Question

Deduce the Vant Hoff equation.

Answer 1

This equation gives the quantitative temperature dependance of equilibrium constant K. The relation between standard free energy change ∆G° and equilibrium constant is

∆G° = – RT in K ……(1) 

We know that, ∆G° = ∆H° – T∆S° …….(2) 

Substituting (1) in equation (2) 

– RT in K = ∆H° – T∆S°

Rearranging, in \(K=\frac{-ΔH°}{RT}+\frac{ΔS°}{R} \)  ….(4) 

Differentiating equation (3) with respect to temperature 

d(in K) ∆H° = d(in K) / dT = ∆H⁰ / RT²

Equation (4) is known as differential form of van’t Hoff equation. On integrating the equation 4, between T₁ and T₂ with their respective equilibrium constants and K₂

Equation is known as integrated form of van’t Hoff equation.