All question types · Thermodynamics

van 't Hoff: K at a new temperature

UKChO Round 2 · IChO · unreviewed

ln(K₂/K₁) = −(ΔH°/R)(1/T₂ − 1/T₁).

Practise this with fresh numbers

Worked example

K = 33.2 at 305 K, and ΔH° = 73.9 kJ mol⁻¹. Estimate K at 432 K.

1. van 't Hoff equation (two-point): solve for K₂
$K_2 = K_1\exp\!\left[-\dfrac{\Delta H^\circ}{R}\left(\dfrac{1}{T_2}-\dfrac{1}{T_1}\right)\right]$
= 1.745 × 10⁵

Answer: K₂ = 1.74 × 10⁵

Method

ln(K₂/K₁) = −(ΔH°/R)(1/T₂ − 1/T₁). Raising T favours the endothermic direction.

Common mistakes

Sign slip in the van 't Hoff exponent: for an endothermic reaction K must increase with temperature.

Formulas used

van 't Hoff equation (two-point)
$\ln\dfrac{K_2}{K_1} = -\dfrac{\Delta H^\circ}{R}\left(\dfrac{1}{T_2}-\dfrac{1}{T_1}\right)$

Practise this with fresh numbers