In the decomposition of H₂O₂ at 300K, the energy of activation was found to be 18 kcal/mol while it decreases to 6kcal/mol when the decomposition was carried out in the presence of a catalyst at 300k. How many times is the catalysed reaction faster than the uncatalyased one?

K = Ae-E/RT                  (E is activation energy)

rate(R)= K(a)ⁿ                             (k=rate constant & a is concentration , n is order of reaction)

rate directily proportional to rate constant so

R1/R2 = K1/K2 = e[-E1+E2]/RT

R₁/R₂ = e^{[-18+6]/RT                           (R=.08321units , T=300)}

          =e^-[0.5]                               (e=2.8 )

R₂ = 1.67R₁               (approx)