8 Given the hypothetical data below determine the order of the reaction P + Q + R S + T

[P] (M) [Q] (M) [R] (M) Rate (Msec)

10 10 10 00365

10 635 10 147

10 10 075 00274

19 47 23 185

9 Given the hypothetical data below determine the order of the reaction V + W + X Y + Z

[V] (M) [W] (M) [X] (M) Rate (Msec)

001 001 001 280 106

001 004 001 448 105

001 002 006 672 105

005 0025 0036 141 104

P E1 (pg 2 of 3) Using Initial Rates to Determine Order

Nitrogen dioxide will decompose into nitrogen oxide and oxygen gas as indicated in the equation below

2 NO2(g) 2 NO(g) + O2(g)

A graph of the concentration of each constituent at various times during the course of the reaction at 300frac14C is presented below Use this graph to understand that the loss of reactant and formation of products is stoichiometrically related

Decomposition of nitrogen dioxide

0

0002

0004

0006

0008

001

0012

0 100 200 300 400 500

time

co

nc

Next you can use the concentration of the reactant vs time data presented in the data table above and manipulate the concentration

values to ln[NO2] and 1

[NO2]

and then graph ln[NO2] vs time and also graph 1

[NO2]

vs time You can use these two graphs to

look for which of the graphs presented will give a straight line in order to determine the order of the reaction These two graphs are shown below

The r2 value which is the coefficient of determination you will learn more about r and r2 when you take a statistics course but for now you can think of it as a Ogravegoodness-of-fitOacute indicator The closer the r2 is to 1 the better the data fits to a straight line Thus

you can see that the r2 value is best for 1

[NO2]

vs time indicating this reaction is second order

P E2 (pg 1 of 6) Rate Laws Using data amp graphs Name_____________________Per____

Decomposition of Nitrogen Dioxide

time (sec) [NO2] [NO] [O2]

0 001 0 0

50 00079 00021 00011

100 00065 00035 00018

150 00055 00045 00023

200 00048 00052 00026

250 00043 00057 00029

300 00038 00062 00031

350 00034 00066 00033

400 00031 00069 00035

$amp()$amp+-

amp++

$-amp

$0amp(

$0amp-

$0amp

$0amp

$0amp

$amp(

$amp-

0 1 10 0 2 20 0

$$

amp(

)$$+amp(

$ampamp()+$-$+++-amp

amp$$$

($$$$

(amp$$$

-$$$$

-amp$$$

0$$$$

0amp$$$

$ amp$ ($$ (amp$ -$$ -amp$ 0$$ 0amp$ $$

$amp

()amp

$+amp-amp()amp

1 The dimerization of butadiene is studied at 500 K and the following reaction and experimental data is presented below

2 C4H6(g) C8H12(g)

a Determine the rate law for this reaction

b Determine the rate constant

c Calculate the half-life for this reaction (If it is not 1st order calculate the half-life at the initial concentration)

P E2 (pg 2 of 6) Rate Law for Dimerization of Butadiene

Time (s) [C4H6(g)] (M)

0 00167

195 00160

604 00150

1246 00130

2180 00110

6210 00068

$

$

amp$

amp$

amp($

amp$

amp$

$ amp$ $ )$ ($ $ $ +$

$

amp$

()$+$amp$

$amp($)amp)+

-amp0+

$0amp+

$0amp

$)amp

$)amp1

$)amp)

$)amp+

$)amp

+ ) 0 1 2

$$

amp(

)$$+amp(

$$amp()+(-

$+

0$$$

1$$$

2$$$

$$$

amp$$$$

ampamp$$$

amp($$$

amp-$$$

amp$$$

amp+$$$

$ amp$$$ ($$$ -$$$ $$$ +$$$ 0$$$ 1$$$

$amp

()amp

$+amp-amp()amp

2 Dinitrogen pentoxide can be decomposed according to the reaction below

2 N2O5(soln) 4 NO2(soln) + O2(g) All Trials are performed at 45frac14C

Data for this reaction can be collected in different ways It is presented in two different ways below instantaneous rates for various concentrations and concentration at various time The concentration vs time data is graphed

Concentration and Initial Rates

a What are a few methods by which you could determine the reaction order

b What are several different methods by which you could determine the rate constant k

c What are a few different methods by which you could determine the half-life

P E2 (pg 3 of 6) Decomposition of Dinitrogen Pentoxide

[N2O5(solOtilden)] (molesL)

Instantaneous rate Msec

10 000060

050 000030

025 000015

Concentration vs Time DataConcentration vs Time Data

Time (s)[N2O5(solOtilden)] (molesL)

0 100

200 088

400 078

600 069

800 061

1000 054

1200 048

1400 043

1600 038

1800 034

2000 030

$amp($amp)

+amp)))-

$amp

$amp

$amp-

$amp

$amp0

$amp

amp

1 1

$$

amp(

)$$+amp(

$$$ampamp($))

+$-$

$0$

amp$$

amp0$

$$

0$

1$$

10$

$ 0$$ amp$$$ amp0$$ $$$

$amp

()amp

$+amp-amp()amp

$

$

amp$

$

($

)$

$

+$

$

$

$ $ amp$ ($ $ $ $ amp$ ($ $ $

$

amp$

()$+$amp$

3 The decomposition of hydrogen peroxide was studied at a particular temperature and experimental data is presented in the table to the right

2 H2O2(g) 2H2O(g) + O2(g)

a What are the two methods that you could use to determine the rate law for this reaction with the data that has been given

b Write out the rate law for this decomposition reaction

c What are the three methods that you could use to determine the rate constant

i Use the easiest of these two methods to determine a value for k

ii What are the units on k

d Now that you know the order of the reaction calculate the half-life for this reaction (if it is not 1st order calculate the half-life at the initial concentration)

yen Show how the conc vs time graph confirms the value that you calculated

P E3 (pg 4 of 6) Decomposition of H2O2

Time (s) [H2O2(g)] (moleL)

0 10

120 091

300 078

600 059

1200 037

1800 022

2400 013

3000 0082

3600 0050

$$$amp()$amp+

-$++

)$$

$$$

$$

amp$$

$$

$$

$$$

$$

amp$$

$$

$$

$$$

$$

$ 0$$ $$$ 0$$ $$$ 0$$ 1$$$ 10$$ amp$$$

$amp

()amp

$+amp-amp()amp

$amp($amp)

+amp-

$amp

$amp

$0amp

$0amp

$1amp

$1amp

$amp

amp

1 1 0 0 )

$$

amp(

)$$+amp(

$

$

amp$

$

($

)$

$

+$

$

$

$ $ amp$ ($ $ $ $ amp$ ($ $ $

$

amp$

()$+$amp$

Please work in PENCIL Please put some work on the page that indicates HOW you did the problem

1 If a 84 g sample of thorium decays with a 10 minute half life how much would the sample weigh in a half hour

2 A sample of radioactive iodine (half life = 3 days) originally weighed 10 g but now weighs 0625 g How old is this sample

You can estimate the half life quickly and easily but youOtildell need a calculator to use the integrated rate equation and half life equations

3 A sample of radioactive calcium originally weighed 24 g and in 12 hours it weighs 125 g What is the half-life

4 If a 500 g sample of barium decays with a 45 day half life how much would the sample weigh in a 18 days

5 A sample of an ancient grass mat containing radioactive carbon (half life = 5730 years) seems to be emitting on 625 of the radiation that a sample of a grass mat woven last year would have How old is this ancient grass mat

6 A sample of radioactive calcium originally weighed 32 kg and in 2 days it weighs 05 kg What is the half-life in hours

7 If a 96 g sample of tin decays with a 25 minute half life how much would the sample weigh in 15 minutes

8 A sample of radioactive magnesium (half life = 183 days) originally weighed 80 g but now weighs 25 g How many years old is this sample

9 A sample of radioactive radium originally weighed 56 g and in three days it weighs just less than a gram What is the half life in hours

P E3 (pg 1 of 2) Half Life ETH The Rate of Radioactive Decay Name________________________Per____

f) the slowest step is the rate determining step -- the rate of the overall reaction is limited by and is exactly equal

to the combined rates of all elementary steps up to and including the slowest step in the mechanism

Exercise 8

Exercise 9

In the reaction 2X+Y rarr Z

For a particular reaction the rate is found to be rate=k[Y]

Which of the below purposed mechanisms is a valid mechanism for this reaction

53 Rate Law Expression pt 2

1 Differential rate law

a Concentration vs rate data

b Use table logic or ugly algebra to find rate law amp value of K

2 Integrated rate law

a Concentration vs time data

b Must choose the straightest line graph and know what it means

c ONLY one reactant

d Done to determine how long a reaction must run to reach a certain concentration of reactant

e The value of the rate constant k is equal to the absolute value of the slope of the best fit line which is

decided by examining 3 linear regressions and analyzing the regression correlation coefficient (r)

i Graphs WILL be provided (except for the lab)

ii Time is ALWAYS X

iii The Y axi are

1 concentration of the reactant

2 natural log of the concentration (ln[A] NOT log[A])

3 reciprocal of the concentration on the y-axis of the third graph

iv If you remember them in this order with the y-axes being ldquoconcentrationrdquo ldquonatural log of

concentrationrdquo and ldquoreciprocal concentrationrdquo the alphabetical order of the y-axis variable

leads to 0 1 2 orders respectively for that reactant

REMEMBER what each variable is

Exercise 10

y = -00002x + 00831Rsup2 = 08871

-005

0

005

01

015

0 200 400 600

[N2O5]

y = -00069x - 23026Rsup2 = 1

-6

-4

-2

0

0 200 400 600

Ln [N2O5] y = 03535x - 78441

Rsup2 = 08841

-100

0

100

200

0 200 400 600

1[N2O5]

Unit 54 Kinetics Clean up

1 Half Life

a the time required for one half of one of the

reactants to disappear

b focus on the half-life for first order reactions only

i Discuss order (what order is it NOT)

ii Determine half life

iii What is the concentration after a set

number of half lives

iv What time would a set concentration be

found

2 In lab we will determine the order of a reaction by ldquoswampingrdquo We maximize one reactants concentration so

that ANY change is negligible

Exercise 11

a) What order is it NOT

b) Determine half life

c) What is the concentration after the second half life

d) When would 75 of the sample have decayed

For the generic reaction A + B C

1 The reaction below was studied at 25frac14C and the following data was obtained

NH4+ + NO2

N2 + 2H2O(L)

a What is the rate law

b What is the rate constant Be sure and include units

2 The reaction below was studied at 10frac14C and the following data was obtained

2NO(g) + Cl2(g) 2NOCl(g)

a What is the rate law

b What is the rate constant Be sure and include units

3 The reaction below was studied and the following data were obtained

2ClO2 + 2OH ClO3 + ClO2

+ H2O

a What is the rate law

b What is the rate constant Be sure and include units

4 The reaction below was studied and the following data were obtained

I + OCl IO + Cl

a What is the rate law

b What is the rate constant Be sure and include units

5 The reaction below was studied and the following data were obtained

BrO3 + 5 Br + 6 H+ 3 Br2 + 3 H2O

a What is the rate law

b What is the rate constant Be sure and include units

P E1 (pg 1 of 3) Using Initial Rates to Determine Order Name_____________________Per___

[NO]0

(molL)[Cl2]0

(molL)Initial Rate

(moleL min)

010 010 018

010 020 035

020 020 145

[I]0

(molL)[OCl]0

(molL)Initial Rate

(molL s)

012 018 791 102

006 018 395 102

003 009 988 103

024 009 791 102

[ClO2]0

(molL)[OH]0

(molL)Initial Rate

(molL s)

0050 0100 0057

0100 0100 023

0100 0050 0115

[NH4+]0

(molL)[NO2

]0

(molL)Initial Rate(moleL sec)

0100 0005 135 107

0100 0010 270 107

0200 0010 540 107

[BrO3]0

(molL)[Br]0

(molL)[H+]0

(molL)Initial Rate

(molL s)

0100 0100 0100 80 104

0200 0100 0100 16 103

0200 0200 0100 32 103

0100 0100 0200 32 103

trial[A]0

(molL)[B]0

(molL)Initial Rate

(moleL hour)

1 4 6 20

2 4 3 10

3 2 6 5

rate1

rate2=k

k

[A]ox

[A]ox

[B]oy

[B]oy

20

10=k

k

[4]ox

[4]ox

[6]oy

[3]oy

2 = [2]y

y = 1

20

5=k

k

[4]o

x

[2]o

x

[6]o

1

[6]o

1

4 = [2]x

x = 2 rate = k[A]2[B]

While it is most likely that any rate laws on the AP exam will only be first or second order it is possible that other orders will show up and are indeed possible When the order is not so obvious it is useful to know a useful log rule

RateRatio = [ConcRatio]x

log[RateRatio] = x log[ConcRatio] thus it is quite simple to solve for the order x log[RateRatio]

log[ConcRatio]= x

6 Given the hypothetical data below determine the order of the reaction A + B + C D + E

[A] (M) [B] (M) [C] (M) Rate (Msec)

10 10 10 00076

20 10 10 00304

10 10 20 00107

10 20 10 00152

7 Given the hypothetical data below determine the order of the reaction H + I + J K

[H] (M) [I] (M) [J] (M) Rate (Msec)

10 10 10 17

23 10 10 391

10 10 40 27

10 18 20 694

8 Given the hypothetical data below determine the order of the reaction P + Q + R S + T

[P] (M) [Q] (M) [R] (M) Rate (Msec)

10 10 10 00365

10 635 10 147

10 10 075 00274

19 47 23 185

9 Given the hypothetical data below determine the order of the reaction V + W + X Y + Z

[V] (M) [W] (M) [X] (M) Rate (Msec)

001 001 001 280 106

001 004 001 448 105

001 002 006 672 105

005 0025 0036 141 104

P E1 (pg 2 of 3) Using Initial Rates to Determine Order

Nitrogen dioxide will decompose into nitrogen oxide and oxygen gas as indicated in the equation below

2 NO2(g) 2 NO(g) + O2(g)

A graph of the concentration of each constituent at various times during the course of the reaction at 300frac14C is presented below Use this graph to understand that the loss of reactant and formation of products is stoichiometrically related

Decomposition of nitrogen dioxide

0

0002

0004

0006

0008

001

0012

0 100 200 300 400 500

time

co

nc

Next you can use the concentration of the reactant vs time data presented in the data table above and manipulate the concentration

values to ln[NO2] and 1

[NO2]

and then graph ln[NO2] vs time and also graph 1

[NO2]

vs time You can use these two graphs to

look for which of the graphs presented will give a straight line in order to determine the order of the reaction These two graphs are shown below

The r2 value which is the coefficient of determination you will learn more about r and r2 when you take a statistics course but for now you can think of it as a Ogravegoodness-of-fitOacute indicator The closer the r2 is to 1 the better the data fits to a straight line Thus

you can see that the r2 value is best for 1

[NO2]

vs time indicating this reaction is second order

P E2 (pg 1 of 6) Rate Laws Using data amp graphs Name_____________________Per____

Decomposition of Nitrogen Dioxide

time (sec) [NO2] [NO] [O2]

0 001 0 0

50 00079 00021 00011

100 00065 00035 00018

150 00055 00045 00023

200 00048 00052 00026

250 00043 00057 00029

300 00038 00062 00031

350 00034 00066 00033

400 00031 00069 00035

$amp()$amp+-

amp++

$-amp

$0amp(

$0amp-

$0amp

$0amp

$0amp

$amp(

$amp-

0 1 10 0 2 20 0

$$

amp(

)$$+amp(

$ampamp()+$-$+++-amp

amp$$$

($$$$

(amp$$$

-$$$$

-amp$$$

0$$$$

0amp$$$

$ amp$ ($$ (amp$ -$$ -amp$ 0$$ 0amp$ $$

$amp

()amp

$+amp-amp()amp

1 The dimerization of butadiene is studied at 500 K and the following reaction and experimental data is presented below

2 C4H6(g) C8H12(g)

a Determine the rate law for this reaction

b Determine the rate constant

c Calculate the half-life for this reaction (If it is not 1st order calculate the half-life at the initial concentration)

P E2 (pg 2 of 6) Rate Law for Dimerization of Butadiene

Time (s) [C4H6(g)] (M)

0 00167

195 00160

604 00150

1246 00130

2180 00110

6210 00068

$

$

amp$

amp$

amp($

amp$

amp$

$ amp$ $ )$ ($ $ $ +$

$

amp$

()$+$amp$

$amp($)amp)+

-amp0+

$0amp+

$0amp

$)amp

$)amp1

$)amp)

$)amp+

$)amp

+ ) 0 1 2

$$

amp(

)$$+amp(

$$amp()+(-

$+

0$$$

1$$$

2$$$

$$$

amp$$$$

ampamp$$$

amp($$$

amp-$$$

amp$$$

amp+$$$

$ amp$$$ ($$$ -$$$ $$$ +$$$ 0$$$ 1$$$

$amp

()amp

$+amp-amp()amp

2 Dinitrogen pentoxide can be decomposed according to the reaction below

2 N2O5(soln) 4 NO2(soln) + O2(g) All Trials are performed at 45frac14C

Data for this reaction can be collected in different ways It is presented in two different ways below instantaneous rates for various concentrations and concentration at various time The concentration vs time data is graphed

Concentration and Initial Rates

a What are a few methods by which you could determine the reaction order

b What are several different methods by which you could determine the rate constant k

c What are a few different methods by which you could determine the half-life

P E2 (pg 3 of 6) Decomposition of Dinitrogen Pentoxide

[N2O5(solOtilden)] (molesL)

Instantaneous rate Msec

10 000060

050 000030

025 000015

Concentration vs Time DataConcentration vs Time Data

Time (s)[N2O5(solOtilden)] (molesL)

0 100

200 088

400 078

600 069

800 061

1000 054

1200 048

1400 043

1600 038

1800 034

2000 030

$amp($amp)

+amp)))-

$amp

$amp

$amp-

$amp

$amp0

$amp

amp

1 1

$$

amp(

)$$+amp(

$$$ampamp($))

+$-$

$0$

amp$$

amp0$

$$

0$

1$$

10$

$ 0$$ amp$$$ amp0$$ $$$

$amp

()amp

$+amp-amp()amp

$

$

amp$

$

($

)$

$

+$

$

$

$ $ amp$ ($ $ $ $ amp$ ($ $ $

$

amp$

()$+$amp$

3 The decomposition of hydrogen peroxide was studied at a particular temperature and experimental data is presented in the table to the right

2 H2O2(g) 2H2O(g) + O2(g)

a What are the two methods that you could use to determine the rate law for this reaction with the data that has been given

b Write out the rate law for this decomposition reaction

c What are the three methods that you could use to determine the rate constant

i Use the easiest of these two methods to determine a value for k

ii What are the units on k

d Now that you know the order of the reaction calculate the half-life for this reaction (if it is not 1st order calculate the half-life at the initial concentration)

yen Show how the conc vs time graph confirms the value that you calculated

P E3 (pg 4 of 6) Decomposition of H2O2

Time (s) [H2O2(g)] (moleL)

0 10

120 091

300 078

600 059

1200 037

1800 022

2400 013

3000 0082

3600 0050

$$$amp()$amp+

-$++

)$$

$$$

$$

amp$$

$$

$$

$$$

$$

amp$$

$$

$$

$$$

$$

$ 0$$ $$$ 0$$ $$$ 0$$ 1$$$ 10$$ amp$$$

$amp

()amp

$+amp-amp()amp

$amp($amp)

+amp-

$amp

$amp

$0amp

$0amp

$1amp

$1amp

$amp

amp

1 1 0 0 )

$$

amp(

)$$+amp(

$

$

amp$

$

($

)$

$

+$

$

$

$ $ amp$ ($ $ $ $ amp$ ($ $ $

$

amp$

()$+$amp$

Please work in PENCIL Please put some work on the page that indicates HOW you did the problem

1 If a 84 g sample of thorium decays with a 10 minute half life how much would the sample weigh in a half hour

2 A sample of radioactive iodine (half life = 3 days) originally weighed 10 g but now weighs 0625 g How old is this sample

You can estimate the half life quickly and easily but youOtildell need a calculator to use the integrated rate equation and half life equations

3 A sample of radioactive calcium originally weighed 24 g and in 12 hours it weighs 125 g What is the half-life

4 If a 500 g sample of barium decays with a 45 day half life how much would the sample weigh in a 18 days

5 A sample of an ancient grass mat containing radioactive carbon (half life = 5730 years) seems to be emitting on 625 of the radiation that a sample of a grass mat woven last year would have How old is this ancient grass mat

6 A sample of radioactive calcium originally weighed 32 kg and in 2 days it weighs 05 kg What is the half-life in hours

7 If a 96 g sample of tin decays with a 25 minute half life how much would the sample weigh in 15 minutes

8 A sample of radioactive magnesium (half life = 183 days) originally weighed 80 g but now weighs 25 g How many years old is this sample

9 A sample of radioactive radium originally weighed 56 g and in three days it weighs just less than a gram What is the half life in hours

P E3 (pg 1 of 2) Half Life ETH The Rate of Radioactive Decay Name________________________Per____

53 Rate Law Expression pt 2

1 Differential rate law

a Concentration vs rate data

b Use table logic or ugly algebra to find rate law amp value of K

2 Integrated rate law

a Concentration vs time data

b Must choose the straightest line graph and know what it means

c ONLY one reactant

d Done to determine how long a reaction must run to reach a certain concentration of reactant

e The value of the rate constant k is equal to the absolute value of the slope of the best fit line which is

decided by examining 3 linear regressions and analyzing the regression correlation coefficient (r)

i Graphs WILL be provided (except for the lab)

ii Time is ALWAYS X

iii The Y axi are

1 concentration of the reactant

2 natural log of the concentration (ln[A] NOT log[A])

3 reciprocal of the concentration on the y-axis of the third graph

iv If you remember them in this order with the y-axes being ldquoconcentrationrdquo ldquonatural log of

concentrationrdquo and ldquoreciprocal concentrationrdquo the alphabetical order of the y-axis variable

leads to 0 1 2 orders respectively for that reactant

REMEMBER what each variable is

Exercise 10

y = -00002x + 00831Rsup2 = 08871

-005

0

005

01

015

0 200 400 600

[N2O5]

y = -00069x - 23026Rsup2 = 1

-6

-4

-2

0

0 200 400 600

Ln [N2O5] y = 03535x - 78441

Rsup2 = 08841

-100

0

100

200

0 200 400 600

1[N2O5]

Unit 54 Kinetics Clean up

1 Half Life

a the time required for one half of one of the

reactants to disappear

b focus on the half-life for first order reactions only

i Discuss order (what order is it NOT)

ii Determine half life

iii What is the concentration after a set

number of half lives

iv What time would a set concentration be

found

2 In lab we will determine the order of a reaction by ldquoswampingrdquo We maximize one reactants concentration so

that ANY change is negligible

Exercise 11

a) What order is it NOT

b) Determine half life

c) What is the concentration after the second half life

d) When would 75 of the sample have decayed

For the generic reaction A + B C

1 The reaction below was studied at 25frac14C and the following data was obtained

NH4+ + NO2

N2 + 2H2O(L)

a What is the rate law

b What is the rate constant Be sure and include units

2 The reaction below was studied at 10frac14C and the following data was obtained

2NO(g) + Cl2(g) 2NOCl(g)

a What is the rate law

b What is the rate constant Be sure and include units

3 The reaction below was studied and the following data were obtained

2ClO2 + 2OH ClO3 + ClO2

+ H2O

a What is the rate law

b What is the rate constant Be sure and include units

4 The reaction below was studied and the following data were obtained

I + OCl IO + Cl

a What is the rate law

b What is the rate constant Be sure and include units

5 The reaction below was studied and the following data were obtained

BrO3 + 5 Br + 6 H+ 3 Br2 + 3 H2O

a What is the rate law

b What is the rate constant Be sure and include units

P E1 (pg 1 of 3) Using Initial Rates to Determine Order Name_____________________Per___

[NO]0

(molL)[Cl2]0

(molL)Initial Rate

(moleL min)

010 010 018

010 020 035

020 020 145

[I]0

(molL)[OCl]0

(molL)Initial Rate

(molL s)

012 018 791 102

006 018 395 102

003 009 988 103

024 009 791 102

[ClO2]0

(molL)[OH]0

(molL)Initial Rate

(molL s)

0050 0100 0057

0100 0100 023

0100 0050 0115

[NH4+]0

(molL)[NO2

]0

(molL)Initial Rate(moleL sec)

0100 0005 135 107

0100 0010 270 107

0200 0010 540 107

[BrO3]0

(molL)[Br]0

(molL)[H+]0

(molL)Initial Rate

(molL s)

0100 0100 0100 80 104

0200 0100 0100 16 103

0200 0200 0100 32 103

0100 0100 0200 32 103

trial[A]0

(molL)[B]0

(molL)Initial Rate

(moleL hour)

1 4 6 20

2 4 3 10

3 2 6 5

rate1

rate2=k

k

[A]ox

[A]ox

[B]oy

[B]oy

20

10=k

k

[4]ox

[4]ox

[6]oy

[3]oy

2 = [2]y

y = 1

20

5=k

k

[4]o

x

[2]o

x

[6]o

1

[6]o

1

4 = [2]x

x = 2 rate = k[A]2[B]

While it is most likely that any rate laws on the AP exam will only be first or second order it is possible that other orders will show up and are indeed possible When the order is not so obvious it is useful to know a useful log rule

RateRatio = [ConcRatio]x

log[RateRatio] = x log[ConcRatio] thus it is quite simple to solve for the order x log[RateRatio]

log[ConcRatio]= x

6 Given the hypothetical data below determine the order of the reaction A + B + C D + E

[A] (M) [B] (M) [C] (M) Rate (Msec)

10 10 10 00076

20 10 10 00304

10 10 20 00107

10 20 10 00152

7 Given the hypothetical data below determine the order of the reaction H + I + J K

[H] (M) [I] (M) [J] (M) Rate (Msec)

10 10 10 17

23 10 10 391

10 10 40 27

10 18 20 694

8 Given the hypothetical data below determine the order of the reaction P + Q + R S + T

[P] (M) [Q] (M) [R] (M) Rate (Msec)

10 10 10 00365

10 635 10 147

10 10 075 00274

19 47 23 185

9 Given the hypothetical data below determine the order of the reaction V + W + X Y + Z

[V] (M) [W] (M) [X] (M) Rate (Msec)

001 001 001 280 106

001 004 001 448 105

001 002 006 672 105

005 0025 0036 141 104

P E1 (pg 2 of 3) Using Initial Rates to Determine Order

Nitrogen dioxide will decompose into nitrogen oxide and oxygen gas as indicated in the equation below

2 NO2(g) 2 NO(g) + O2(g)

A graph of the concentration of each constituent at various times during the course of the reaction at 300frac14C is presented below Use this graph to understand that the loss of reactant and formation of products is stoichiometrically related

Decomposition of nitrogen dioxide

0

0002

0004

0006

0008

001

0012

0 100 200 300 400 500

time

co

nc

Next you can use the concentration of the reactant vs time data presented in the data table above and manipulate the concentration

values to ln[NO2] and 1

[NO2]

and then graph ln[NO2] vs time and also graph 1

[NO2]

vs time You can use these two graphs to

look for which of the graphs presented will give a straight line in order to determine the order of the reaction These two graphs are shown below

The r2 value which is the coefficient of determination you will learn more about r and r2 when you take a statistics course but for now you can think of it as a Ogravegoodness-of-fitOacute indicator The closer the r2 is to 1 the better the data fits to a straight line Thus

you can see that the r2 value is best for 1

[NO2]

vs time indicating this reaction is second order

P E2 (pg 1 of 6) Rate Laws Using data amp graphs Name_____________________Per____

Decomposition of Nitrogen Dioxide

time (sec) [NO2] [NO] [O2]

0 001 0 0

50 00079 00021 00011

100 00065 00035 00018

150 00055 00045 00023

200 00048 00052 00026

250 00043 00057 00029

300 00038 00062 00031

350 00034 00066 00033

400 00031 00069 00035

$amp()$amp+-

amp++

$-amp

$0amp(

$0amp-

$0amp

$0amp

$0amp

$amp(

$amp-

0 1 10 0 2 20 0

$$

amp(

)$$+amp(

$ampamp()+$-$+++-amp

amp$$$

($$$$

(amp$$$

-$$$$

-amp$$$

0$$$$

0amp$$$

$ amp$ ($$ (amp$ -$$ -amp$ 0$$ 0amp$ $$

$amp

()amp

$+amp-amp()amp

1 The dimerization of butadiene is studied at 500 K and the following reaction and experimental data is presented below

2 C4H6(g) C8H12(g)

a Determine the rate law for this reaction

b Determine the rate constant

c Calculate the half-life for this reaction (If it is not 1st order calculate the half-life at the initial concentration)

P E2 (pg 2 of 6) Rate Law for Dimerization of Butadiene

Time (s) [C4H6(g)] (M)

0 00167

195 00160

604 00150

1246 00130

2180 00110

6210 00068

$

$

amp$

amp$

amp($

amp$

amp$

$ amp$ $ )$ ($ $ $ +$

$

amp$

()$+$amp$

$amp($)amp)+

-amp0+

$0amp+

$0amp

$)amp

$)amp1

$)amp)

$)amp+

$)amp

+ ) 0 1 2

$$

amp(

)$$+amp(

$$amp()+(-

$+

0$$$

1$$$

2$$$

$$$

amp$$$$

ampamp$$$

amp($$$

amp-$$$

amp$$$

amp+$$$

$ amp$$$ ($$$ -$$$ $$$ +$$$ 0$$$ 1$$$

$amp

()amp

$+amp-amp()amp

2 Dinitrogen pentoxide can be decomposed according to the reaction below

2 N2O5(soln) 4 NO2(soln) + O2(g) All Trials are performed at 45frac14C

Data for this reaction can be collected in different ways It is presented in two different ways below instantaneous rates for various concentrations and concentration at various time The concentration vs time data is graphed

Concentration and Initial Rates

a What are a few methods by which you could determine the reaction order

b What are several different methods by which you could determine the rate constant k

c What are a few different methods by which you could determine the half-life

P E2 (pg 3 of 6) Decomposition of Dinitrogen Pentoxide

[N2O5(solOtilden)] (molesL)

Instantaneous rate Msec

10 000060

050 000030

025 000015

Concentration vs Time DataConcentration vs Time Data

Time (s)[N2O5(solOtilden)] (molesL)

0 100

200 088

400 078

600 069

800 061

1000 054

1200 048

1400 043

1600 038

1800 034

2000 030

$amp($amp)

+amp)))-

$amp

$amp

$amp-

$amp

$amp0

$amp

amp

1 1

$$

amp(

)$$+amp(

$$$ampamp($))

+$-$

$0$

amp$$

amp0$

$$

0$

1$$

10$

$ 0$$ amp$$$ amp0$$ $$$

$amp

()amp

$+amp-amp()amp

$

$

amp$

$

($

)$

$

+$

$

$

$ $ amp$ ($ $ $ $ amp$ ($ $ $

$

amp$

()$+$amp$

3 The decomposition of hydrogen peroxide was studied at a particular temperature and experimental data is presented in the table to the right

2 H2O2(g) 2H2O(g) + O2(g)

a What are the two methods that you could use to determine the rate law for this reaction with the data that has been given

b Write out the rate law for this decomposition reaction

c What are the three methods that you could use to determine the rate constant

i Use the easiest of these two methods to determine a value for k

ii What are the units on k

d Now that you know the order of the reaction calculate the half-life for this reaction (if it is not 1st order calculate the half-life at the initial concentration)

yen Show how the conc vs time graph confirms the value that you calculated

P E3 (pg 4 of 6) Decomposition of H2O2

Time (s) [H2O2(g)] (moleL)

0 10

120 091

300 078

600 059

1200 037

1800 022

2400 013

3000 0082

3600 0050

$$$amp()$amp+

-$++

)$$

$$$

$$

amp$$

$$

$$

$$$

$$

amp$$

$$

$$

$$$

$$

$ 0$$ $$$ 0$$ $$$ 0$$ 1$$$ 10$$ amp$$$

$amp

()amp

$+amp-amp()amp

$amp($amp)

+amp-

$amp

$amp

$0amp

$0amp

$1amp

$1amp

$amp

amp

1 1 0 0 )

$$

amp(

)$$+amp(

$

$

amp$

$

($

)$

$

+$

$

$

$ $ amp$ ($ $ $ $ amp$ ($ $ $

$

amp$

()$+$amp$

Please work in PENCIL Please put some work on the page that indicates HOW you did the problem

1 If a 84 g sample of thorium decays with a 10 minute half life how much would the sample weigh in a half hour

2 A sample of radioactive iodine (half life = 3 days) originally weighed 10 g but now weighs 0625 g How old is this sample

You can estimate the half life quickly and easily but youOtildell need a calculator to use the integrated rate equation and half life equations

3 A sample of radioactive calcium originally weighed 24 g and in 12 hours it weighs 125 g What is the half-life

4 If a 500 g sample of barium decays with a 45 day half life how much would the sample weigh in a 18 days

5 A sample of an ancient grass mat containing radioactive carbon (half life = 5730 years) seems to be emitting on 625 of the radiation that a sample of a grass mat woven last year would have How old is this ancient grass mat

6 A sample of radioactive calcium originally weighed 32 kg and in 2 days it weighs 05 kg What is the half-life in hours

7 If a 96 g sample of tin decays with a 25 minute half life how much would the sample weigh in 15 minutes

8 A sample of radioactive magnesium (half life = 183 days) originally weighed 80 g but now weighs 25 g How many years old is this sample

9 A sample of radioactive radium originally weighed 56 g and in three days it weighs just less than a gram What is the half life in hours

P E3 (pg 1 of 2) Half Life ETH The Rate of Radioactive Decay Name________________________Per____

Exercise 10

y = -00002x + 00831Rsup2 = 08871

-005

0

005

01

015

0 200 400 600

[N2O5]

y = -00069x - 23026Rsup2 = 1

-6

-4

-2

0

0 200 400 600

Ln [N2O5] y = 03535x - 78441

Rsup2 = 08841

-100

0

100

200

0 200 400 600

1[N2O5]

Unit 54 Kinetics Clean up

1 Half Life

a the time required for one half of one of the

reactants to disappear

b focus on the half-life for first order reactions only

i Discuss order (what order is it NOT)

ii Determine half life

iii What is the concentration after a set

number of half lives

iv What time would a set concentration be

found

2 In lab we will determine the order of a reaction by ldquoswampingrdquo We maximize one reactants concentration so

that ANY change is negligible

Exercise 11

a) What order is it NOT

b) Determine half life

c) What is the concentration after the second half life

d) When would 75 of the sample have decayed

For the generic reaction A + B C

1 The reaction below was studied at 25frac14C and the following data was obtained

NH4+ + NO2

N2 + 2H2O(L)

a What is the rate law

b What is the rate constant Be sure and include units

2 The reaction below was studied at 10frac14C and the following data was obtained

2NO(g) + Cl2(g) 2NOCl(g)

a What is the rate law

b What is the rate constant Be sure and include units

3 The reaction below was studied and the following data were obtained

2ClO2 + 2OH ClO3 + ClO2

+ H2O

a What is the rate law

b What is the rate constant Be sure and include units

4 The reaction below was studied and the following data were obtained

I + OCl IO + Cl

a What is the rate law

b What is the rate constant Be sure and include units

5 The reaction below was studied and the following data were obtained

BrO3 + 5 Br + 6 H+ 3 Br2 + 3 H2O

a What is the rate law

b What is the rate constant Be sure and include units

P E1 (pg 1 of 3) Using Initial Rates to Determine Order Name_____________________Per___

[NO]0

(molL)[Cl2]0

(molL)Initial Rate

(moleL min)

010 010 018

010 020 035

020 020 145

[I]0

(molL)[OCl]0

(molL)Initial Rate

(molL s)

012 018 791 102

006 018 395 102

003 009 988 103

024 009 791 102

[ClO2]0

(molL)[OH]0

(molL)Initial Rate

(molL s)

0050 0100 0057

0100 0100 023

0100 0050 0115

[NH4+]0

(molL)[NO2

]0

(molL)Initial Rate(moleL sec)

0100 0005 135 107

0100 0010 270 107

0200 0010 540 107

[BrO3]0

(molL)[Br]0

(molL)[H+]0

(molL)Initial Rate

(molL s)

0100 0100 0100 80 104

0200 0100 0100 16 103

0200 0200 0100 32 103

0100 0100 0200 32 103

trial[A]0

(molL)[B]0

(molL)Initial Rate

(moleL hour)

1 4 6 20

2 4 3 10

3 2 6 5

rate1

rate2=k

k

[A]ox

[A]ox

[B]oy

[B]oy

20

10=k

k

[4]ox

[4]ox

[6]oy

[3]oy

2 = [2]y

y = 1

20

5=k

k

[4]o

x

[2]o

x

[6]o

1

[6]o

1

4 = [2]x

x = 2 rate = k[A]2[B]

While it is most likely that any rate laws on the AP exam will only be first or second order it is possible that other orders will show up and are indeed possible When the order is not so obvious it is useful to know a useful log rule

RateRatio = [ConcRatio]x

log[RateRatio] = x log[ConcRatio] thus it is quite simple to solve for the order x log[RateRatio]

log[ConcRatio]= x

6 Given the hypothetical data below determine the order of the reaction A + B + C D + E

[A] (M) [B] (M) [C] (M) Rate (Msec)

10 10 10 00076

20 10 10 00304

10 10 20 00107

10 20 10 00152

7 Given the hypothetical data below determine the order of the reaction H + I + J K

[H] (M) [I] (M) [J] (M) Rate (Msec)

10 10 10 17

23 10 10 391

10 10 40 27

10 18 20 694

8 Given the hypothetical data below determine the order of the reaction P + Q + R S + T

[P] (M) [Q] (M) [R] (M) Rate (Msec)

10 10 10 00365

10 635 10 147

10 10 075 00274

19 47 23 185

9 Given the hypothetical data below determine the order of the reaction V + W + X Y + Z

[V] (M) [W] (M) [X] (M) Rate (Msec)

001 001 001 280 106

001 004 001 448 105

001 002 006 672 105

005 0025 0036 141 104

P E1 (pg 2 of 3) Using Initial Rates to Determine Order

Nitrogen dioxide will decompose into nitrogen oxide and oxygen gas as indicated in the equation below

2 NO2(g) 2 NO(g) + O2(g)

A graph of the concentration of each constituent at various times during the course of the reaction at 300frac14C is presented below Use this graph to understand that the loss of reactant and formation of products is stoichiometrically related

Decomposition of nitrogen dioxide

0

0002

0004

0006

0008

001

0012

0 100 200 300 400 500

time

co

nc

Next you can use the concentration of the reactant vs time data presented in the data table above and manipulate the concentration

values to ln[NO2] and 1

[NO2]

and then graph ln[NO2] vs time and also graph 1

[NO2]

vs time You can use these two graphs to

look for which of the graphs presented will give a straight line in order to determine the order of the reaction These two graphs are shown below

The r2 value which is the coefficient of determination you will learn more about r and r2 when you take a statistics course but for now you can think of it as a Ogravegoodness-of-fitOacute indicator The closer the r2 is to 1 the better the data fits to a straight line Thus

you can see that the r2 value is best for 1

[NO2]

vs time indicating this reaction is second order

P E2 (pg 1 of 6) Rate Laws Using data amp graphs Name_____________________Per____

Decomposition of Nitrogen Dioxide

time (sec) [NO2] [NO] [O2]

0 001 0 0

50 00079 00021 00011

100 00065 00035 00018

150 00055 00045 00023

200 00048 00052 00026

250 00043 00057 00029

300 00038 00062 00031

350 00034 00066 00033

400 00031 00069 00035

$amp()$amp+-

amp++

$-amp

$0amp(

$0amp-

$0amp

$0amp

$0amp

$amp(

$amp-

0 1 10 0 2 20 0

$$

amp(

)$$+amp(

$ampamp()+$-$+++-amp

amp$$$

($$$$

(amp$$$

-$$$$

-amp$$$

0$$$$

0amp$$$

$ amp$ ($$ (amp$ -$$ -amp$ 0$$ 0amp$ $$

$amp

()amp

$+amp-amp()amp

1 The dimerization of butadiene is studied at 500 K and the following reaction and experimental data is presented below

2 C4H6(g) C8H12(g)

a Determine the rate law for this reaction

b Determine the rate constant

c Calculate the half-life for this reaction (If it is not 1st order calculate the half-life at the initial concentration)

P E2 (pg 2 of 6) Rate Law for Dimerization of Butadiene

Time (s) [C4H6(g)] (M)

0 00167

195 00160

604 00150

1246 00130

2180 00110

6210 00068

$

$

amp$

amp$

amp($

amp$

amp$

$ amp$ $ )$ ($ $ $ +$

$

amp$

()$+$amp$

$amp($)amp)+

-amp0+

$0amp+

$0amp

$)amp

$)amp1

$)amp)

$)amp+

$)amp

+ ) 0 1 2

$$

amp(

)$$+amp(

$$amp()+(-

$+

0$$$

1$$$

2$$$

$$$

amp$$$$

ampamp$$$

amp($$$

amp-$$$

amp$$$

amp+$$$

$ amp$$$ ($$$ -$$$ $$$ +$$$ 0$$$ 1$$$

$amp

()amp

$+amp-amp()amp

2 Dinitrogen pentoxide can be decomposed according to the reaction below

2 N2O5(soln) 4 NO2(soln) + O2(g) All Trials are performed at 45frac14C

Data for this reaction can be collected in different ways It is presented in two different ways below instantaneous rates for various concentrations and concentration at various time The concentration vs time data is graphed

Concentration and Initial Rates

a What are a few methods by which you could determine the reaction order

b What are several different methods by which you could determine the rate constant k

c What are a few different methods by which you could determine the half-life

P E2 (pg 3 of 6) Decomposition of Dinitrogen Pentoxide

[N2O5(solOtilden)] (molesL)

Instantaneous rate Msec

10 000060

050 000030

025 000015

Concentration vs Time DataConcentration vs Time Data

Time (s)[N2O5(solOtilden)] (molesL)

0 100

200 088

400 078

600 069

800 061

1000 054

1200 048

1400 043

1600 038

1800 034

2000 030

$amp($amp)

+amp)))-

$amp

$amp

$amp-

$amp

$amp0

$amp

amp

1 1

$$

amp(

)$$+amp(

$$$ampamp($))

+$-$

$0$

amp$$

amp0$

$$

0$

1$$

10$

$ 0$$ amp$$$ amp0$$ $$$

$amp

()amp

$+amp-amp()amp

$

$

amp$

$

($

)$

$

+$

$

$

$ $ amp$ ($ $ $ $ amp$ ($ $ $

$

amp$

()$+$amp$

3 The decomposition of hydrogen peroxide was studied at a particular temperature and experimental data is presented in the table to the right

2 H2O2(g) 2H2O(g) + O2(g)

a What are the two methods that you could use to determine the rate law for this reaction with the data that has been given

b Write out the rate law for this decomposition reaction

c What are the three methods that you could use to determine the rate constant

i Use the easiest of these two methods to determine a value for k

ii What are the units on k

d Now that you know the order of the reaction calculate the half-life for this reaction (if it is not 1st order calculate the half-life at the initial concentration)

yen Show how the conc vs time graph confirms the value that you calculated

P E3 (pg 4 of 6) Decomposition of H2O2

Time (s) [H2O2(g)] (moleL)

0 10

120 091

300 078

600 059

1200 037

1800 022

2400 013

3000 0082

3600 0050

$$$amp()$amp+

-$++

)$$

$$$

$$

amp$$

$$

$$

$$$

$$

amp$$

$$

$$

$$$

$$

$ 0$$ $$$ 0$$ $$$ 0$$ 1$$$ 10$$ amp$$$

$amp

()amp

$+amp-amp()amp

$amp($amp)

+amp-

$amp

$amp

$0amp

$0amp

$1amp

$1amp

$amp

amp

1 1 0 0 )

$$

amp(

)$$+amp(

$

$

amp$

$

($

)$

$

+$

$

$

$ $ amp$ ($ $ $ $ amp$ ($ $ $

$

amp$

()$+$amp$

Please work in PENCIL Please put some work on the page that indicates HOW you did the problem

1 If a 84 g sample of thorium decays with a 10 minute half life how much would the sample weigh in a half hour

2 A sample of radioactive iodine (half life = 3 days) originally weighed 10 g but now weighs 0625 g How old is this sample

You can estimate the half life quickly and easily but youOtildell need a calculator to use the integrated rate equation and half life equations

3 A sample of radioactive calcium originally weighed 24 g and in 12 hours it weighs 125 g What is the half-life

4 If a 500 g sample of barium decays with a 45 day half life how much would the sample weigh in a 18 days

5 A sample of an ancient grass mat containing radioactive carbon (half life = 5730 years) seems to be emitting on 625 of the radiation that a sample of a grass mat woven last year would have How old is this ancient grass mat

6 A sample of radioactive calcium originally weighed 32 kg and in 2 days it weighs 05 kg What is the half-life in hours

7 If a 96 g sample of tin decays with a 25 minute half life how much would the sample weigh in 15 minutes

8 A sample of radioactive magnesium (half life = 183 days) originally weighed 80 g but now weighs 25 g How many years old is this sample

9 A sample of radioactive radium originally weighed 56 g and in three days it weighs just less than a gram What is the half life in hours

P E3 (pg 1 of 2) Half Life ETH The Rate of Radioactive Decay Name________________________Per____

Unit 54 Kinetics Clean up

1 Half Life

a the time required for one half of one of the

reactants to disappear

b focus on the half-life for first order reactions only

i Discuss order (what order is it NOT)

ii Determine half life

iii What is the concentration after a set

number of half lives

iv What time would a set concentration be

found

2 In lab we will determine the order of a reaction by ldquoswampingrdquo We maximize one reactants concentration so

that ANY change is negligible

Exercise 11

a) What order is it NOT

b) Determine half life

c) What is the concentration after the second half life

d) When would 75 of the sample have decayed

For the generic reaction A + B C

1 The reaction below was studied at 25frac14C and the following data was obtained

NH4+ + NO2

N2 + 2H2O(L)

a What is the rate law

b What is the rate constant Be sure and include units

2 The reaction below was studied at 10frac14C and the following data was obtained

2NO(g) + Cl2(g) 2NOCl(g)

a What is the rate law

b What is the rate constant Be sure and include units

3 The reaction below was studied and the following data were obtained

2ClO2 + 2OH ClO3 + ClO2

+ H2O

a What is the rate law

b What is the rate constant Be sure and include units

4 The reaction below was studied and the following data were obtained

I + OCl IO + Cl

a What is the rate law

b What is the rate constant Be sure and include units

5 The reaction below was studied and the following data were obtained

BrO3 + 5 Br + 6 H+ 3 Br2 + 3 H2O

a What is the rate law

b What is the rate constant Be sure and include units

P E1 (pg 1 of 3) Using Initial Rates to Determine Order Name_____________________Per___

[NO]0

(molL)[Cl2]0

(molL)Initial Rate

(moleL min)

010 010 018

010 020 035

020 020 145

[I]0

(molL)[OCl]0

(molL)Initial Rate

(molL s)

012 018 791 102

006 018 395 102

003 009 988 103

024 009 791 102

[ClO2]0

(molL)[OH]0

(molL)Initial Rate

(molL s)

0050 0100 0057

0100 0100 023

0100 0050 0115

[NH4+]0

(molL)[NO2

]0

(molL)Initial Rate(moleL sec)

0100 0005 135 107

0100 0010 270 107

0200 0010 540 107

[BrO3]0

(molL)[Br]0

(molL)[H+]0

(molL)Initial Rate

(molL s)

0100 0100 0100 80 104

0200 0100 0100 16 103

0200 0200 0100 32 103

0100 0100 0200 32 103

trial[A]0

(molL)[B]0

(molL)Initial Rate

(moleL hour)

1 4 6 20

2 4 3 10

3 2 6 5

rate1

rate2=k

k

[A]ox

[A]ox

[B]oy

[B]oy

20

10=k

k

[4]ox

[4]ox

[6]oy

[3]oy

2 = [2]y

y = 1

20

5=k

k

[4]o

x

[2]o

x

[6]o

1

[6]o

1

4 = [2]x

x = 2 rate = k[A]2[B]

While it is most likely that any rate laws on the AP exam will only be first or second order it is possible that other orders will show up and are indeed possible When the order is not so obvious it is useful to know a useful log rule

RateRatio = [ConcRatio]x

log[RateRatio] = x log[ConcRatio] thus it is quite simple to solve for the order x log[RateRatio]

log[ConcRatio]= x

6 Given the hypothetical data below determine the order of the reaction A + B + C D + E

[A] (M) [B] (M) [C] (M) Rate (Msec)

10 10 10 00076

20 10 10 00304

10 10 20 00107

10 20 10 00152

7 Given the hypothetical data below determine the order of the reaction H + I + J K

[H] (M) [I] (M) [J] (M) Rate (Msec)

10 10 10 17

23 10 10 391

10 10 40 27

10 18 20 694

8 Given the hypothetical data below determine the order of the reaction P + Q + R S + T

[P] (M) [Q] (M) [R] (M) Rate (Msec)

10 10 10 00365

10 635 10 147

10 10 075 00274

19 47 23 185

9 Given the hypothetical data below determine the order of the reaction V + W + X Y + Z

[V] (M) [W] (M) [X] (M) Rate (Msec)

001 001 001 280 106

001 004 001 448 105

001 002 006 672 105

005 0025 0036 141 104

P E1 (pg 2 of 3) Using Initial Rates to Determine Order

Nitrogen dioxide will decompose into nitrogen oxide and oxygen gas as indicated in the equation below

2 NO2(g) 2 NO(g) + O2(g)

A graph of the concentration of each constituent at various times during the course of the reaction at 300frac14C is presented below Use this graph to understand that the loss of reactant and formation of products is stoichiometrically related

Decomposition of nitrogen dioxide

0

0002

0004

0006

0008

001

0012

0 100 200 300 400 500

time

co

nc

Next you can use the concentration of the reactant vs time data presented in the data table above and manipulate the concentration

values to ln[NO2] and 1

[NO2]

and then graph ln[NO2] vs time and also graph 1

[NO2]

vs time You can use these two graphs to

look for which of the graphs presented will give a straight line in order to determine the order of the reaction These two graphs are shown below

The r2 value which is the coefficient of determination you will learn more about r and r2 when you take a statistics course but for now you can think of it as a Ogravegoodness-of-fitOacute indicator The closer the r2 is to 1 the better the data fits to a straight line Thus

you can see that the r2 value is best for 1

[NO2]

vs time indicating this reaction is second order

P E2 (pg 1 of 6) Rate Laws Using data amp graphs Name_____________________Per____

Decomposition of Nitrogen Dioxide

time (sec) [NO2] [NO] [O2]

0 001 0 0

50 00079 00021 00011

100 00065 00035 00018

150 00055 00045 00023

200 00048 00052 00026

250 00043 00057 00029

300 00038 00062 00031

350 00034 00066 00033

400 00031 00069 00035

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1 The dimerization of butadiene is studied at 500 K and the following reaction and experimental data is presented below

2 C4H6(g) C8H12(g)

a Determine the rate law for this reaction

b Determine the rate constant

c Calculate the half-life for this reaction (If it is not 1st order calculate the half-life at the initial concentration)

P E2 (pg 2 of 6) Rate Law for Dimerization of Butadiene

Time (s) [C4H6(g)] (M)

0 00167

195 00160

604 00150

1246 00130

2180 00110

6210 00068

$

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2 Dinitrogen pentoxide can be decomposed according to the reaction below

2 N2O5(soln) 4 NO2(soln) + O2(g) All Trials are performed at 45frac14C

Data for this reaction can be collected in different ways It is presented in two different ways below instantaneous rates for various concentrations and concentration at various time The concentration vs time data is graphed

Concentration and Initial Rates

a What are a few methods by which you could determine the reaction order

b What are several different methods by which you could determine the rate constant k

c What are a few different methods by which you could determine the half-life

P E2 (pg 3 of 6) Decomposition of Dinitrogen Pentoxide

[N2O5(solOtilden)] (molesL)

Instantaneous rate Msec

10 000060

050 000030

025 000015

Concentration vs Time DataConcentration vs Time Data

Time (s)[N2O5(solOtilden)] (molesL)

0 100

200 088

400 078

600 069

800 061

1000 054

1200 048

1400 043

1600 038

1800 034

2000 030

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3 The decomposition of hydrogen peroxide was studied at a particular temperature and experimental data is presented in the table to the right

2 H2O2(g) 2H2O(g) + O2(g)

a What are the two methods that you could use to determine the rate law for this reaction with the data that has been given

b Write out the rate law for this decomposition reaction

c What are the three methods that you could use to determine the rate constant

i Use the easiest of these two methods to determine a value for k

ii What are the units on k

d Now that you know the order of the reaction calculate the half-life for this reaction (if it is not 1st order calculate the half-life at the initial concentration)

yen Show how the conc vs time graph confirms the value that you calculated

P E3 (pg 4 of 6) Decomposition of H2O2

Time (s) [H2O2(g)] (moleL)

0 10

120 091

300 078

600 059

1200 037

1800 022

2400 013

3000 0082

3600 0050

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Please work in PENCIL Please put some work on the page that indicates HOW you did the problem

1 If a 84 g sample of thorium decays with a 10 minute half life how much would the sample weigh in a half hour

2 A sample of radioactive iodine (half life = 3 days) originally weighed 10 g but now weighs 0625 g How old is this sample

You can estimate the half life quickly and easily but youOtildell need a calculator to use the integrated rate equation and half life equations

3 A sample of radioactive calcium originally weighed 24 g and in 12 hours it weighs 125 g What is the half-life

4 If a 500 g sample of barium decays with a 45 day half life how much would the sample weigh in a 18 days

5 A sample of an ancient grass mat containing radioactive carbon (half life = 5730 years) seems to be emitting on 625 of the radiation that a sample of a grass mat woven last year would have How old is this ancient grass mat

6 A sample of radioactive calcium originally weighed 32 kg and in 2 days it weighs 05 kg What is the half-life in hours

7 If a 96 g sample of tin decays with a 25 minute half life how much would the sample weigh in 15 minutes

8 A sample of radioactive magnesium (half life = 183 days) originally weighed 80 g but now weighs 25 g How many years old is this sample

9 A sample of radioactive radium originally weighed 56 g and in three days it weighs just less than a gram What is the half life in hours

P E3 (pg 1 of 2) Half Life ETH The Rate of Radioactive Decay Name________________________Per____

For the generic reaction A + B C

1 The reaction below was studied at 25frac14C and the following data was obtained

NH4+ + NO2

N2 + 2H2O(L)

a What is the rate law

b What is the rate constant Be sure and include units

2 The reaction below was studied at 10frac14C and the following data was obtained

2NO(g) + Cl2(g) 2NOCl(g)

a What is the rate law

b What is the rate constant Be sure and include units

3 The reaction below was studied and the following data were obtained

2ClO2 + 2OH ClO3 + ClO2

+ H2O

a What is the rate law

b What is the rate constant Be sure and include units

4 The reaction below was studied and the following data were obtained

I + OCl IO + Cl

a What is the rate law

b What is the rate constant Be sure and include units

5 The reaction below was studied and the following data were obtained

BrO3 + 5 Br + 6 H+ 3 Br2 + 3 H2O

a What is the rate law

b What is the rate constant Be sure and include units

P E1 (pg 1 of 3) Using Initial Rates to Determine Order Name_____________________Per___

[NO]0

(molL)[Cl2]0

(molL)Initial Rate

(moleL min)

010 010 018

010 020 035

020 020 145

[I]0

(molL)[OCl]0

(molL)Initial Rate

(molL s)

012 018 791 102

006 018 395 102

003 009 988 103

024 009 791 102

[ClO2]0

(molL)[OH]0

(molL)Initial Rate

(molL s)

0050 0100 0057

0100 0100 023

0100 0050 0115

[NH4+]0

(molL)[NO2

]0

(molL)Initial Rate(moleL sec)

0100 0005 135 107

0100 0010 270 107

0200 0010 540 107

[BrO3]0

(molL)[Br]0

(molL)[H+]0

(molL)Initial Rate

(molL s)

0100 0100 0100 80 104

0200 0100 0100 16 103

0200 0200 0100 32 103

0100 0100 0200 32 103

trial[A]0

(molL)[B]0

(molL)Initial Rate

(moleL hour)

1 4 6 20

2 4 3 10

3 2 6 5

rate1

rate2=k

k

[A]ox

[A]ox

[B]oy

[B]oy

20

10=k

k

[4]ox

[4]ox

[6]oy

[3]oy

2 = [2]y

y = 1

20

5=k

k

[4]o

x

[2]o

x

[6]o

1

[6]o

1

4 = [2]x

x = 2 rate = k[A]2[B]

While it is most likely that any rate laws on the AP exam will only be first or second order it is possible that other orders will show up and are indeed possible When the order is not so obvious it is useful to know a useful log rule

RateRatio = [ConcRatio]x

log[RateRatio] = x log[ConcRatio] thus it is quite simple to solve for the order x log[RateRatio]

log[ConcRatio]= x

6 Given the hypothetical data below determine the order of the reaction A + B + C D + E

[A] (M) [B] (M) [C] (M) Rate (Msec)

10 10 10 00076

20 10 10 00304

10 10 20 00107

10 20 10 00152

7 Given the hypothetical data below determine the order of the reaction H + I + J K

[H] (M) [I] (M) [J] (M) Rate (Msec)

10 10 10 17

23 10 10 391

10 10 40 27

10 18 20 694

8 Given the hypothetical data below determine the order of the reaction P + Q + R S + T

[P] (M) [Q] (M) [R] (M) Rate (Msec)

10 10 10 00365

10 635 10 147

10 10 075 00274

19 47 23 185

9 Given the hypothetical data below determine the order of the reaction V + W + X Y + Z

[V] (M) [W] (M) [X] (M) Rate (Msec)

001 001 001 280 106

001 004 001 448 105

001 002 006 672 105

005 0025 0036 141 104

P E1 (pg 2 of 3) Using Initial Rates to Determine Order

Nitrogen dioxide will decompose into nitrogen oxide and oxygen gas as indicated in the equation below

2 NO2(g) 2 NO(g) + O2(g)

A graph of the concentration of each constituent at various times during the course of the reaction at 300frac14C is presented below Use this graph to understand that the loss of reactant and formation of products is stoichiometrically related

Decomposition of nitrogen dioxide

0

0002

0004

0006

0008

001

0012

0 100 200 300 400 500

time

co

nc

Next you can use the concentration of the reactant vs time data presented in the data table above and manipulate the concentration

values to ln[NO2] and 1

[NO2]

and then graph ln[NO2] vs time and also graph 1

[NO2]

vs time You can use these two graphs to

look for which of the graphs presented will give a straight line in order to determine the order of the reaction These two graphs are shown below

The r2 value which is the coefficient of determination you will learn more about r and r2 when you take a statistics course but for now you can think of it as a Ogravegoodness-of-fitOacute indicator The closer the r2 is to 1 the better the data fits to a straight line Thus

you can see that the r2 value is best for 1

[NO2]

vs time indicating this reaction is second order

P E2 (pg 1 of 6) Rate Laws Using data amp graphs Name_____________________Per____

Decomposition of Nitrogen Dioxide

time (sec) [NO2] [NO] [O2]

0 001 0 0

50 00079 00021 00011

100 00065 00035 00018

150 00055 00045 00023

200 00048 00052 00026

250 00043 00057 00029

300 00038 00062 00031

350 00034 00066 00033

400 00031 00069 00035

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1 The dimerization of butadiene is studied at 500 K and the following reaction and experimental data is presented below

2 C4H6(g) C8H12(g)

a Determine the rate law for this reaction

b Determine the rate constant

c Calculate the half-life for this reaction (If it is not 1st order calculate the half-life at the initial concentration)

P E2 (pg 2 of 6) Rate Law for Dimerization of Butadiene

Time (s) [C4H6(g)] (M)

0 00167

195 00160

604 00150

1246 00130

2180 00110

6210 00068

$

$

amp$

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2 Dinitrogen pentoxide can be decomposed according to the reaction below

2 N2O5(soln) 4 NO2(soln) + O2(g) All Trials are performed at 45frac14C

Data for this reaction can be collected in different ways It is presented in two different ways below instantaneous rates for various concentrations and concentration at various time The concentration vs time data is graphed

Concentration and Initial Rates

a What are a few methods by which you could determine the reaction order

b What are several different methods by which you could determine the rate constant k

c What are a few different methods by which you could determine the half-life

P E2 (pg 3 of 6) Decomposition of Dinitrogen Pentoxide

[N2O5(solOtilden)] (molesL)

Instantaneous rate Msec

10 000060

050 000030

025 000015

Concentration vs Time DataConcentration vs Time Data

Time (s)[N2O5(solOtilden)] (molesL)

0 100

200 088

400 078

600 069

800 061

1000 054

1200 048

1400 043

1600 038

1800 034

2000 030

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3 The decomposition of hydrogen peroxide was studied at a particular temperature and experimental data is presented in the table to the right

2 H2O2(g) 2H2O(g) + O2(g)

a What are the two methods that you could use to determine the rate law for this reaction with the data that has been given

b Write out the rate law for this decomposition reaction

c What are the three methods that you could use to determine the rate constant

i Use the easiest of these two methods to determine a value for k

ii What are the units on k

d Now that you know the order of the reaction calculate the half-life for this reaction (if it is not 1st order calculate the half-life at the initial concentration)

yen Show how the conc vs time graph confirms the value that you calculated

P E3 (pg 4 of 6) Decomposition of H2O2

Time (s) [H2O2(g)] (moleL)

0 10

120 091

300 078

600 059

1200 037

1800 022

2400 013

3000 0082

3600 0050

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Please work in PENCIL Please put some work on the page that indicates HOW you did the problem

1 If a 84 g sample of thorium decays with a 10 minute half life how much would the sample weigh in a half hour

2 A sample of radioactive iodine (half life = 3 days) originally weighed 10 g but now weighs 0625 g How old is this sample

You can estimate the half life quickly and easily but youOtildell need a calculator to use the integrated rate equation and half life equations

3 A sample of radioactive calcium originally weighed 24 g and in 12 hours it weighs 125 g What is the half-life

4 If a 500 g sample of barium decays with a 45 day half life how much would the sample weigh in a 18 days

5 A sample of an ancient grass mat containing radioactive carbon (half life = 5730 years) seems to be emitting on 625 of the radiation that a sample of a grass mat woven last year would have How old is this ancient grass mat

6 A sample of radioactive calcium originally weighed 32 kg and in 2 days it weighs 05 kg What is the half-life in hours

7 If a 96 g sample of tin decays with a 25 minute half life how much would the sample weigh in 15 minutes

8 A sample of radioactive magnesium (half life = 183 days) originally weighed 80 g but now weighs 25 g How many years old is this sample

9 A sample of radioactive radium originally weighed 56 g and in three days it weighs just less than a gram What is the half life in hours

P E3 (pg 1 of 2) Half Life ETH The Rate of Radioactive Decay Name________________________Per____

Nitrogen dioxide will decompose into nitrogen oxide and oxygen gas as indicated in the equation below

2 NO2(g) 2 NO(g) + O2(g)

A graph of the concentration of each constituent at various times during the course of the reaction at 300frac14C is presented below Use this graph to understand that the loss of reactant and formation of products is stoichiometrically related

Decomposition of nitrogen dioxide

0

0002

0004

0006

0008

001

0012

0 100 200 300 400 500

time

co

nc

Next you can use the concentration of the reactant vs time data presented in the data table above and manipulate the concentration

values to ln[NO2] and 1

[NO2]

and then graph ln[NO2] vs time and also graph 1

[NO2]

vs time You can use these two graphs to

look for which of the graphs presented will give a straight line in order to determine the order of the reaction These two graphs are shown below

The r2 value which is the coefficient of determination you will learn more about r and r2 when you take a statistics course but for now you can think of it as a Ogravegoodness-of-fitOacute indicator The closer the r2 is to 1 the better the data fits to a straight line Thus

you can see that the r2 value is best for 1

[NO2]

vs time indicating this reaction is second order

P E2 (pg 1 of 6) Rate Laws Using data amp graphs Name_____________________Per____

Decomposition of Nitrogen Dioxide

time (sec) [NO2] [NO] [O2]

0 001 0 0

50 00079 00021 00011

100 00065 00035 00018

150 00055 00045 00023

200 00048 00052 00026

250 00043 00057 00029

300 00038 00062 00031

350 00034 00066 00033

400 00031 00069 00035

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1 The dimerization of butadiene is studied at 500 K and the following reaction and experimental data is presented below

2 C4H6(g) C8H12(g)

a Determine the rate law for this reaction

b Determine the rate constant

c Calculate the half-life for this reaction (If it is not 1st order calculate the half-life at the initial concentration)

P E2 (pg 2 of 6) Rate Law for Dimerization of Butadiene

Time (s) [C4H6(g)] (M)

0 00167

195 00160

604 00150

1246 00130

2180 00110

6210 00068

$

$

amp$

amp$

amp($

amp$

amp$

$ amp$ $ )$ ($ $ $ +$

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2 Dinitrogen pentoxide can be decomposed according to the reaction below

2 N2O5(soln) 4 NO2(soln) + O2(g) All Trials are performed at 45frac14C

Data for this reaction can be collected in different ways It is presented in two different ways below instantaneous rates for various concentrations and concentration at various time The concentration vs time data is graphed

Concentration and Initial Rates

a What are a few methods by which you could determine the reaction order

b What are several different methods by which you could determine the rate constant k

c What are a few different methods by which you could determine the half-life

P E2 (pg 3 of 6) Decomposition of Dinitrogen Pentoxide

[N2O5(solOtilden)] (molesL)

Instantaneous rate Msec

10 000060

050 000030

025 000015

Concentration vs Time DataConcentration vs Time Data

Time (s)[N2O5(solOtilden)] (molesL)

0 100

200 088

400 078

600 069

800 061

1000 054

1200 048

1400 043

1600 038

1800 034

2000 030

$amp($amp)

+amp)))-

$amp

$amp

$amp-

$amp

$amp0

$amp

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+$

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$

$ $ amp$ ($ $ $ $ amp$ ($ $ $

$

amp$

()$+$amp$

3 The decomposition of hydrogen peroxide was studied at a particular temperature and experimental data is presented in the table to the right

2 H2O2(g) 2H2O(g) + O2(g)

a What are the two methods that you could use to determine the rate law for this reaction with the data that has been given

b Write out the rate law for this decomposition reaction

c What are the three methods that you could use to determine the rate constant

i Use the easiest of these two methods to determine a value for k

ii What are the units on k

d Now that you know the order of the reaction calculate the half-life for this reaction (if it is not 1st order calculate the half-life at the initial concentration)

yen Show how the conc vs time graph confirms the value that you calculated

P E3 (pg 4 of 6) Decomposition of H2O2

Time (s) [H2O2(g)] (moleL)

0 10

120 091

300 078

600 059

1200 037

1800 022

2400 013

3000 0082

3600 0050

$$$amp()$amp+

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$ $ amp$ ($ $ $ $ amp$ ($ $ $

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()$+$amp$

Please work in PENCIL Please put some work on the page that indicates HOW you did the problem

1 If a 84 g sample of thorium decays with a 10 minute half life how much would the sample weigh in a half hour

2 A sample of radioactive iodine (half life = 3 days) originally weighed 10 g but now weighs 0625 g How old is this sample

You can estimate the half life quickly and easily but youOtildell need a calculator to use the integrated rate equation and half life equations

3 A sample of radioactive calcium originally weighed 24 g and in 12 hours it weighs 125 g What is the half-life

4 If a 500 g sample of barium decays with a 45 day half life how much would the sample weigh in a 18 days

5 A sample of an ancient grass mat containing radioactive carbon (half life = 5730 years) seems to be emitting on 625 of the radiation that a sample of a grass mat woven last year would have How old is this ancient grass mat

6 A sample of radioactive calcium originally weighed 32 kg and in 2 days it weighs 05 kg What is the half-life in hours

7 If a 96 g sample of tin decays with a 25 minute half life how much would the sample weigh in 15 minutes

8 A sample of radioactive magnesium (half life = 183 days) originally weighed 80 g but now weighs 25 g How many years old is this sample

9 A sample of radioactive radium originally weighed 56 g and in three days it weighs just less than a gram What is the half life in hours

P E3 (pg 1 of 2) Half Life ETH The Rate of Radioactive Decay Name________________________Per____

2 Dinitrogen pentoxide can be decomposed according to the reaction below

2 N2O5(soln) 4 NO2(soln) + O2(g) All Trials are performed at 45frac14C

Data for this reaction can be collected in different ways It is presented in two different ways below instantaneous rates for various concentrations and concentration at various time The concentration vs time data is graphed

Concentration and Initial Rates

a What are a few methods by which you could determine the reaction order

b What are several different methods by which you could determine the rate constant k

c What are a few different methods by which you could determine the half-life

P E2 (pg 3 of 6) Decomposition of Dinitrogen Pentoxide

[N2O5(solOtilden)] (molesL)

Instantaneous rate Msec

10 000060

050 000030

025 000015

Concentration vs Time DataConcentration vs Time Data

Time (s)[N2O5(solOtilden)] (molesL)

0 100

200 088

400 078

600 069

800 061

1000 054

1200 048

1400 043

1600 038

1800 034

2000 030

$amp($amp)

+amp)))-

$amp

$amp

$amp-

$amp

$amp0

$amp

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3 The decomposition of hydrogen peroxide was studied at a particular temperature and experimental data is presented in the table to the right

2 H2O2(g) 2H2O(g) + O2(g)

a What are the two methods that you could use to determine the rate law for this reaction with the data that has been given

b Write out the rate law for this decomposition reaction

c What are the three methods that you could use to determine the rate constant

i Use the easiest of these two methods to determine a value for k

ii What are the units on k

d Now that you know the order of the reaction calculate the half-life for this reaction (if it is not 1st order calculate the half-life at the initial concentration)

yen Show how the conc vs time graph confirms the value that you calculated

P E3 (pg 4 of 6) Decomposition of H2O2

Time (s) [H2O2(g)] (moleL)

0 10

120 091

300 078

600 059

1200 037

1800 022

2400 013

3000 0082

3600 0050

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Please work in PENCIL Please put some work on the page that indicates HOW you did the problem

1 If a 84 g sample of thorium decays with a 10 minute half life how much would the sample weigh in a half hour

2 A sample of radioactive iodine (half life = 3 days) originally weighed 10 g but now weighs 0625 g How old is this sample

You can estimate the half life quickly and easily but youOtildell need a calculator to use the integrated rate equation and half life equations

3 A sample of radioactive calcium originally weighed 24 g and in 12 hours it weighs 125 g What is the half-life

4 If a 500 g sample of barium decays with a 45 day half life how much would the sample weigh in a 18 days

5 A sample of an ancient grass mat containing radioactive carbon (half life = 5730 years) seems to be emitting on 625 of the radiation that a sample of a grass mat woven last year would have How old is this ancient grass mat

6 A sample of radioactive calcium originally weighed 32 kg and in 2 days it weighs 05 kg What is the half-life in hours

7 If a 96 g sample of tin decays with a 25 minute half life how much would the sample weigh in 15 minutes

8 A sample of radioactive magnesium (half life = 183 days) originally weighed 80 g but now weighs 25 g How many years old is this sample

9 A sample of radioactive radium originally weighed 56 g and in three days it weighs just less than a gram What is the half life in hours

P E3 (pg 1 of 2) Half Life ETH The Rate of Radioactive Decay Name________________________Per____

Please work in PENCIL Please put some work on the page that indicates HOW you did the problem

1 If a 84 g sample of thorium decays with a 10 minute half life how much would the sample weigh in a half hour

2 A sample of radioactive iodine (half life = 3 days) originally weighed 10 g but now weighs 0625 g How old is this sample

You can estimate the half life quickly and easily but youOtildell need a calculator to use the integrated rate equation and half life equations

3 A sample of radioactive calcium originally weighed 24 g and in 12 hours it weighs 125 g What is the half-life

4 If a 500 g sample of barium decays with a 45 day half life how much would the sample weigh in a 18 days

5 A sample of an ancient grass mat containing radioactive carbon (half life = 5730 years) seems to be emitting on 625 of the radiation that a sample of a grass mat woven last year would have How old is this ancient grass mat

6 A sample of radioactive calcium originally weighed 32 kg and in 2 days it weighs 05 kg What is the half-life in hours

7 If a 96 g sample of tin decays with a 25 minute half life how much would the sample weigh in 15 minutes

8 A sample of radioactive magnesium (half life = 183 days) originally weighed 80 g but now weighs 25 g How many years old is this sample

9 A sample of radioactive radium originally weighed 56 g and in three days it weighs just less than a gram What is the half life in hours

P E3 (pg 1 of 2) Half Life ETH The Rate of Radioactive Decay Name________________________Per____