Advanced Topic 417 of 1102 Thermodynamics & Energetics
Van't Hoff Equation
Gives how the equilibrium constant changes with temperature through the reaction enthalpy.
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In-depth explanation of Van't Hoff Equation
The van't Hoff equation describes how the equilibrium constant of a reaction changes with temperature: d ln K by dT equals delta H divided by R T squared, where R is the gas constant. Integrating this relation between two temperatures gives ln(K2/K1) equal to minus delta H over R times the quantity 1/T2 minus 1/T1. A plot of ln K against 1/T yields a straight line with slope minus delta H divided by R, so the enthalpy can be determined from the experimental slope. Endothermic reactions have K increasing with temperature, while exothermic reactions have K decreasing as temperature rises, in line with Le Chatelier's principle. This equation is important for industrial process optimization.
Going deeper: Van't Hoff Equation
Key ideas: Plot ln K against 1 over T to get a straight line with slope minus delta H over R. Between two temperatures use ln(K2 over K1) equals minus delta H over R times (1 over T2 minus 1 over T1). Use kelvin and R in J per mole kelvin, with delta H in joules.
Common mistakes and connections: Unit mismatch between kJ and J is the usual slip. The straight-line assumption fails if delta H changes with temperature. Do not confuse with the van't Hoff factor in colligative properties. It lets you determine thermodynamic data from equilibrium measurements.
Visualization of Van't Hoff Equation
ln K against 1/T has slope -delta H / R: for an exothermic reaction such as ammonia synthesis (-92 kJ/mol), K falls as temperature rises. The interactive lesson shows this as a live animation or chart.
Worked example and use case
The Haber process for ammonia is exothermic, so its equilibrium yield falls at higher temperature.
Frequently asked questions about Van't Hoff Equation
What is Van't Hoff Equation?
Gives how the equilibrium constant changes with temperature through the reaction enthalpy.
Is Van't Hoff Equation a beginner, intermediate or advanced topic?
Van't Hoff Equation is a advanced topic in Thermodynamics & Energetics. It builds on beginner and intermediate topics, so review those first if needed.
What should I learn before Van't Hoff Equation?
Study these earlier topics in Thermodynamics & Energetics first: Heat of Vaporization of Water, Thermodynamics of Dissolution, Gibbs-Helmholtz Equation.
What comes after Van't Hoff Equation?
The next topics in Thermodynamics & Energetics are Maxwell Relations and Residual Entropy.
Can I practise Van't Hoff Equation with quizzes?
Yes. The interactive lesson includes a self-check question on Van't Hoff Equation, and the Thermodynamics & Energetics quiz draws on every topic in this area.
Where Van't Hoff Equation fits in Thermodynamics & Energetics
Van't Hoff Equation is topic 89 of 91 in Thermodynamics & Energetics.