For the decomposition of hydrogen peroxide in dilute sodium hydroxide at 20 °C 2 H2O2 (aq) 2 H2O (l) + O2 (g) the following data have been obtained: [H2O2], M 8.92*10-2 4.72*10-2 2.50*10-2 1.32*10-2 time, min 0 9.63 19.3 28.9 The average rate of disappearance of H2O2 over the time period from t = 0 min to t = 9.63 min is - 4.36x10^-3 M min-1.

K = 0.06611

Explanation: The rate of reaction is defined as the change in concentration of any of reactant or products per unit time. From the given reaction, the rate of reaction may be equal to the rate of disappearance of reactant which is equal to the rate of appearance of products.

The average rate of disappearance of H2O2 over the time period from t=0 min at 8.92*10^-2 to t=9.63min at 4.72*10^-2 is given as - 4.36*10^-3Mmin-1.

We can say:

•The initial concentration [H2O2]o is 8.92*10^-2M

•The concentration at time t. [H2O2]t is 4.72*10^-2

•The time (t) is 9.63 min

The expression of rate constant for a first order reaction is shown as

K=2.303/t log[H2O2]o / [H2O2]t

Substitute the values of t, [H2O2]o and [H2O2]t in the equation of rate constant.

K=2.303/9.63 log [8.92*10^-2] / [4.72*10^-2]

K = 0.2391 (log 8.92*10^-2 - log 4.72*10^-2)

K = 0.2391 [-1.0496 - (-1.3261) ]

K = 0.2391 (-1.0496+1.3261)

K = 0.2391 (0.2765)

K = 0.06611

Since the value of k is almost constant, the decomposition of H2O2 is a first order reaction.