The rate constant for the first order decomposition of `H_(2)O_(2)` is given by the following equation:
`logk=14.34-1.25xx10^(4)K//T`
Calculate `E_(a)` for this reaction and rate constant k if its half-life period is 256 minutes.

Explanation

According to Arrhenius equation , `k=Ae^(-E_(a)//Rt)`
or, `Ink=InA-(E_(a))/(RT) " or, "logk=logA-(E_(a))/(2.303RT)`
Comparing with given equation,
`(E_(a))/(2.303xx8.314T)=(1.25xx10^(4))/(T)`
or , `E_(a)=2.303Rxx1.25xx10^(4)xx8.314=239.34"kJ.mol"^(-1)`
when `t_(1//2)=256"min",k=(0.693)/(t_(1//2))=(0.693)/(256xx60)=4.512xx10^(-5)s^(-1)`
`thereforelog(4.512xx10^(-5))=14.34-(1.25xx10^(4))/(T)`
or, `(1.25xx10^(4))/(T)=18.6856 " or, "T=669K`