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Exercises · 1.11

Q.Why do gases always tend to be less soluble in liquids as the temperature is raised?

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Gas solubility decreases with temperature because dissolution is exothermic—heat is released when gas molecules enter the liquid. Raising temperature shifts the equilibrium backward, driving dissolved gas out.

Why heating drives gases out of solution

When a gas dissolves in a liquid, the process nearly always releases energy. Think about what happens at the molecular level: gas molecules in the vapor phase are far apart, moving freely with essentially no intermolecular forces acting on them. When they enter the liquid, they become surrounded by solvent molecules and form new interactions—hydrogen bonds with water, dipole interactions, or at minimum van der Waals forces. Forming these attractions releases energy as heat.

This makes gas dissolution an exothermic process. The equilibrium we're dealing with is:

Gas (in air)⇌Gas (dissolved in liquid)+Heat\text{Gas (in air)} \rightleftharpoons \text{Gas (dissolved in liquid)} + \text{Heat}

Le Chatelier's principle tells us exactly what happens when we add heat to an exothermic equilibrium: the system shifts to counteract the disturbance. If we raise the temperature, we're effectively adding heat to the right side of the equation. The equilibrium responds by shifting left—toward the gaseous state—to absorb that excess energy.

The thermodynamic picture

Henry's Law quantifies gas solubility:

p=KH⋅xp = K_H \cdot x

where pp is the partial pressure of the gas, xx is its mole fraction in solution, and KHK_H is Henry's constant. The key insight: KHK_H increases with temperature for nearly all gas-liquid systems.

A larger KHK_H means you need a higher partial pressure to maintain the same dissolved concentration. Equivalently, at fixed pressure, the mole fraction xx must decrease. The gas becomes less soluble.

We can see this through the van 't Hoff equation, which relates how an equilibrium constant changes with temperature:

dln⁡KdT=ΔH∘RT2\frac{d \ln K}{dT} = \frac{\Delta H^\circ}{RT^2}

For gas dissolution, ΔH∘<0\Delta H^\circ < 0 (exothermic), so dln⁡KHdT>0\frac{d \ln K_H}{dT} > 0. Henry's constant climbs as temperature rises.

Everyday observations

  1. Warm soda goes flat faster. Carbon dioxide escapes more readily from a warm soft drink than a cold one. Refrigeration keeps the CO2\text{CO}_2 dissolved.

  2. Boiling drives out dissolved air. When you heat water, you see bubbles forming well before it boils—that's dissolved air (mostly N2\text{N}_2 and O2\text{O}_2) being expelled as solubility drops.

  3. Thermal pollution harms aquatic life. Power plants discharge warm water into rivers. The elevated temperature reduces dissolved oxygen, stressing fish and other organisms that depend on it. …

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