Question

If the binding of M to –CH2- occurs at a rate 1.5 times the rate of M binding to –CH3, what is the difference in activation energy for those two elementary reactions? Assume T=298 K

Answer 1

The rate of the reaction is related to activaation energy and temperture according to Arrhenius equation

k = A e^-Ea/RT   where k is the rate constant, A is the Arrhensius factor, E_a is the activation energy , R is the gas constant and T is the absolute temperature.

So for the binding of M to -CH2 k₁ = 1.5 and for the binding of M to -CH3 k₂ = 1.0 (given data)

Then k₁ / k₂ = (e-^{E_a1 /RT}) /(  e^{-E_a2 /RT})

1.5/1.0 = e(^{E_a2 -E_a1)/RT}

Substituting R = 8.314 J/ K.mol and T = 298K

the difference between activation energies = 436. 3 J