Chemistry, Third edition

MORE ABOUT FIRST-ORDER REACTIONS 257

What if there is no change in initial rate as [A] doubles?

If experiments show that the initial rate of reaction remains unchanged, even though

[A] in experiment 2 is double [A] in experiment 1, then

initial rate 2 initial rate 1

i.e.

constant[0.2]xconstant[0.1]x

This can be true only if x0, since ‘anything to the power of zero is one’. This

means that the reaction is zeroth-order with respect to reactant A.

Similar arguments can be applied to reactant B, by carrying out experiments in

which [A] 0 remains constant and in which the concentration of B is varied from

experiment to experiment.

Initial rates, 1

The reaction:

MYproducts

was studied by the initial rates method at 25 °C. It was found that the initial rate of reaction

halved when [M] was halved and that doubling [Y] had no effect upon the initial rate. Write

down the rate expression for the reaction.

Exercise 14J

Initial rates, 2

The kinetics of the reaction between bromide (Br(aq)), bromate (BrO 3 (aq)) and H(aq) ions:

5Br(aq) BrO 3 (aq) 6H+(aq)3Br 2 (l) 3H 2 O(l)

was studied by the initial rates method and the following data obtained:

Initial concentration/mol dm^3

Experiment [Br(aq)] 0 [BrO 3 (aq)] 0 [H(aq)] 0 Relative initial

rate of reaction

1 0.01 0.01 0.01 1.00

2 0.02 0.01 0.01 2.00

3 0.01 0.04 0.01 4.00

4 0.01 0.01 0.02 4.00

Write down a rate expression for the reaction.

Exercise 14K

More about first-order reactions

If the simple reaction ABis first-order, then

rate of reaction k[A]

For such a first-order reaction, the concentration of A at time tseconds after the start

of the reaction, symbolized [A]t, is related to the initial concentration of A, i.e. [A] 0 ,

by the equation

[A]t[A] 0 ekt

14.6