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.

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