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Chapter 14 Chemical Kinetics Chemical Kinetics CH 14 1

Chapter 14 Chemical Kinetics Chemical Kinetics CH 141

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Page 1: Chapter 14 Chemical Kinetics Chemical Kinetics CH 141

Chemical Kinetics CH 14 1

Chapter 14 Chemical Kinetics

Page 2: Chapter 14 Chemical Kinetics Chemical Kinetics CH 141

Chemical Kinetics CH 14 2

• Factors affecting chemical reaction• Rate of reaction• Average rate, Instantaneous rate• Rate law• Order of reaction• First order reaction• Second order reaction• Half - life time

Page 3: Chapter 14 Chemical Kinetics Chemical Kinetics CH 141

Chemical Kinetics CH 14 3

Chemical Kinetics: How fast is the chemical reaction, (i.e. studying of rates of chemical

processes).

Page 4: Chapter 14 Chemical Kinetics Chemical Kinetics CH 141

Chemical Kinetics CH 14 4

Factors That Affect Reaction Rates 1. Reactant concentration: As the concentration of reactants increases, so does that reactant molecules will collide and rate of reaction increases. 2. Temperature: As temperature increases, the reaction rate increases, reactant molecules have more kinetic energy, move faster, and collide more often and with greater energy. 3. Catalysts: catalyst increases chemical reactions by changing mechanism.

Page 5: Chapter 14 Chemical Kinetics Chemical Kinetics CH 141

Chemical Kinetics CH 14 5

Speed of a reaction is measured by: the change in

concentration with time.

For a reaction A B

Reaction Rates

t

Bof moles

timein change

Bof moles ofnumber in changerate Average

Page 6: Chapter 14 Chemical Kinetics Chemical Kinetics CH 141

Chemical Kinetics CH 14 6

Reaction Rates

Rates of reactions can be determined by monitoring the change in concentration of either reactants or products

as a function of time. [A] / t

A B

Page 7: Chapter 14 Chemical Kinetics Chemical Kinetics CH 141

Chemical Kinetics CH 14 7

At t = 0 (time zero) there is 1.00 mol A (100 red spheres) and no B present = zero.

At t = 20 min, there is 0.54 mol A and 0.46 mol B. At t = 40 min, there is 0.30 mol A and 0.70 mol B. Calculating average rate:

Reaction Rates

mol/min 023.0min 0min 20

mol 0 mol 46.0min 0min 20

0at Bof moles20at Bof moles

Bof molesrate Average

ttt

Page 8: Chapter 14 Chemical Kinetics Chemical Kinetics CH 141

Chemical Kinetics CH 14 8

For the reaction:

A B There are two ways of measuring rate:

1. The speed at which the products appear (i.e. change in moles of B per unit time), or

2. The speed at which the reactants disappear (i.e. the change in moles of A per unit time).

Reaction Rates

t

A

t

][A of molesA respect to withrate Average

Page 9: Chapter 14 Chemical Kinetics Chemical Kinetics CH 141

Chemical Kinetics CH 14 9

Example: Reaction of butyl chloride to give butanol.

Average rate decreases as the reaction goes on.

Page 10: Chapter 14 Chemical Kinetics Chemical Kinetics CH 141

Chemical Kinetics CH 14 10

The average rate of the reaction over each interval = the change in concentration divided by the change in time:

Average Rate, M/s

C4H9Cl(aq) + H2O(l) C4H9OH(aq) + HCl(aq)

SMx /109.10.00.50

1000.00905.0 4

t

ClHCeaveragerat

]94[

Page 11: Chapter 14 Chemical Kinetics Chemical Kinetics CH 141

Chemical Kinetics CH 14 11

• Instantaneous rate defines as The rate at any instant in time and it is the slope of the tangent to the curve.

• Average rate: is the change in reactant or product concentration to the change of time.

Instantaneous Rate & Average Rate

Page 12: Chapter 14 Chemical Kinetics Chemical Kinetics CH 141

Chemical Kinetics CH 14 12

Example:

C4H9Cl(aq) + H2O(l) C4H9OH(aq) + HCl(aq)– If We plot [C4H9Cl] with respect to t.

–The units for average rate are mol/L·s or M/s.

Instantaneous Rate & Average Rate

Page 13: Chapter 14 Chemical Kinetics Chemical Kinetics CH 141

Chemical Kinetics CH 14 13

Calculate: 1. average rate?SMxeaveragerat /106.1

200

4.0

0200

1.00671.0 4

2. instantaneous rate at Z point?

Average rate= Y2-Y1

X2-X1

ZSMxousrateIns /1067.6

200

4.0

600

030.0tantan 4

Page 14: Chapter 14 Chemical Kinetics Chemical Kinetics CH 141

Chemical Kinetics CH 14 14

Reaction Rates and Stoichiometry

•What if the ratio is not 1:1?

H2(g) + I2(g) 2 HI(g)

• Only 1/2 HI is made for each H2 used.

Page 15: Chapter 14 Chemical Kinetics Chemical Kinetics CH 141

Chemical Kinetics CH 14 15

• In General, for the reaction

aA + bB cC + dD

(-) sign because Reactants (decrease) with time

(+) sign because Products (increase) with time

Reaction Rates and Stoichiometry

Page 16: Chapter 14 Chemical Kinetics Chemical Kinetics CH 141

Chemical Kinetics CH 14 16

• For Example

C4H9Cl(aq) + H2O(l) C4H9OH(aq) + HCl(aq)

tt

OHHCClHCRate 9494

Page 17: Chapter 14 Chemical Kinetics Chemical Kinetics CH 141

Chemical Kinetics CH 14 17

• For Example

Page 18: Chapter 14 Chemical Kinetics Chemical Kinetics CH 141

Chemical Kinetics CH 14 18

• In general rates increase as concentrations increase.

NH4+(aq) + NO2

-(aq) N2(g) + 2H2O(l)

Concentration and Rate

Constant

Constant increases

increases

Page 19: Chapter 14 Chemical Kinetics Chemical Kinetics CH 141

Chemical Kinetics CH 14 19

• From previous table, for the reaction

NH4+(aq) + NO2

-(aq) N2(g) + 2H2O(l)

we note:

as [NH4

+] doubles with [NO2-] constant the rate doubles,

as [NO2-] doubles with [NH4

+] constant, the rate doubles

Concentration and Rate

Page 20: Chapter 14 Chemical Kinetics Chemical Kinetics CH 141

Chemical Kinetics CH 14 20

Concentration and Rates

The above equation is called the rate law, and k is the rate constant.

For the reaction

Page 21: Chapter 14 Chemical Kinetics Chemical Kinetics CH 141

Chemical Kinetics CH 14 21

• For a general reaction with rate law

m: order in reactant 1 and n: order in reactant 2.

• The total order of reaction = (m + n + ….)• The total order of reaction = zero, if m = 0, n = 0.

Rate Law

nmk ]2reactant []1reactant [Rate

Page 22: Chapter 14 Chemical Kinetics Chemical Kinetics CH 141

Chemical Kinetics CH 14 22

Concentration and Rate

• This reaction is

First-order in [NH4+]

First-order in [NO2−]

• The overall reaction order: is the sum of the exponents on the reactants in the rate law.

• The overall order of this reaction= 1+1= 2 ( i.e. second-order).

Page 23: Chapter 14 Chemical Kinetics Chemical Kinetics CH 141

Chemical Kinetics CH 14 23

AB

Differential Rate Law

Page 24: Chapter 14 Chemical Kinetics Chemical Kinetics CH 141

Chemical Kinetics CH 14 24

ktt

ktt

t

t

t

tA

A

x

x

eAA

eA

A

ktA

A

ktAA

multiply

ktAA

AAt

ktcA

kdtA

Ad

cxx

dx

t

t

0

0

0

0

0

0

0

][

][

][][

][

][

][

][ln

]ln[]ln[

]ln[]ln[

][][,0

]ln[

][

][

ln

0

0

[A]0: the initial concentration at t = 0.[A]t: the concentration after time, t >0.

Page 25: Chapter 14 Chemical Kinetics Chemical Kinetics CH 141

Chemical Kinetics CH 14 25

When [A]t is plotted as a function of time, a curve results.• Slope = - k

First Order Reactions

Page 26: Chapter 14 Chemical Kinetics Chemical Kinetics CH 141

Chemical Kinetics CH 14 26

Straight Line Equation y = mx + bSlope= + mintercept = b

First Order Reactions

Page 27: Chapter 14 Chemical Kinetics Chemical Kinetics CH 141

Chemical Kinetics CH 14 27

0AlnAln kttA plot of ln[A]t vs t is a straight line. slope = -k intercept = ln[A]0

First Order Reactions

ln[A]t

Page 28: Chapter 14 Chemical Kinetics Chemical Kinetics CH 141

Chemical Kinetics CH 14 28

• Half-life t1/2: is the time taken for the concentration of

a reactant to drop to half its original value.• For a first order process, when t = t½,

so [A]t = ½[A]0.

kk

t693.0ln

21

21

First Order Reactions

ktA

A t 0][

][ln

Half- life time doesn’t depend on concentration of reactant

Page 29: Chapter 14 Chemical Kinetics Chemical Kinetics CH 141

Chemical Kinetics CH 14 29

• For a second order reaction with just one reactant.

Second Order Reactions

kdtA

Ad

Akdt

Adrate

2

2

][

][

][][

tA

A

kdtA

Adt

0

][

][2

0][

][

cxx

dx

12

ktAA t

0][

1

][

1

[A] = [A]0 , t=0

0][

1

][

1

Akt

A t

Differential Equation

Page 30: Chapter 14 Chemical Kinetics Chemical Kinetics CH 141

Chemical Kinetics CH 14 30

Second Order Reactions

The Change of Concentration with Time

0A1

A1 ktt

y = mx + b A plot of 1/[A] vs. t is a straight line with a slope of k. Intercept= 1/[A]0

Page 31: Chapter 14 Chemical Kinetics Chemical Kinetics CH 141

Chemical Kinetics CH 14 31

0A1

21

kt

For a second-order process, set [A]t=0.5 [A]0 .

Half-Life of Second Order

21

00

][

1

][2

11

ktAA

Page 32: Chapter 14 Chemical Kinetics Chemical Kinetics CH 141

Chemical Kinetics CH 14 32

The decomposition of NO2 at 300°C is described by the equation

NO2 (g) NO (g) + 1/2 O2 (g)

and yields these data:

Time (s) [NO2], M

0.0 0.01000

50.0 0.00787

100.0 0.00649

200.0 0.00481

300.0 0.00380

Determining the order of chemical reaction

Example

Page 33: Chapter 14 Chemical Kinetics Chemical Kinetics CH 141

Chemical Kinetics CH 14 33

Graphing ln [NO2] vs. t yields:

Time (s) [NO2], M ln [NO2]

0.0 0.01000 -4.610

50.0 0.00787 -4.845

100.0 0.00649 -5.038

200.0 0.00481 -5.337

300.0 0.00380 -5.573

The plot is not a straight line, so the process is not first-order in [A].

Does not fit:

Determining the order of chemical reaction

Page 34: Chapter 14 Chemical Kinetics Chemical Kinetics CH 141

Chemical Kinetics CH 14 34

A graph of 1/[NO2] vs. t gives this plot.

Time (s) [NO2], M 1/[NO2]

0.0 0.01000 100

50.0 0.00787 127

100.0 0.00649 154

200.0 0.00481 208

300.0 0.00380 263

• This is a straight line. Therefore, the process is second-order in [NO2].

Determining the order of chemical reaction

Page 35: Chapter 14 Chemical Kinetics Chemical Kinetics CH 141

Chemical Kinetics CH 14 35

Practice Problems CH.14 in the book