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 reaction with different activation energies `(E_(a))` are given as .
`log (k_(1))/(k_(2)) = (1)/(2.303 RT) [ E_(a_(2)) - E_(a_(1))] = ((350-162)1000)/(2.303 xx 8.314 xx 298)`
Therefore the ratio of rates , `k_(1)//K_(2) = 8.9 xx 10^(32)`
In the presence fo a catalyst rate is increased by ` 8.9 xx 10^(32)` times .