# Approximating entropy change in a reaction using Arrhenius equation

Recently my teacher finished teaching the chapter Chemical kinetics in which I have gone through Arrhenius equation.Can we estimate the change in entropy using it? I have done my calculation, considering the reversible reaction, $$\ce{A <=> B}$$ which has forward and backward rate constants $$\mathrm{k_f}$$ and $$\mathrm{k_b}$$ with pre-exponential factors $$\mathrm{A_f}$$ , $$\mathrm{A_b}$$ with activation energies of $$\mathrm{E_f}$$ and $$\mathrm{E_b}$$ respectively.

According to Arrhenius Equation,

$$\mathrm{k_f= A_f.e^{-E_f/RT}}$$ and

$$\mathrm{k_b=A_b.e^{-E_b/RT}}$$

$$\mathrm{ k_f/k_b = {A_f/A_b}.e^{{-E_f+E_b}/RT}}$$

and $$\mathrm{k_f/k_b}$$ = $$\mathrm{{A_f/A_b}.e^{-\Delta H^0/RT}}$$

$$\mathrm{k_f/k_b}$$=$$\mathrm{k_{eq}}$$=$$\mathrm{e^{-\Delta G^0/RT}}$$

but, $$\mathrm{\Delta G^0 = \Delta H^0 - T \Delta S^0}$$

which gives $$\mathrm{\Delta S^0 = Rln(A_f/A_b)}$$

Will the final expression give an approximate value of change in entropy of reaction?

• The thermodynamic quantities are the enthalpy and entropy of activation and are different to 'normal' $\Delta H^\text{o}$ etc. but come from the transition state approach to reactions where reactants and products are assumed to be in equilibrium. We write down directly $K=(k_BT/h)\exp(-\Delta G^{o*}/RT)$ Feb 25 '21 at 8:46