Van’t Hoff (Temperature Dependence of K)
Why the Van’t Hoff relation matters
The Van’t Hoff equation predicts how the equilibrium constant K changes with temperature. It helps you estimate whether heating shifts equilibrium toward products or reactants.
For exothermic reactions (ΔH° < 0), K often decreases when temperature rises. For endothermic reactions (ΔH° > 0), K usually increases with temperature. This is useful for selecting operating windows in laboratory and process chemistry.
- Quantify equilibrium shifts vs. temperature
- Choose process temperatures for target conversion
- Translate equilibrium data between temperatures
Formulas
Note: R = 8.314 J·mol⁻¹·K⁻¹; ΔH° in kJ/mol is internally converted to J/mol.
Formula symbol legend
- K₁, K₂ = equilibrium constant at T₁ and T₂
- ΔH° = standard reaction enthalpy
- R = universal gas constant
- T₁, T₂ = absolute temperature in Kelvin
- ln = natural logarithm
Detailed examples
Given K₁ = 5.2 at 298.15 K; ΔH° = -45 kJ/mol; T₂ = 318.15 K.
Result: K₂ becomes smaller than K₁, indicating a shift toward reactants at higher temperature.
Use ΔH° = +35 kJ/mol with the same temperatures.
Then K₂ increases relative to K₁, showing stronger product favorability at higher temperature.
With measured K₁ at T₁ and K₂ at T₂, you can back-calculate ΔH°.
This is useful when literature data is missing or system-specific calibration is needed.
• Always use Kelvin.
• K must be positive and dimensionless.
• Very small |ΔH°| leads to weak temperature dependence and higher sensitivity to input uncertainty.
Deeper context
Thermodynamic link
The Van’t Hoff relation is directly connected to \(\Delta G^\circ = -RT\ln K\). It captures the slope of \(\ln K\) versus \(1/T\), allowing direct interpretation of enthalpy effects on equilibrium.
Limitations
This form is typically used over temperature ranges where ΔH° can be treated as approximately constant. Over wider ranges or with strong heat-capacity effects, higher-order models may be required.
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