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

(311.34 K)
Arrhenius equation is: `log k = log A-(Ea)/(2.303 RT)`
When `t_(1//2) =10" m in, "k =("In "2)/(t_(1//2)) =(0.693)/(10xx60)=1.15xx10^(-3) s^(-1)`
`(E_(a))/(2.303 RT) =log A-log k = log k =log ""(A)/(k) =16.54`
`T=(E_(a))/(2.303 R xx 16.54) =(98.6xx1000)/(2.303xx16.54xx8.314) =311.34 K`