In a Arrhenius equation for a certain reaction, the values of `A and E_(a)` ( energy of activation)are `4xx10^(13)s^(-1)` and `98.6KJ mol^(-1)`, respectively. If the reaction of first order at, what temperature will its life periof be `10 min`.

Explanation

Accroding to Arrhenius equation,
`k=Ae^(-E_(a)//RT)`
or `log_(e)k=log_(e)A-(E_(a))/(RT)`
or `2.303 log_(10)k=2.303 log _(10)A-(E_(a))/(RT)`
For a first order reaction `t_(1//2)=(0693)/(k)`
So, `k=(0.693)/(600) sec^(-1)(t_(1//2)=10min=600 sec)`
`=1.1xx10^(-3)sec^(-1)`
Hence, log `(1.1xx10^(-3))=log(4xx10^(13))-(98.6xx10^(3))/(2.303xx8.314xxT)`
T=310.95K`