Henry's law — calculate solubility of gas in liquid at different pressures

Question

State Henry’s law. The solubility of a gas in water at 2 atm is 0.05 mol/L. Calculate its solubility at 5 atm at the same temperature.

(NCERT Class 12, Chapter 2)

Solution — Step by Step

Henry’s law states: The partial pressure of a gas above a solution is directly proportional to the mole fraction of the gas dissolved in the solution (at constant temperature):

p = K_H \cdot x

where $p$ is the partial pressure of the gas, $x$ is the mole fraction in solution, and $K_H$ is Henry’s law constant (units: pressure).

In simpler terms: higher pressure above the liquid → more gas dissolves.

Since temperature is constant, $K_H$ is the same in both cases. If solubility is proportional to pressure:

\frac{S_1}{p_1} = \frac{S_2}{p_2}

where $S$ is the solubility (concentration) and $p$ is the pressure.

Given: $S_1 = 0.05$ mol/L at $p_1 = 2$ atm. Find $S_2$ at $p_2 = 5$ atm.

S_2 = S_1 \times \frac{p_2}{p_1} = 0.05 \times \frac{5}{2} = \mathbf{0.125 \text{ mol/L}}

The solubility increases proportionally with pressure.

Why This Works

At higher pressure, more gas molecules hit the liquid surface per unit time, and more of them get captured by the solvent. Equilibrium shifts towards more dissolved gas. This linear relationship holds well for gases that do not react chemically with the solvent (like O $_2$ and N $_2$ in water).

Practical applications: carbonated drinks are bottled under high CO $_2$ pressure (Henry’s law keeps the gas dissolved). When you open the bottle, pressure drops and CO $_2$ escapes as bubbles.

Alternative Method — Using Mole Fraction Form

If the problem gives mole fraction instead of molarity:

p = K_H \cdot x \implies x = \frac{p}{K_H}

At 2 atm: $x_1 = 2/K_H$ . At 5 atm: $x_2 = 5/K_H$ . Ratio: $x_2/x_1 = 5/2 = 2.5$ . Same proportionality.

Henry’s law constant $K_H$ is different for every gas-solvent pair and increases with temperature (gases become less soluble at higher temperatures). This explains why warm soda goes flat faster. For CBSE/NEET, know these applications: scuba diving (N $_2$ dissolves at depth → bends on rapid ascent) and carbonated beverages.

Common Mistake

Students apply Henry’s law to gases that react with the solvent — like HCl, NH $_3$ , or SO $_2$ in water. Henry’s law applies best to gases with low solubility that do not chemically react with the solvent (O $_2$ , N $_2$ , He, Ar). For reactive gases, the actual solubility is much higher than Henry’s law predicts because the chemical reaction pulls more gas into solution.

Question

Solution — Step by Step

Why This Works

Alternative Method — Using Mole Fraction Form

Common Mistake

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