At a given temperature , for a reaction , the activation energy in absence of catalyst is greater than that in presence of catalyst be an amount of RT. If the value of the rate constant in presence of catalyst is x times that in absence of catalyst, then find the value of x.

Explanation

Activation energy in presence of a catalyst is lower than that in absence of catalyst . If activation energy in absence of catalyst is `E_(a)` ,then in presence of catalyst it will be `(E_(a)-RT)`.
Thus , rate constant in absence of catalyst , `k_(1)=Ae^(-(E_(a))/(RT))`
rate constant in presence of catalyst , `k_(2)=Ae^(-(E_(a)-RT)/(RT))`
`therefore (k_(2))/(k_(1))=e^(1)=x, "or, "x=2.718.`