Van't Hoff Equation
Relating equilibrium constants to temperature changes
The Van't Hoff Equation
ln(K2/K1) = -(ΔH/R)(1/T2 - 1/T1)
T in Kelvin, R = 8.314 J/mol·K
Variables
- K1, K2 = equilibrium constants at T1, T2
- T1, T2 = absolute temperatures (K)
- ΔH = enthalpy change (J/mol)
- R = gas constant (8.314 J/mol·K)
When to Use
- Estimate K at a new temperature
- Predict temperature dependence of equilibria
- Derive ΔH from slope of lnK vs 1/T
Step-by-Step Example
Problem:
K1 = 2.5 at 298 K. ΔH = -50.0 kJ/mol. Find K2 at 320 K.
1) Convert units
ΔH = -50.0 kJ/mol = -50,000 J/mol
2) Apply Van't Hoff
ln(K2/2.5) = -(-50,000/8.314)(1/320 - 1/298)
ln(K2/2.5) = 6013 × (-0.000231)
ln(K2/2.5) = -1.39
3) Solve for K2
K2/2.5 = e^-1.39 = 0.25
K2 = 0.63
Answer:
K at 320 K is 0.63 (equilibrium shifts toward reactants as temperature rises for exothermic reaction).
Common Mistakes to Avoid
Using Celsius
Always convert temperatures to Kelvin.
Sign of ΔH
Keep track of the sign; exothermic is negative.
Unit mismatch
Use ΔH in J/mol if R is 8.314 J/mol·K.
T ordering
Use (1/T2 - 1/T1) exactly as written; reversing flips the sign.
Related Calculators
Frequently Asked Questions
When is the Van't Hoff equation most accurate?
Over moderate temperature ranges where ΔH is roughly constant.
Can I use log base 10?
Yes, but change R to 1.987 cal/mol·K and convert the logarithm consistently.
How do I find ΔH from data?
Plot ln K versus 1/T; slope = -ΔH/R.