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

Given, `K=?, A=4xx10^(13) sec^(-1)`
`E_(a)=98.6xx10^(3) J mol^(-1), t_(1//2)=10xx60 sec`
`:' K=Ae^(-E_(a)//RT)`
`:. K=4xx10^(13) e^(-(98.6xx10^(3))//8.314xxT)`
Now for `I` order reaction, `K=0.693/t_(1//2)=0.693/600 sec^(-1)`
`:. 0.693/600=4xx10^(13) e^(-(98.6xx10^(3))//8.314xxT)`
or `"log_(e)"``0.693/600=``log_(e)` `4xx10^(13) -(98.6xx10^(3))/(8.314xxT)`
or `"log"_(10)0.693/600=log_(10) 4xx10^(13)-(98.6xx10^(3))/(8.314xx2.303xxT)`
`:. T=311.35 K`