Chemistry 102(001) Fall 2014

13-2-1CHEM 102, Spring 2014, LA TECH

Instructor: Dr. Upali Siriwardane

e-mail: [email protected]

Office: CTH 311

Phone 257-4941

Office Hours: M,W 8:00-9:30 & 11:00-12:30 am; Tu,Th, F 8:00 - 10:00 am. or by appointment.;

Test Dates:

Chemistry 102(001) Fall 2014

September 23, 2014 (Test 1): Chapter 13

October 16, 2014 (Test 2): Chapter 14 &15

November 11, 2014 (Test 3): Chapter 16 &7

November 13, 2014 (Make-up test) comprehensive:

Chapters 13-17


Chapter 13. Chemical Kinetics 13.1 Catching Lizards 563

13.2 The Rate of a Chemical Reaction 564

13.3 The Rate Law: The Effect of Concentration

on Reaction Rate 569

13.4 The Integrated Rate Law: The Dependence of

Concentration on Time 573

13.5 The Effect of Temperature on Reaction Rate 581

13.6 Reaction Mechanisms 588

13.7 Catalysis 593


Chemical Kinetics Definitions and Concepts

a) rate of reactions

b) rate law

b) rate constant

c) order

d) differential rate law

c) integral rate law

d) Half-life law


Every chemical reaction has a Rate Law

The rate law is an expression that relates

the rate of a chemical reaction to a constant

(rate constant-k) and concentration of

reactants raised to a power.

The power of a concentration is called the order

with respect to a particular reactant.

Rate Law


Rate LawE.g. aA + bB -----> cC

rate a [A]l[B]m

rate = -1/a d[A]/dt = k [A]l[B]m; k = rate constant

[A] = concentration of A

[B] = concentration of B

l = order with respect to A

m = order with respect to B

l & m have nothing to do with stoichiometric coefficients


Differential Rate Law E.g.

2 N2O5(g) -----> 4 NO2 (g) + O2 (g)

rate= - ½ d[N2O5]/dt a [N2O5]1

rate = - ½ d[N2O5]/dt = k [N2O5]1

k = rate constant

[N2O5] = concentration of N2O5

1 = order with respect to N2O5

Rate and the order are obtained by experiments


Order The power of the concentrations is the order with

respect to the reactant.

E.g. a A + b B -----> c C

If the rate law: rate = k [A]1[B]2

The order of the reaction with respect to A is one (1).

The order of the reaction with respect to B is two (2).

Overall order of a chemical reaction is equal to the

sum of all orders (3).


Graphical methodOrder

RateLaw

Integrated Rate Law GraphX vs. time

Slope

0 rate = k [A]t = -kt + [A]0 [A]t -k

1 rate = k[A] ln[A]t = -kt + ln[A]0 ln[A]t -k

2 rate=k[A]2 = kt + k1

[A]0

1

[A]t

1

[A]t


Rate Law Differential Rate Law Integral Rate

rate = k [A]0 - D [A]/Dt = k ; ([A]0=1) [A]f-[A]0 = -kt

- d [A]/dt = k ; ([A]0=1 [A]f= -kt + [A]0

[A]f- [A]0= -kt

rate = k [A]1 - D [A]/ D t = k [A] ln [A]t/[A]0= - kt

d [A]/dt = - k [A]

rate = k [A]2 - D [A]/Dt = k [A]2 1/ [A]f - 1/[A]0 = kt

d [A]/dt = - k [A]2

1/ [A]f = kt - 1/[A]0

Differential and Integral Rate Law


Integral Law

[A]f-[A]0 = -kt

ln [A]t/[A]0 = -kt

1/[A]f = kt +

1/[A]0

Integral and Half-life forms

First order

-d[A]/dt = k [A]0

-d[A]/dt = k

- d[A]/dt = k[A]2

Second order

t½ Law

t½ = [A] o/ 2k

t½ = 0.693 / k

t½ = 1 / k [A]o

Zero order

Differential Law




1) The reaction A ---> B + C is known to follow the rate law: rate = k [A]1

What are the differential, integral and half-life (t½) form of this rate law?


This plot of ln[cis-platin] vs.

time produces a straight line,

suggesting that the reaction

is first-order.

Comparing graphs


Time / min [N2O5] / moldm-3 ln N2O5]

0 0.0175620 0.0093340 0.0053160 0.0029580 0.00167

100 0.00094160 0.00014

2. Using graphical method, show that

2 N2O5 ---> 4 NO2 + O2, is a first order reaction.


Method of initial rates

The order for each reactant is found by:

•Changing the initial concentration of that reactant.

•Holding all other initial concentrations and conditions constant.

•Measuring the initial rates of reaction

The change in rate is used to determine the order for that specific reactant. The process is repeated

for each reactant.

Finding rate laws by Initial rates


Decomposition Reaction


Graphical Ways to get Order


Initial rate


How do get order of reactants E.g. a A + b B -----> c C

Hold [B] constant and change (double) [A]

a A + b B -----> c C

If the rate law: rate = k [A]x[B]y

rate = k [A]1 k1

First order: 1 x rate = k [2A]1 k1 = k 21[A]1 k1

rate1 = k [A ]1 k1 rate1 = 1

rate2 = k 21[A ]1 k1 rate2 = 21 (doubles)

Second order: 2 x rate = k [2A]1 k1 = k 22[A]2 k1

rate1 = k [A ]2 k1 rate1 = 1

rate2 = k 22[A ]2 k1 rate2 = 22 (quadruples)


How do you find order? A + B -----> C

rate = k [A]l[B]m;

Hold concentration of other reactants constant

If [A] doubled, rate doubled• 1st order, [2A]1 = 2 1 x [A]1 , 2 1 = 2

b) If [A] doubled, rate quadrupled• 2nd order, [2A]2 = 2 2 x [A]2 , 2 2 = 4

c) If [A] doubled, rate increased 8 times • 3rd order, [2A]3 = 2 3 x [A]3 , 2 3 = 8


Rate data


3. For the reaction: A ---> D, Find the order of [A] for each case.

It was found in separate experiments that

a) The rate doubled when [A] doubled

b) The rate tripled when [A] tripled

c) The rate quadrupled when [A] doubled

d) The rate increased 8 times when [A] doubled


Units of the Rate Constant (k) 1first order: k = ─── = s-1

s L second order k = ─── mol s

L2 third order k = ─── mol2 s


4. For the chemical reaction: A + B ----> C

Using the following initial data to deduce:

a) Order of each reactant

b) Rate constant

[A],mol/L [B],mol/L rate,mol/Ls

_____________________________

2.0 3.0 0.10

6.0 3.0 0.90

6.0 6.0 0.90


Overall order


Rate Constant

E.g. a A + b B -----> c C

rate a [A]l[B]m

rate = k [A]l[B]m;

k = rate constant

proportionality constant of the rate law

Larger the k faster the reaction

It is related inversely to t½


Determining K, Rate Constant


First Order Reactions and t½

A ----> B


Radio Activity and Nuclear KineticsNuclear reactions?

Fusion

Fission

What kinetics fission follow?


Half-life t½

Radioisotope Half-life

Polonium-215 0.0018 seconds

Bismuth-212 60.5 seconds

Sodium-24 15 hours

Iodine-131 8.07 days

Cobalt-60 5.26 years

Carbon-14 5730 years

Radium-226 1600 years

Uranium-238 4.5 billion years


Nuclear Reactions : First order kinetics


t1/2 equation 0.693 = k t1/2

0.693 t1/2 =---- k


The half-life and the rate constant are related.

t1/2 =

Half-life can be used to calculate the first order rate constant.

For our N2O5 example, the reaction took 1900 seconds to react half way so:

k = = = 3.65 x 10-4

s-1

0.693

k

0.693

t1/2

0.693

1900 s

Half-life - t1/2


5. The rate constant for the first-order conversion of A to B is 2.22 hr-1. How much time will be required for the concentration of A to reach 75% of its original value?


6) The half-life of a radioactive (follows first order rate law) isotope is 10 days. How many days would be required for the isotope to degrade to one eighth of its original radioactivity?


7) The rate constant for the first order decomposition of SO2Cl2 (SO2Cl2 SO2 +Cl2) at

very high temperature is 1.37 × 10-3 min-1. If the initial concentration is 0.500 M, predict the concentration after five hours (300 min).

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Chemistry 102(001) Fall 2014