From the following data show that the decomposition of hydrogen peroxide in aqueous solution is a first order reaction what is the value of the rate constant
Time (t) in minutes 0 10 20 30 40

V(mL) 25.0 20.0 15.7 12.5 9.6
Where V is volume of `kMnO_(4)` solution required decompose a definite volume of hydrogen peroixde

Explanation

Here a=25 mL
Time (min) (a-) `k=(1)/(t)ln(a)/(a-x)`
10 minutes 20 mL `k=1/10 ln 25/20.0 =0.022287 min^(-1) =0.00374s^(-1)`
20 minutes 15.7 mL `k=1/20 ln 25/15.7 =0.023230 min^(-1) =0.00387 s^(-1)`
40 minutes 9.6 mL `k=1/40 ln 25/9.6 =0.023897 min^(-1) =0.003849 s^(-1)`
The constancy of k shows that decomposition of `H_(2)O_(2)` is a first order reaction Average value of rate constant =0.003819 `s^(-1)`