The activation energy of a first order reaction at `300 K` is `kJ mol^(-1)`. In the presence of a catalyst, the activation energy gets lowered to `50kJ mol^(-1)` at `300 K`. How many times the reaction rate change in the presence of a catalyst at the same temperature ?

Explanation

`k_(1) = Ae^(E_(a)//RT)`
`k_(2) = Ae^(E_(a(c ))//RT)`
`log.(k_(2))/(k_(1)) = (E_(a) - E_(a( c)))/(2.303 RT)`
`log.(k_(2))/(k_(1)) = (6000-5000)/(2.303 xx 8.314 xx 300) = 1.741`
`(k_(2))/(k_(1)) = 55.08`
`:.` The reaction rate increases by `55.08` times.