Module 6 : Reaction Kinetics and Dynamics
Lecture 26 : Integrated Rate Laws
 

Table 26.1 gives a list of integrated rate laws for for integer orders. x = consentration of a product, rate r = dx / dt, M = moles, L = liter.

Order

Reaction

Rate Law

Units of k

Half life (t ½ )

    Differential form Integrated form    
           

0

A Products

r = k [A]o

x = kt for x [A]0

M L 1 s 1

[A]0 / 2k

           

1

A Products

r = k [A]

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

S 1

Ln 2 / k

           

2

A Products

r = k [A]2

kt = x / [A]0 ( [ A]0 x)

L M 1 s 1

1 / k [A]0

           

2

A Products

r = k [A] [B]

kt = 1 / ( [A]0 [B]0) ln ([B]0 ( [A]0 x) / [A]0 ( [B]0 x)) {See Eq (26.24)}

L M 1 s 1

           

n 2

A Products

r = k [A] n

kt = ([A0] x)1-n -[A0]1-n) / ( n-1 )

(LM 1) n-1 s 1

2 n 1 1 /  (n-1)k[A0]n-1

 

In many reactions, the concentrations of all but one of the reactants is in large excess. In such a situation, it is easier to follow the changes in concentration of this particular species. Eg, in the reaction A + B Products = [P], dP / dt may be actually k [ A] [B], but if [B] is in large excess, the concentration of B is likely to remain constant [ B] 0 for a considerable length of time. In this situation, the rate law may be written as

 
= k [ A] [ B] 0 = k ' [ A] where k ' = k [B] 0 (26.25)
 
The above reaction is said to follow a pseudo first order rate law.