p = KH × x. Gas solubility decreases with temperature.

Henry's Law — Why Scuba Divers Get Bends

Question

A scuba diver is breathing compressed air at a depth where the pressure is 4 atm. When he surfaces too quickly, he experiences joint pain and dizziness. Using Henry’s Law, explain why this happens and calculate the mole fraction of nitrogen dissolved in blood at 4 atm, given $K_H$ for N₂ in blood ≈ 8.65 × 10⁴$ atm at body temperature.

Solution — Step by Step

Henry’s Law: the amount of gas dissolved in a liquid is directly proportional to the partial pressure of that gas above the liquid.

p = K_H \cdot x

Here, $p$ is partial pressure of the gas, $K_H$ is Henry’s Law constant (unique to each gas-solvent pair at a given temperature), and $x$ is the mole fraction of dissolved gas.

Air is approximately 78% nitrogen by volume, so the partial pressure of N₂ at total pressure 4 atm:

p_{N_2} = 0.78 \times 4 = 3.12 \text{ atm}

We use partial pressure, not total pressure — this is where most students make the first error.

Rearranging $p = K_H \cdot x$ :

x = \frac{p}{K_H} = \frac{3.12}{8.65 \times 10^4}

x_{N_2} = 3.6 \times 10^{-5}

At the surface (1 atm), the same calculation gives $x = 9.0 \times 10^{-6}$ — four times less dissolved nitrogen.

At depth, the diver’s blood dissolves four times more nitrogen than normal. When he surfaces slowly, the excess nitrogen escapes gradually through the lungs — no problem. Surfacing fast means the pressure drops suddenly, and dissolved nitrogen comes out of solution as bubbles inside the blood and tissues, just like opening a soda bottle abruptly.

These bubbles lodge in joints and capillaries, causing the condition called decompression sickness (the bends).

Why This Works

Henry’s Law is essentially a proportionality law for dilute solutions of gases. At greater depth, the surrounding water exerts higher pressure, which forces more gas molecules into solution in the blood — the equilibrium shifts toward dissolution.

The key insight: solubility of a gas is not a fixed property. It depends entirely on the pressure above the solution. Raise the pressure, more gas dissolves; lower the pressure, it comes back out. Temperature works the opposite way — higher temperature means less gas dissolves (you’ve seen this when heating water: bubbles appear before boiling, that’s dissolved air escaping).

For JEE and NEET, remember that $K_H$ values are large numbers for sparingly soluble gases (like O₂, N₂) and small for highly soluble gases (like NH₃, SO₂, HCl). A large $K_H$ means a small mole fraction at a given pressure — the gas doesn’t like dissolving much.

Alternative Method — Using Concentration Ratio

Instead of calculating absolute mole fractions, many NEET questions ask us to compare solubilities at two pressures. Since $x \propto p$ (at constant temperature and same $K_H$ ):

\frac{x_2}{x_1} = \frac{p_2}{p_1}

If pressure doubles, dissolved gas doubles. If pressure drops to one-fourth (from 4 atm to 1 atm), dissolved nitrogen drops to one-fourth. This ratio approach is faster for MCQs and avoids dealing with large $K_H$ values.

In NEET MCQs, you’ll often be given two pressures and asked which scenario dissolves more gas. Skip the full calculation — just use the ratio. The answer follows directly from Henry’s Law since $K_H$ cancels out.

Common Mistake

Using total pressure instead of partial pressure. At 4 atm total, nitrogen’s partial pressure is 0.78 × 4 = 3.12 atm, not 4 atm. This appeared directly in NEET 2024 — options were designed to trap students who plug in 4 atm directly. Always identify which gas you’re working with and find its partial pressure first using its mole fraction in the mixture.

A related trap: students sometimes apply Henry’s Law to liquids (like ethanol-water mixtures) or to gases at very high pressures where the solution is no longer dilute. Henry’s Law only holds for dilute solutions of gases in liquids. For concentrated solutions, it breaks down — this is a board exam favourite for a 1-mark “state the limitations” question.

Final answer: $x_{N_2} = 3.6 \times 10^{-5}$ at 4 atm, compared to $9.0 \times 10^{-6}$ at 1 atm — four times higher, which is exactly why the bends occur during rapid ascent.

Question

Solution — Step by Step

Why This Works

Alternative Method — Using Concentration Ratio

Common Mistake

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