The rate constant for the first order decomposition of `H_(2)O_(2)` is given by the
following equation:
`"log"k=14.34-1.25xx10^(4)k//t`
Calculate `E_(a)` for this reaction and at what temperature will its half-period be 256 minutes?

Explanation

(i) `E_(a) =239.33" kJ/mol"` (ii) 669 K
(i) The Arrhenius equation is log k = log `A -(E_(a))/(2.303 RT)`
Comparing with the given equation : `1.25xx10^(4) =(E_(a))/(2.303 R) rArr E_(a) =239.33" kJ mol"^(-1)`
(ii) When half-life = 256 min, `k =("In 2")/(t_(1//2))=(0.693)/(256xx60) s^(-1) =4.5xx10^(-5) s^(-1)`
`rArr (1.25 xx 10^(4))/(T) =14.34 - log 4.5 xx10^(-5) =16.68 rArr T=(1.25xx10^(4))/(16.68) =669 K`