Van't Hoff Equation

\[\ln\left(\frac{K_2}{K_1}\right)=-\frac{\Delta H}{R}\left(\frac{1}{T_2}-\frac{1}{T_1}\right)\]

Variables

K1equilibrium constant at temperature T1

K2equilibrium constant at temperature T2

dH[ΔH]enthalpy change of reaction (J/mol)

Rgas constant (8.314 J·mol⁻¹·K⁻¹)

T1initial temperature (K)

T2final temperature (K)

Description

What is this formula?

The Van't Hoff equation describes how the equilibrium constant of a chemical reaction changes with temperature.

When to use it

Use this equation when estimating equilibrium constants at different temperatures, analyzing temperature effects on equilibrium, or studying thermodynamic properties of reactions.

Example

Given:

K1 = 10

ΔH = 50000 J/mol

T1 = 298 K

T2 = 350 K

R = 8.314 J·mol⁻¹·K⁻¹

Formula:

ln(K2/K1) = -(ΔH/R)(1/T2 - 1/T1)

Substitution:

ln(K2/10) = -(50000/8.314)(1/350 - 1/298)

Result:

K2 ≈ 0.51

The equilibrium constant decreases as temperature increases, indicating behavior consistent with an exothermic reaction.

Applications

Chemical thermodynamics

Equilibrium analysis

Reaction engineering

Industrial chemistry

Process optimization

Note

The Van't Hoff equation assumes that the reaction enthalpy remains approximately constant over the temperature range considered. For large temperature intervals, heat capacity effects may become important and more advanced thermodynamic models may be required.

The sign of ΔH determines how equilibrium responds to temperature changes. Exothermic reactions (ΔH < 0) generally exhibit decreasing equilibrium constants as temperature increases, while endothermic reactions (ΔH > 0) typically show the opposite behavior.