Use the van ’t Hoff equation to see how an equilibrium constant changes with temperature: from K₁ at T₁ and a second temperature T₂, solve for K₂ or for ΔH°.
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From the article Van't Hoff Equation — How the Equilibrium Constant Changes with Temperature.
Question: A reaction has ΔH° = +58.0 kJ mol⁻¹ and K = 0.113 at 298 K. Estimate K at 348 K.
Prediction first: endothermic, temperature raised → K must increase.
Step 1 — put ΔH° in joules: ΔH° = 58 000 J mol⁻¹
ΔH°/R = 58 000 / 8.314 = 6976.2
Step 2 — the reciprocal temperatures:
1/T₁ = 1/298 = 3.355705 × 10⁻³
1/T₂ = 1/348 = 2.873563 × 10⁻³
(1/T₁ − 1/T₂) = 4.82142 × 10⁻⁴
Step 3 — multiply:
ln(K₂/K₁) = 6976.2 × 4.82142 × 10⁻⁴ = 3.3635
Step 4 — undo the logarithm:
K₂/K₁ = e³·³⁶³⁵ = 28.89
K₂ = 0.113 × 28.89 = 3.2646
K at 348 K ≈ 3.26 — it rose, as predicted, by a factor of about 29 for a 50 K rise.
Worked in full in Van't Hoff Equation — How the Equilibrium Constant Changes with Temperature.
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