The rate constant of a reaction is `1.5 xx 10^(7)s^(-1)` at `50^(@)C` and `4.5 xx 10^(7) s^(-1)` at `100^(@)C`. Evaluate the Arrhenius parameters `A` and `E_(a)`.

Answer

`A = 5.42 xx 10^(10) s^(-1)`
`E_(a) = 2.2 xx 10^(4)J mol^(-1)`

Explanation

`k = Ae^(-E_(a)//RT)`
or `log k = log A - (E_(a))/(2.303 RT)`
`:. log.(k_(2))/(k_(1)) = (E_(a))/(2.303 R)[(1)/(T_(1))-(1)/(T_(2))]`
or `log.(4.5 xx 10^(7))/(1.5 xx 10^(7)) = (E_(a))/(2.303 xx 8.314)[(1)/(323)-(1)/(373)]`
or `E_(a) = 2.2 xx 10^(4) J mol^(-1)`
`k = Ae^(-E_(a)//RT)`
or `log k = log A -(E_(a))/(2.303 RT)`
or `log 4.5 xx 10^(7) = log A - (2.2 xx 10^(4))/(2.303 xx 8.314 xx 373)`
or `A = 5.42 xx 10^(10) s^(-1)`