Van't Hoff Equation

The Van't Hoff equation, ln(K₂/K₁) = ΔH⁰/R (1/T₁ - 1/T₂), provides information about the temperature dependence of the equilibrium constant. T

INSTRUCTIONS: Choose units and enter the following:

• (K₁) Equilibrium constant at absolute temperature T₁.
• (K₂) Equilibrium constant at absolute temperature T₂.
• (T₁) Absolute temperature one.
• (T₂ ) Absolute temperature two.

ΔH⁰: The calculator returns the reaction enthalpy (the standard heat of the reaction).  This calculator uses the Ideal Gas Constant (R):8.3144626181532 J/(mol·K).

All temperatures are automatically converted to Kelvin.

The Math/Science

The Van't Hoff equation was proposed in 1884 by Jacobus Henricus van't Hoff. Van't Hoff made great contributions to physical chemistry, specifically in chemical kinetics, stereochemistry, and chemical equilibrium.
The formula in this equation is as follows:

          `ΔH^0 = R * ( -ln(K_2/K_1))/ (1/T_1 - 1/T_2)` 

It is a form of : ln(K₂/K₁) = ΔH⁰/R (1/T₁ - 1/T₂) solved for  ΔH⁰.

If equilibrium constants are known for two different temperatures, then ΔH⁰ can be found for a substance. Likewise, if an equilibrium constant (K₁) for T₁ and ΔH⁰ are known, then the equilibrium constant (K₂) can be calculated for a second temperature. The Van't Hoff equation does, however, assume that ΔH⁰ does not change with temperature. This is not necessarily true; ΔH⁰ does change with temperature, but the change is small enough that it is considered negligible when estimating K₂. 

When the equilibrium constant and temperature are plotted against each other, both an exothermic and endothermic reaction will have a characteristic shape to its graph. Exothermic graphs tend to be linear with a positive slope, while endothermic reactions are linear with a negative slope, as shown below.

Chemistry Calculators

• R - Gas Constant: 8.3144626181532 J/(K⋅mol)
• Boyle's Law Calculator:  P₁ • V₁ = P₂ • V₂
• Charles Law Calculator: V₁• T₂ = V₂ • T₁
• Combined Gas Law Calculator:   P•V / T= k
• Gay-Lussac Law:  T₁•P₂ =T₂•P₁ 
• Ideal Gas Law: P•V = n•R•T
• Bragg's Law:   n·λ = 2d·sinθ
• Hess' Law:  ΔH⁰_rxn=ΔH⁰_a+ΔH⁰_b+ΔH⁰_c+ΔH⁰_d
• Internal Energy: ΔU = q + ω 
• Activation Energy:  E_a = (R*T₁⋅T₂)/(T₁ - T₂) ⋅  ln(k₁/k₂)
• Arrhenius Equation:  k = Ae^E_a/(RT)
• Clausius-Clapeyron Equation:  ln(P₂/P₁) = (ΔH_vap)/R * (1/T₁ - 1/T₂)
• Compressibility Factor: Z = (p*V_m)/(R*T)
• Peng-Robinson Equation of State:  p = (R*T)/(V_m - b) - (a*α)/(V_m² + 2*b*V_m - b²)
• Reduced Specific Volume:  v_r = v/(R* T_cr / P_c)
• Van't Hoff Equation:  ΔH⁰ = R * ( -ln(K₂/K₁))/ (1/T₁ - 1/T₂)

References

Whitten, et al. "Chemistry" 10th Edition. Pp. 699

Wikipedia: Van't Hoff Equation