Derivation of Van't Hoff equation.

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 ln K ……(1) 

We know that, 

∆G° = ∆H° – T∆S° -(2)  

Substituting (1) in equation (2)  

– RT ln K = ∆H° – T∆S° 

Rearranging, 

ln K = − Δ H °/R T + T ΔS °/R T

ln K = − Δ 𝐻 °/ 𝑅 𝑇 + Δ 𝑆 °/ 𝑅   ….(3) 

Differentiating equation (3) with respect to temperature  

d(in K) = d(in K) / dT = ∆H° / RT2

Equation (4) is known as differential form of van't Hoff equation. 

On integrating the equation (4), between T1 and T2 with the respective equilibrium constants and K2 

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