the rate of reaction

The rate of reaction

dt

Bd

dt

Ad

dt

Cd

dt

Dd

dt

dn

dnddt

d

i

i

ii

2

1

3

1

D3C2BA

1

Rate Law

• Relation between rate of reaction and concentration of the reactants

.............

..,.........,

ba BAk

BAf

Three important problems

• Determination of rate law and rate constant from experimental data.

• Construct reaction mechanism that are consistent with rate law.

• Value of rate constant and their temperature dependence

Determination of rate law

• Isolation method: Add large excess

• Methods of initial rate: measurement of rate of reaction for several different initial concentration of reactants.

Integrated Rate LawsConsider a simple 1st order rxn: A B

How much A is left after time t? Integrate:

Differential form:

Integrated Rate Laws

The integrated form of first order rate law:

Can be rearranged to give:

[A]0 is the initial concentration of A (t=0).[A]t is the concentration of A at some time, t, during the course of the reaction.

Integrated Rate Laws

Manipulating this equation produces…

…which is in the form y = mx + b

First-Order Processes

If a reaction is first-order, a plot of ln [A]t vs. t will yield a straight line with a slope of –k.

Second-Order Processes

Similarly, integrating the rate law for a process that is second-order in reactant A:

also in the form y = mx + b

Rearrange, integrate:

Second-Order Processes

So if a process is second-order in A, a plot of 1/[A] vs. t will yield a straight line with a slope of k.

Half-Life• Half-life is defined

as the time required for one-half of a reactant to react.

• Because [A] at t1/2 is one-half of the original [A],

[A]t = 0.5 [A]0.

Half-LifeFor a first-order process, set [A]t=0.5 [A]0 in integrated

rate equation:

NOTE: For a first-order process, the half-life does not depend on [A]0.

Half-Life- 2nd orderFor a second-order process, set

[A]t=0.5 [A]0 in 2nd order equation.

Outline: Kinetics

First order Second order Second order

Rate Laws

Integrated Rate Laws

complicated

Half-life complicated

Most important application of studying the order of a reaction is to establish the mechanism of reaction.

Reactions proceed in one or more elementary steps.

In elementary step molecularity = order of reaction

Reaction order and reaction mechanism

Overall order of reaction corresponds to stoichiometric equation => The reaction mechanism most probably involves one elementary step that is identical to stoichiometric equation.

When the reaction order does not corresponds to the stoichiometry of the reaction, the reaction certainly involves more than one elementary reaction.

When the reaction order does not corresponds to the stoichiometry of the reaction, the reaction certainly involves more than one elementary reaction.

Elementary Reaction(i) Reversible elementary reaction

A B

(ii) Consecutive elementary reaction

A B C

(iii) Parallel Reaction:

AB

C

Consecutive Reaction

IktkAkdt

Id

IkAkdt

Id

tkAAkdt

Ad

PIA

baa

ba

aa

kk ba

exp

expA

0

0

Consecutive Reaction

ab

abba

baba

a

aab

baa

kk

tkktkkA

IAAP

Atktkkk

kI

tkAkIkdt

Id

IktkAkdt

Id

expexp1

)exp()exp(

exp

exp

0

0

0

0

0

Consecutive Reaction

0

b

b

0

exp1

k Also

expexp

k if

expexp1 P

AtkP

kk

tktk

k

PIA

kk

tkktkkA

a

ba

ab

a

kk

ab

abba

ba

Consecutive Reaction

• Rate of formation of the final product P depends on only the smaller of two rate constants.

g)determinin (Rate IA Slow

Consecutive Reaction

PIA fastslow

A

I

P

Conc

Time

This is the basis of steady-State approximation.

0

dt

Id

Consecutive Reaction

PIA fastslow

0

0

)exp(1

exp

0

AtkP

tkAk

AkIkdt

Pd

Ak

kI

IkAkdt

Id

a

aa

ab

b

a

ba

PIA slowfast

[I]

[P]

Case II: when 12 kk

PIA fastslow

[P]

[I]

[I]

[I]

When are consecutive and Single-Step reactions distinguishable ?

01exp1 AtkP

Rate of formation of product is different from rate of decay of A

02exp1 AtkP

Rate of formation of product is same as rate of decay of A

Parallel Reaction

Parallel Reaction

Thermodynamic vs. Kinetic Control

k2 >k1, K2>K1 k2 < k1, K2>K1

k2 >k1, K2<K1k2 < k1, K2 < K1

A

BC

A

A A

B

B B

C

C C

Parallel Reaction

Reversible Reaction

Reversible reaction

Reversible reaction

Higher order reversible Reaction