Chemistry, Third edition

REACTION RATE EXPRESSIONS 251

The rate constant

●One way to look at kis to think of it as the rate of reaction when all of the reactant

concentrations are exactly 1 mol dm^3.

●kincreases with the temperature of the reaction mixture. Therefore, the reaction

rate also increases with temperature (Box 14.2).

●The size of kis decided by the activation energy for the reaction (a low EAmeans a

highkvalue and vice versa). Naturally fast reactions have high rate constants.

●The units of kdepend upon the overall order of reaction (Table 14.2).

Example 14.2

The reaction between A and B follows the rate expression

rate of reaction k[A][B]

What is the overall order of reaction? What are the units of k?

Answer

We can rewrite this as

Rate of reaction k[A]x[B]ywherexy 1

The reaction is therefore first order with respect to the reactants A and B. Overall,

the reaction order is xy 1  1 2, i.e. it is second order overall.

For the units of k, rearranging for kgives

krate of reaction

[A][B]

The units of kare therefore

mol dm^3 s^1

mol dm^3 mol dm^3

Cancelling

mol dm^3 s^1

mol dm^3 mol dm^3

mol^1 dm^3 s^1

Note that a reaction which is overallsecond order would also be obtained if the

rate expression was:

rate of reaction k[A]^2 or rate of reaction k[B]^2

Working out the overall order from the rate expression

What is the overall order of reactions possessing the following rate expressions?

(i) rate of reaction k[A][B]^0 (iii)rate of reaction k[E]0.5[G]0.5

(ii)rate of reaction k[D]^2 (iv)rate of reaction k[B][J][N].

Exercise 14G

Table 14.2Units of

rate constants

Overall order Units of rate

of reaction constant

Zeroth mol dm^3 s^1

First s^1

Second mol^1 dm^3 s^1

Third mol^2 dm^6 s^1