At `25^(@)C` the activation energy for a catalysed reaction is `126 KJ mol^(-1)` and for uncatalysed reaction is `350 KJ mol^(-1)` . How many times the rates is increased in the presence of catalyst ?

Explanation

According to Arrhenius equation, the specific rates (k) of a reaction with different activation energies `(E_(a))` are given as
`log.(k_(1))/(k_(2))=(1)/(2.303RT)[E_(a_(2))-E_(a_(1))]=((350-162)1000)/(2.303xx8.314xx298)`
Therefore the ratio of rates, `k_(1)//k_(2)=8.9xx10^(32)`.
In the presence of a catalyst rate is increased by `8.9xx10^(32)` times.