cm1502 chapter 6 chemical kinetics

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Chapter 6

Chemical Kinetics

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Chemical kinetics

Chemical kinetics is the study of reaction rates, or the changes in the concentrations of reactants or products with time.

By studying kinetics, insights are gained to control reaction conditions to achieve a desired outcome.

One of the main goals of chemical kinetics is to understand the reaction mechanism.

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Reaction Rate Reaction rate - changes in the concentrations of reactants or products per unit time.

aA + bB cC + dD

rate = 1

a - = -

[A]

t

1

b

[B]

t

1

c

[C]

t = +

1

d

[D]

t = +

Units for rate: mol L-1 s-1

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In order to measure the reaction rate you need to measure the concentration of at least one component in the mixture at many points in time.

There are two ways of approaching this problem:

1) for reactions that are complete in a short time, it is best to use continuous monitoring of the concentration, or

2) for reactions that happen over a very long time,

sampling of the mixture at various times can be used.

Measuring Reaction Rate

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Spectrophotometric monitoring of a reaction.

Measurements must be fast and reproducibly.

Conductometric monitoring of a reaction

When non-ionic reactants form ionic products or vice versa, the change in conductivity of the solution over time can be used to measure the rate.

Manometric monitoring of a reaction

When a reaction results in a change in the number of moles of gas, the change in pressure with time corresponds to a change in reaction rate.

N2O4 (colorless) 2NO2 (brown) 5

Average, Instantaneous and Initial reaction rates

Initial rate

average rate

average rate

Instantaneous rate

C2H4(g) + O3(g) C2H4O(g) + O2(g)

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Instantaneous, Initial and Average rate

Average rate is the change in measured concentrations in any particular time period linear approximation of a curve The larger the time interval, the more the average

rate deviates from the instantaneous rate

The instantaneous rate is the change in concentration at any one particular time/point on the curve. determined by taking the slope of a line tangent to

the curve at that particular point The initial rate is the slope of a line tangent to the curve

at t=0

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Because it has a nonpolluting product (water vapor), hydrogen gas is used for fuel aboard the space shuttle and may be used by Earth-bound engines in the near future. 2H2(g) + O2(g) 2H2O(g)

(b) When [O2] is decreasing at 0.23 mol/L*s, at what rate is

[H2O] increasing?

- 1 2

[H2]

t = -

[O2]

t = +

[H2O]

t 1 2

0.23mol/L*s = + [H2O]

t 1 2

; = 0.46mol/L*s [H2O]

t

rate = (a)

[O2]

t - = - (b)

(a) Express the rate in terms of changes in [H2], [O2], and [H2O]

with time.

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The Rate Law (or rate equation) expresses the rate as a function of reactant concentrations and temperature.

The rate of a reaction is directly proportional to the concentration of

each reactant raised to a power.

For the reaction aA + bB products the rate law would be

n and m are called the orders for each reactant. Can take the value as integer, zero or fraction defines how reaction rate is affected by reactant concentration. Overall order of the reaction = m+n k is called the rate constant, is specific for a given reaction at a given temperature.

mnk [B][A] Rate =

The Rate Law

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Types of Rate Laws

Differential rate law is the one that expresses rate dependence of rate on concentration.

Integrated rate law expresses how the concentrations

depend on time.

Once we determine experimentally either type of rate law for a reaction, we automatically know the other one.

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Reaction order Differential rate law

Zero order

First order

Second order

k Rate =

k[B] Rate or k[A] Rate ==

22 k[B] Rate or k[A] Rate or k[A][B] Rate ===

Zero, First and Second order reactions.

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Integrated Rate Laws

rate = - [A]

t = k [A]

rate = - [A]

t = k [A]0

rate = - [A]

t = k [A]2

first order rate equation

second order rate equation

zero order rate equation

ln [A]0

[A]t = kt ln [A]0 = kt + ln [A]t

1

[A]t

1

[A]0 - = kt

1

[A]t

1

[A]0 + = kt

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

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HelloSticky Noteinstantaneous rate, no divided by 2

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rate = - [A]

t = k [A]0

- [A] t = k [A]0

[ ][ ]

[ ]

=t

0

0A

A

t d[A] kAd0

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

OR

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

Zero First Second

ln [A]0

[A]t = kt

ln [A]t = - kt + ln [A]0 OR

rate = - [A]

t = k [A]

- [A] t = k [A]1

[ ][ ]

[ ]

kt[A][A]In-

t d kAd[A]1

tk[A][A]1

0

t

0

A

A 0

=

=

=

1

[A]t

1

[A]0 - = kt

1

[A]t

1

[A]0 + = kt

OR

rate = - [A]

t = k [A]2

- [A] t = k [A]2

[ ][ ]

[ ]

kt[A]

1[A]1

kt[A]

1[A]1

t d kAd[A]

1

tk[A][A]

1

0

0

t

0

A

A2

2

0

=+

=

=

=

)(

)(

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Second order reaction Type II Assuming the reaction is first order in both A and B

The rate with respect to time derivative of reactant concentration is

The loss rate for the reactants is equal

(1)

(2)

Consider the case where 0

d[A]/dt = - k[A][B] = - k[A]( + [A])

d[A]

[A]( + [A]) [A]0

[A]

= -

0

t k dt

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This equation is applicable when [B]0 [A]0

The concept of half life does not apply to second order reactions of type II

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Determining the Reaction orders

can ONLY be determined experimentally. Initial rates method. Isolation method Graphical method Half life method

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Initial Rate Method

Experiment Initial Reactant

Concentrations (mol/L) Initial Rate (mol/L*s)

1

2

3

4

5

O2 NO

1.10x10-2 1.30x10-2 3.21x10-3

1.10x10-2 3.90x10-2 28.8x10-3

2.20x10-2

1.10x10-2

3.30x10-2

1.30x10-2

2.60x10-2

1.30x10-2

6.40x10-3

12.8x10-3

9.60x10-3

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

Table 16.2 Principles of General Chemistry, Silberberg, McGraw-Hill Education (Asia)

rate = k [O2]m[NO]n

Change the initial concentration of that reactants one by one and monitor the initial rate

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Determining Reaction Orders Compare experiments 1 and 2

k [O2]2m[NO]2n

k [O2]1m[NO]1n =

rate2

rate1 =

[O2]2

[O2]1

m

6.40x10-3mol/L*s

3.21x10-3mol/L*s =

1.10x10-2mol/L

2.20x10-2mol/L m ; 2 = 2m m = 1

k [O2]3m[NO]3n

k [O2]1m[NO]1n =

rate3

rate1 =

[NO]3

[NO]1

n Compare experiments 1 and 3

12.8x10-3mol/L*s

3.21x10-3mol/L*s =

1.30x10-2mol/L

2.60x10-2mol/L n ; 22 = 2n n = 2

rate = k [NO]2[O2]1 18 CM1502 2013-14

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Many gaseous reactions occur in a car engine and exhaust system. One of these is

Use the following data to determine the differential rate law.

Experiment Initial Rate(mol/L*s) Initial [NO2] (mol/L) Initial [CO] (mol/L)

1 2 3

0.0050 0.080 0.0050

0.10

0.10 0.40 0.10

0.10 0.20

rate = k [NO2]m[CO]n

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0.080

0.0050

rate 2

rate 1

[NO2] 2

[NO2] 1

m =

k [NO2]m2[CO]n2

k [NO2]m1 [CO]n1 =

0.40

0.10 =

m ; 16 = 4m and m = 2

k [NO2]m3[CO]n3

k [NO2]m1 [CO]n1

[CO] 3

[CO] 1

n =

rate 3

rate 1 =

0.0050

0.0050 =

0.20

0.10

n ; 1 = 2n and n = 0

The reaction is 2nd order in NO2.

The reaction is zero order in CO.

rate = k [NO2]2[CO]0 = k [NO2]2

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Isolation method Consider

The rate law is

The reaction is performed with one reactant [A] in excess

The reaction becomes pseudo th order with respect to B and can be determined by the previously mentioned method. For , we can make [B]0 in excess and determine in the same way as above.

Integrated rate laws and reaction order

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

1/[A]t = kt + 1/[A]0

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

Units of k (t in seconds)

0

mol L-1 s-1

s-1

L mol -1 s-1

Figure16.5 Principles of General Chemistry, Silberberg, McGraw-Hill Education (Asia)

t[A][A]k 0t =

1

[A]t

1

[A]0 - = kt

ln [A]0

[A]t = kt

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Graphical determination of the reaction order for the decomposition of N2O5.

The overall reaction order is first order. k = 4.82 x 10-3 s-1

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Reaction half-life (t1/2)

ln [A]0

[A]t = kt ln [A]0 = kt + ln [A]t

2/1

0

0

][21

][ln ktA

A=

2/12ln kt=

By substituting, t = t1/2 and [A]t = 1/2[A]0

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A plot of [N2O5] vs. time for three half-lives.

t1/2 =

for a first-order process

ln 2

k 0.693

k =

Figure 16.9 Principles of General Chemistry, Silberberg, McGraw-Hill Education (Asia)

1/8 [A]0

1/2 [A]0

1/4 [A]0

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1

[A]t

1

[A]0 - = kt

1

[A]t

1

[A]0 + = kt

[A]t - [A]0 = - kt [A]t = - kt + [A]0 Zero

Second



1/2[A]0 - [A]0 = - kt1/2

-1/2[A]0 = - kt1/2

1/2[A]0/k = t1/2 1/2[A]0 x 1/k = t1/2

t1/2 = [A]0/2k

1

1/2[A]0

1

[A]0 - = kt1/2

2

[A]0

1

[A]0 - = kt1/2

1

k[A]0 t1/2 =

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measure t1/2 vs [A]0 zero order: t1/2 is proportional to [A]0 first order: t1/2 is independent of [A]0 second order: t1/2 is proportional to 1/[A]0

Half life method to determine rate law.

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For most reactions, in order for a reaction to take place, the reacting molecules must collide with each other.

once molecules collide they may react together or they

may not, depending on two factors

1) whether the collision has enough energy to "break the bonds holding reactant molecules together";

2) whether the reacting molecules collide in the proper

orientation for new bonds to form.

Collision Theory of Kinetics

Takes into account the reaction rate as the result of particles colliding with a certain frequency and minimum energy 29 CM1502 2013-14

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The number of collisions are the product of reactant concentrations.

A

A

B

B

A

A B

B A

2 molecules of A

2 molecules of B

number of collisions = 4

A

A

B

B

A B

3 molecules of A

2 molecules of B


3 molecules of A

3 molecules of B


Why concentrations are multiplied in the rate law

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The Arrhenius Equation

k = AeEa

RT

ln k = ln A - Ea/RT

ln k2

k1 =

Ea

R -

1

T2

1

T1 -

where k is the kinetic rate constant at T

Ea is the activation energy

R is the universal gas constant

T is the Kelvin temperature

A is the collision frequency factor

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Temperature and Kinetics

REACTANTS

PRODUCTS

ACTIVATED STATE

Col

lisio

n E

nerg

y

Col

lisio

n E

nerg

y

Ea (forward)

Ea (reverse)

Activation Energy An energy threshold that the colliding molecules must exceed in order to react

H

Hrxn = Ea(fwd) Ea(rev) 32 CM1502 2013-14

Graphical determination of the activation energy

ln k = -Ea/R (1/T) + ln A

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Ea (kJ/mol) f (at T = 298 K)

50 1.70x10-9

75 7.03x10-14

100 2.90x10-18

T f (at Ea = 50 kJ/mol)

250C(298K) 1.70x10-9

350C(308K) 3.29x10-9

450C(318K) 6.12x10-9

f = Fraction of collisions

Smaller Ea or higher T Larger k

Higher rate

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The effect of temperature on the distribution

of collision energies

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The Arrhenius Equation : k = A e-Ea/RT

A : Frequency factor or Arrhenius pre-exponential factor

A = pZ

Collision frequency Orientation probability factor

The orientation probability factor p is Specific for each reaction Related to the structural

complexity of the colliding particles Ratio of effectively oriented

collisions to all possible collisions

How molecular structure affects rate

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Collision frequency is controlled by concentration and temperature

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Transition State Theory Molecular nature of the activated complex

Transition state or activated complex is formed only if the molecules collide in an

effective orientation and with energy equal to or greater than the Ea.

Every reaction (and every step in an overall

reaction) goes through its own transition state, from which it can continue in either direction.

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Reaction energy diagram for the reaction of CH3Br and OH-.

Visualizing the Transition State

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Reaction energy diagrams and possible transition states for 3 reactions

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

NO(g) + O3 (g) NO2(g) + O2 (g)

2ClO(g) Cl2(g) + O2 (g)

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Conclusions Collision Theory Reactant particles

must collide with the right orientation and enough energy in order to react

Transition State Theory The reactant species forms an unstable, high energy transition state, which either forms product(s) or reverts to reactant(s).

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HelloSticky Notetwo theories describe how the reaction happen, not necessarily about mathematical description

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Sequential First order Reactions I = intermediate

The differential rate expressions are

To determine the concentration of each species as a function of time, we integrate them

At t = 0,

The expression for [A] from the integrated rate law-first order expression,

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Substitute for [A] in the differential rate expression for I

When solved for [I] we get

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kA = 2kI kA = 8kI kA = 0.25kI

Inference : If the intermediate undergoes decay at a faster rate than the rate at which it is being formed then the intermediate concentration will be small

When is the maximum [I] reached?

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Rate determining step in sequential reactions If kA >> kI

If kI >> kA

In each case only the rate constant of the slow step appears in the rate equation. The rate determining step in sequential reactions is the slowest step . It determines the rate of the product formation

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Parallel reactions In this reaction reactant A can form one of the two products B and C.

The differential rate expressions for reactant and product are

kB = 2kC = 0.1s-1

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Assume [A]0 > 0 and [B]0 = [C]0 = 0, After integration:

What will the expressions when kB > kC ? Which step is the rate determining step in each case?

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Reversible reactions

Differential rate expression for each species

Assume [A]0 > 0 and [B]0 =0, after integration

A and B reach equilibrium after a long time

Reaction Mechanism Any chemical reaction can be broken down into a set of

elementary reactions/steps. Describing the series of steps that occur to produce the overall

observed reaction is called a reaction mechanism Chemists propose a reaction mechanism to explain how a

particular reaction might occur and then test the mechanism. The rate law for elementary reaction can be deduced from the

reaction stoichiometry [reaction order equals molecularity]

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Reaction Mechanism An Example Overall reaction:

H2(g) + 2 ICl(g) 2 HCl(g) + I2(g)

Proposed mechanism: 1) H2(g) + ICl(g) HCl(g) + HI(g) 2) HI(g) + ICl(g) HCl(g) + I2(g)

the steps in this mechanism are elementary steps, meaning

that they cannot be broken down into simpler steps and that the molecules actually interact directly in this manner without any other steps

materials that are products in an early step, but then a reactant in a later step are called intermediates. 49 CM1502 2013-14

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Reaction intermediates

A substance that is formed and used up Do not appear in the overall equation Unstable relative to reactants or products but more stable than

transition states Reactive intermediates are usually short lived and are very seldom

isolated.

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Molecularity the number of reactant particles in an elementary

step is called its molecularity a unimolecular step involves 1 reactant particle a bimolecular step involves 2 reactant particles

though they may be the same kind of particle. a termolecular step involves 3 reactant particles

though these are exceedingly rare in elementary steps 51 CM1502 2013-14

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Rate Laws for General Elementary Steps

Elementary Step Molecularity Rate Law

A product

2A product

A + B product

2A + B product

Unimolecular

Bimolecular

Bimolecular

Termolecular

Rate = k [A]

Rate = k [A]2

Rate = k [A][B]

Rate = k [A]2[B]

Reaction order equals molecularity 52 CM1502 2013-14

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HelloSticky Notereaction order the overall reaction equals molecularity of the slowest step or the determining step

PLAN:

SOLUTION:

Determining Molecularity and Rate Laws for Elementary Steps

PROBLEM: The following two reactions are proposed as elementary steps in the mechanism of an overall reaction:

(1) NO2Cl(g) NO2(g) + Cl (g)

(2) NO2Cl(g) + Cl (g) NO2(g) + Cl2(g) (a) Write the overall balanced equation. (b) Determine the molecularity of each step.

(a) The overall equation is the sum of the steps. (b) The molecularity is the sum of the reactant particles in the step.

2NO2Cl(g) 2NO2(g) + Cl2(g)

(c) Write the rate law for each step.

rate2 = k2 [NO2Cl][Cl]

(1) NO2Cl(g) NO2(g) + Cl (g)

(2) NO2Cl(g) + Cl (g) NO2(g) + Cl2(g) (a)

Step(1) is unimolecular. Step(2) is bimolecular.

(b)

rate1 = k1 [NO2Cl] (c)

(1) NO2Cl(g) NO2(g) + Cl (g)

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The Rate-Determining Step of a Reaction Mechanism

The overall rate of a reaction is related to the rate of the slowest, or rate-determining step

Example : 2 ICl + H2 2 HCl + I2 Rate = k[ICl][H2] rate-determining step

Proposed mechanism: Step 1: ICl + H2 HCl + HI slow..(1)

Step 2: HI + ICl HCl + I2 fast....(2)

Overall: 2ICl + H2 2HCl + I2 .... (1) + (2) Step 1 is the rate-determining step = slow step

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Example : Given that the decomposition of 2N2O5 is a first order

reaction, propose a possible mechanism for the reaction

2N2O5 4NO2 + O2

Rate = k[N2O5] Mechanism: N2O5 NO2 + NO3 (slow, rate determining) N2O5 + NO3 3NO2 + O2 2N2O5 4NO2 + O2

slow

fast

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Rate Laws for Overall Reactions

NO3(g) + CO(g) NO2(g) + CO2(g)

NO2(g) + NO2(g) NO(g) + NO3(g)

NO2(g) + CO(g) NO(g) + CO2(g)

fast step

overall reaction

slow step

Based on the slow step: rate = k1[NO2]2

k2

k1

Initial Slow Step

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N2O(g) + H2(g) N2(g) + H2O(g)

2NO(g) + 2H2(g) N2(g) + 2H2O(g)

slow step

overall reaction

fast step, reversible

Based on the slow step: rate = k2[N2O2][H2]

k3

k-1

Initial Fast Step

2NO(g) N2O2(g) k1

N2O2(g) + H2(g) N2O(g) + H2O(g) k2

fast step

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The rate law of the slowest step determines how fast the overall reaction occurs.


rate = k2[N2O2][H2]

intermediate

First step: Ratereverse = k-1[N2O2] Rateforward = k1[NO]2

k1[NO]2 = k-1[N2O2]

[NO]2 [N2O2] = k-1 k1

Slow step: rate = k2[N2O2][H2] rate = k2 [NO]2[H2] k-1 k1

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The steady state approximation

I1 and I2 are intermediates

To determine the concentration of the species we have two ways. Numerical method Steady state approximation

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Concentrations determined by numerical evaluation Where kA =0.02s-1 and k1 =k2 =0.2 s-1

I1 and I2 undergo very little change with time

This is called steady state approximation.

[P]ss: curve corresponding to steady state approximation

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Within steady state approximation, [P] is predicted with first order decay of A

Steady state approximation is valid when k1 >> kA k2 >> kA

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Procedure for Studying Reaction Mechanisms

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Proposed mechanism must add up to the overall reaction, be physically reasonable, and conform to the overall rate law.

Catalysts

A catalyzed reaction yields the products more quickly, but DOES NOT yield more product than the uncatalyzed reaction.

A catalyst increases the reaction rate by providing a

different mechanism, through which the activation energy is lower.

A catalyst increases the rate of the forward AND the reverse reactions.

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Reaction energy diagram of a catalyzed and an uncatalyzed process.

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Enzyme kinetics

Michaelis Menten rate law

Where

Km signifies the rate constants of ES dissociation over the rate constants of ES formation.

Summary 1. Measuring Reaction Rates 2. Rate Expressions 3. The Rate Law and Its Components 4. k dependence on T 5. Collision Theory 6. Reaction Mechanism 7. Use of catalysts

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Slide Number 1Chemical kinetics Slide Number 3Measuring Reaction RateSlide Number 5Slide Number 6Instantaneous, Initial and Average rateSlide Number 8Slide Number 9Types of Rate LawsSlide Number 11Slide Number 12Slide Number 13Slide Number 14Slide Number 15Determining the Reaction ordersSlide Number 17Slide Number 18Slide Number 19Slide Number 20Slide Number 21Slide Number 22Slide Number 23Reaction half-life (t1/2)Slide Number 25Slide Number 26Slide Number 27Slide Number 28Slide Number 29Slide Number 30Slide Number 31Slide Number 32Slide Number 33Slide Number 34Slide Number 35Slide Number 36Transition State TheoryMolecular nature of the activated complexSlide Number 38Slide Number 39ConclusionsSlide Number 41Slide Number 42Slide Number 43Slide Number 44Slide Number 45Slide Number 46Slide Number 47Reaction MechanismReaction Mechanism An ExampleReaction intermediatesMolecularitySlide Number 52Slide Number 53Slide Number 54Slide Number 55Rate Laws for Overall ReactionsRate Laws for Overall ReactionsRate Laws for Overall ReactionsSlide Number 59Slide Number 60Slide Number 61Rate Laws for Overall ReactionsCatalystsSlide Number 64Slide Number 65Summary

cm1502 chapter 6 chemical kinetics

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