The Arrehenius equation for the rate constant of decompoistion of methyl nitrite and ethyl nitrite are
`k_(1) (s^(-1)) =10^(13) exp ((-152300 J mol^(-1))/(RT))`
and `k_(2)(s^(-1)) = 10^(14)exp((-157700 J mol^(-1))/(RT))` respectively. Find the temperature at which the rate constant are equal.

Explanation

At temeprature `TK`, rate constant are equal, hence
`10^(13) exp((-152300 J mol^(-1))/(RT)) = 10^(14) ((-157700 J mol^(-1))/(RT))`
`exp((157700 - 152300)/(RT)) = 10`
or `log_(e) exp ((157700 - 152300)/(RT)) = log 10 = 2.303 log_(10) 10`
or `(157700-152300)/(8.314 T) = 2.303`
Thus, `T = 282 K`