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 period be `10 min`.

Options

A. `280 K`
B. `290 K`
C. `311.35 k`
D. `418.26K`

Answer

C

Explanation

Calculation of `K`
We know that `k = (0.693)/(t_(1//2)) = (0.693)/(10 xx 60) (t_(1//2) = 10 xx 60 sec)`
`= 1.1558 xx 10^(-3)`
According to Arrhenius equation
`log k = log A -(E_(a))/(2.303 RT)`
Subsitituting the various values in the above equation
`log 1.155 xx 10^(-3) = log4 xx 10^(13) - (98.6)/(2.303 xx 8.314 xx 10^(-3) xx T)`
On usual calculation, `T = 311.35 K`