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Van't Hoff Equation (Equilibrium Constant vs. Temperature) Calculator

Relates the equilibrium constant of a reaction to temperature, standard enthalpy change, and standard entropy change.

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Natural Log of Equilibrium Constant

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Overview

The Van't Hoff equation is a fundamental thermodynamic relationship that describes how the equilibrium constant (K) of a chemical reaction changes with temperature (T). It connects the macroscopic observable K with the microscopic thermodynamic properties of the reaction: the standard enthalpy change (ΔH°) and standard entropy change (ΔS°). This equation is crucial for predicting the shift in equilibrium position under varying thermal conditions and for determining thermodynamic parameters from experimental equilibrium data.

Symbols

Variables

K = Equilibrium Constant, K = Natural Log of Equilibrium Constant, H^ = Standard Enthalpy Change, R = Gas Constant, T = Temperature

Equilibrium Constant
dimensionless
Natural Log of Equilibrium Constant
dimensionless
Standard Enthalpy Change
J/mol
Gas Constant
Temperature
Standard Entropy Change

Apply it well

When To Use

When to use: Apply this equation when you need to predict the equilibrium constant at a different temperature, or when you want to determine the standard enthalpy or entropy change of a reaction from experimental equilibrium constant data at various temperatures. It's particularly useful for understanding the temperature dependence of industrial processes and biological systems.

Why it matters: The Van't Hoff equation is vital for optimizing chemical processes, designing catalysts, and understanding natural phenomena. It allows chemists to predict how changes in temperature will affect product yield, which is critical in industrial synthesis. In biochemistry, it helps explain how temperature influences enzyme activity and biological equilibria.

Avoid these traps

Common Mistakes

  • Using Celsius instead of Kelvin for temperature.
  • Inconsistent units for R, ΔH°, and ΔS° (e.g., kJ for ΔH° and J for R/ΔS°).
  • Confusing the Van't Hoff equation with the Arrhenius equation (which relates rate constant to temperature).

One free problem

Practice Problem

For a reaction, the standard enthalpy change (ΔH°) is -50,000 J/mol and the standard entropy change (ΔS°) is -100 J/mol K. Calculate the natural logarithm of the equilibrium constant (ln K) at 298 K. Use R = 8.314 J/mol K.

Standard Enthalpy Change-50000 J/mol
Standard Entropy Change-100 J mol^{-1} K^{-1}
Temperature298 K
Gas Constant8.314 J mol^{-1} K^{-1}

Solve for: lnK

Hint: Ensure all units are consistent (Joules for energy terms).

The full worked solution stays in the interactive walkthrough.

References

Sources

  1. Atkins' Physical Chemistry
  2. Wikipedia: Van 't Hoff equation
  3. Callen, Herbert B. Thermodynamics and an Introduction to Thermostatistics
  4. NIST CODATA
  5. IUPAC Gold Book: 'equilibrium constant'
  6. IUPAC Gold Book: 'standard enthalpy of reaction'
  7. IUPAC Gold Book: 'standard entropy of reaction'
  8. Atkins' Physical Chemistry, 11th ed.