If for a hypothetical reaction, E_a=0 at 273 ~K , then find the ratio of the rate constants at 383 ~K and 273 ~K .

Step-by-step solution

Relation between activation energy (E_a ) and rate constant (k), k=A e^ - E_a R T Here, A = frequency factor or pre-exponential factor. T = temperature (in K) R = gas constant e = mathematical quantity Now, at 273 ~K , E_a=0 aligned k₁ & =A e^ - 0 R 273 k₁ & =A 1 k₁ & =A...(i) aligned Similarly at, 383 K, k₂=A e^ - E_a 383 ...(ii) Ratio of Eqs. (i) and (ii) is k₂=k₁ e^ - E_a 383 If, E_a=0 k₂=k₁ Hence, ratio of rate constant at 383 ~K is 1 .