Temperature Changes and Equilibrium

Introduction

Temperature is special among common equilibrium disturbances because it can change the equilibrium constant itself. Heating favors the endothermic direction in the standard qualitative treatment, while cooling favors the exothermic direction. This statement concerns the new equilibrium composition, not merely a momentary change in reaction speed.

Core explanation

For a forward exothermic reaction, ΔrH° is negative. Raising temperature typically decreases K for that written direction, making its equilibrium less product-favored. For a forward endothermic reaction, ΔrH° is positive; raising temperature increases K and favors products. The reverse reaction has the opposite enthalpy sign, so both descriptions agree when the equation direction is changed correctly.

An approximate quantitative relation is d(ln K)/dT = ΔrH°/(RT²) when the standard reaction enthalpy is treated appropriately over the range. Its sign gives the qualitative rule: positive ΔrH° yields increasing K with T; negative ΔrH° yields decreasing K. For a modest interval with approximately constant enthalpy, ln(K₂/K₁) ≈ −ΔrH°/R(1/T₂ − 1/T₁). Use kelvin and consistent energy units.

Immediately after a temperature change, molecular rate constants of forward and reverse reactions may both change, often by different factors. The mixture's composition has not yet had time to respond, but the new K is different. The system then moves until Q equals that new K. It is misleading to describe heating solely as “speeding the forward reaction”; both directions can speed up while equilibrium shifts toward reactants.

The heat-as-reactant or heat-as-product mnemonic can help: for an endothermic forward reaction, treat heat as though it were on the reactant side, so heating favors products. It is only a mnemonic. Temperature is not a chemical species with an activity factor in K, and the van 't Hoff relation is the more precise basis.

Temperature effects may also change phase behavior or reaction mechanisms over a wide range. A simple ΔH sign prediction assumes the same reaction and phases remain relevant. Industrial process choices additionally balance yield against kinetics and energy cost.

Step-by-step reasoning

1. Identify the sign of forward reaction enthalpy. 2. For heating, predict K rises if endothermic and falls if exothermic. 3. For cooling, reverse the qualitative prediction. 4. Separate the final equilibrium shift from possible changes in both reaction rates.

Visual explanation

Draw K versus temperature curves: one rising for a forward endothermic reaction and one falling for a forward exothermic reaction, with the same written reaction maintained.

Real-world analogy

Changing the height of a valley changes where a rolling ball settles, not just how rapidly it moves. Temperature changes the thermodynamic equilibrium landscape as well as kinetic rates.

Real-world example

Ammonia synthesis is exothermic in the forward direction. Higher temperature can improve reaction speed but lowers the equilibrium ammonia fraction under otherwise comparable reactor conditions.

Why?

Why does heating an endothermic reaction raise K? The positive reaction enthalpy gives a positive temperature derivative of ln K in the van 't Hoff relation.

Common misconception

“A higher temperature always increases product yield.” It raises K only for a forward endothermic reaction; for an exothermic forward reaction it generally lowers K.

Worked example

For A ⇌ B with forward ΔrH° > 0, suppose K is 2.0 at a lower temperature. Heating at comparable phase conditions should increase K above 2.0, though the new numerical value requires enthalpy and temperature data. A mixture initially at the old equilibrium has Q = 2.0 immediately after heating, so Q < new K and net forward change follows.

Quick check

1. What happens to K when an exothermic forward reaction is heated? Answer: It generally decreases for that written direction, assuming the same reaction and phase regime.

Exam focus

Use the sign of ΔrH° for the written reaction. State that temperature changes K and avoid equating equilibrium preference with reaction speed.

Advanced insight

Reaction enthalpy can itself vary with temperature, so integrating the van 't Hoff relation over a broad interval may require heat-capacity data rather than a constant-ΔH approximation.

Summary

Heating raises K for a forward endothermic reaction and lowers it for a forward exothermic reaction. Temperature can alter both kinetics and the final thermodynamic equilibrium composition.

Practice questions

1. Does cooling favor products for an exothermic forward reaction? Answer: Usually yes; it increases K for that written direction. 2. Can both forward and reverse reactions become faster when temperature rises? Answer: Yes. Their rate changes need not be equal, and the equilibrium constant can also change. 3. Is heat written as an ordinary concentration factor in K? Answer: No. Temperature affects K, but heat is not a chemical activity term.