Question

The data in the table below were obtained for the reaction: 2ClO2(aq) + 2OH-(aq) ---> ClO3-(aq) + ClO2-(aq) + H2O(l) Experiment number [ClO2](M) [OH-](M) Initial Rate (M/s)

1 .020 .030 .00276

2 .060 .030 .0248

3 .020 .090 .00828

a. What is the order of the reaction with respect to ClO2?

b. What is the order of the reaction with the respect to OH-?

c. What is the overall order of the reaction?

d. What is the magnitude of the rate constant for the reaction?

Answer 1

The reaction being studied is

2ClO2(aq) + 2OH-(aq) ---> ClO3-(aq) + ClO2-(aq) + H2O(l)

Now as per the data provided

Experiment number [ClO2](M) [OH-](M) Initial Rate (M/s)

1 .020 .030 .00276

2 .060 .030 .0248

3 .020 .090 .00828

What we see by comparing experiment 1 and 2 is that concentration of OH^- is kept constant but the concentration of [ClO₂] has been increased 3 times and the initial rate of the reaction has changed by 0.0248/0.00276 = 9 times. This tells us that the rate is

rate [ClO₂]²

So in answer to question a.

a) This is a second order reaction with respect to ClO₂

Now let us compare experiment 1 and 3 where ClO₂ is kept constant but the concentration of OH^- has chnage by 3 times. The initial rates differ by 0.00828/0.00276 = 3.

This tells us that the rate is

rate [OH^-]

So in answer to question b.

b) This is a first order reaction with respect to OH^-

The overall order of a reaction is the sum of the exponents of the individual reactants.

c) The overall order of the reaction is 2+1 = 3.

d) The rate constant for this reaction is got from the expression

rate = k[ClO₂]²[OH^-]

so from any one of the data points we will get get the value of k

0.00276 M/s = k (0.02M)² x (0.03M)

0.00276 M/s = k x 0.000012 M³

k = 0.00276/0.000012 M^-2s^-1

k = 2.3 x 10²M^-2s^-1 magnitude of the rate constant for the reaction