Chemistry, Third edition

CALCULATIONS USING RATE EXPRESSIONS 255

Finding the order of a reaction using the initial rates

method

We now look at the use of initial rates of reaction in helping us find the individual

orders in a rate expression.

Suppose that we wish to find the overall order of the reaction

A Bproducts

This is another way of saying that we want to find out the values of xandyin the rate

expression

rate of reaction k[A]x[B]y

The initial rate of this reaction is given by the expression

initial rate k[A]x 0 [B]y 0

where [A] 0 and [B] 0 are the initial concentrations of A and B.

Now suppose that we carry out two experiments at the same temperature (so that

kremains fixed) and using the same initial concentration of B but different initial

concentrations (0.1 mol dm^3 and 0.2 mol dm^3 respectively) of A.

For the first experiment,

initial rate 1 k[0.1]x[B]y 0

For the second experiment

initial rate 2 k[0.2]x[B]y 0

Bothkand [B]

y
0 feature in both expressions. The initial rates in these experiments
will be different only because the initial concentrations of A are different. We can see

this more easily by writing the above equations in the form:

initial rate 1 constant[0.1]x

initial rate 2 constant[0.2]x

where

constantk[B]y 0

What if the initial rate doubles as [A] doubles?

If, in doubling [A], experiments show that the initial rate doubles, so that

initial rate 2  2  initial rate 1

i.e.

constant[0.2]x 2 constant[0.1]x

the equation can only be true if the order xis one. This means that the reaction is

first-order with respect to A.

What if the initial rate increases by a factor of four as [A] doubles?

If, in doubling [A], the initial rateis found to have quadrupled, so that

initial rate 2  4  initial rate 1

i.e.

constant[0.2]x 4 constant[0.1]x

then the order x mustbe two. This means that the reaction is second-order with

respect to A.