Question

Data for the decomposition of hydrogen peroxide at some set temperature T is provided below. The rate law depends only on the concentration of H2O2. (These same data will be used for questions 6, 7 and 8.) 2 H2O2 ---> 2 H2O O2 t (seconds) 0 60 120 180 240 360 420 600 [H2O2] (M) 0.882 0.697 0.566 0.458 0.372 0.236 0.188 0.094 What is the value of the rate constant, k

Answer 1

Answer:

$0.00442 s^{-1}$ is the value of the rate constant.

Explanation:

$2 H_2O_2\rightarrow 2 H_2O + O_2$

Let the order of the reaction be x.

The rate law of the reaction can be written as:

$R=k[H_2O_2]^x$

1. Rate of the reaction when concentration changes from 0.882 M to 0.697 M in 0 seconds  to 60 seconds.

$R=-\frac{0.697 M-0.882 M}{60 s-0 s}=0.00308 M/s$

$0.00308 M/s=k[0.697 M]^x$..[1]

2. Rate of the reaction when concentration changes from  0.697 M to 0.566 M in 240 seconds to 360 seconds.

$R=-\frac{0.236M-0.372M}{120s-60 s}=0.00227 M/s$

$0.00218 M/s=k[0.236 M]^x$..[2]

[1] ÷ [2]

$\frac{0.00308 M/s}{0.00227 M/s}=\frac{k[0.697 M]^x}{k[0.236M]^x}$

Solving fro x:

x = 0.92 ≈ 1

$R=k[H_2O_2]^1$

$0.00308 M/s=k[0.697 M]^1$

$k=\frac{0.00308 M/s}{[0.697 M]^1}=0.00442 s^{-1}$

$0.00442 s^{-1}$ is the value of the rate constant.