Q.The mole fraction of a gas dissolved in water at $298\ \text{K}$ and a partial pressure of $1\ \text{bar}$ is found to be $2 \times 10^{-5}$. Calculate the Henry's law constant of the gas at this temperature.

Henry's law describes the equilibrium reached when a gas dissolves in a liquid: at a fixed temperature, the amount

of gas dissolved is directly proportional to the partial pressure of that gas maintained above the liquid,

where $p$ is the gas's partial pressure, $x$ is its mole fraction actually dissolved in the liquid, and $K_H$ is

the Henry's law constant — a proportionality constant characteristic of the particular gas-solvent pair and

temperature. A plot of $p$ against $x$ is a straight line through the origin, and a larger $K_H$ corresponds to

lower solubility, since a greater pressure is then needed to dissolve the same mole fraction.

Gas solubility depends on the identity of both the gas and the solvent, and — importantly — falls as temperature

rises, since dissolving a gas is normally exothermic, so by Le Chatelier's principle warming the liquid shifts the

dissolution equilibrium back toward undissolved gas (equivalently, $K_H$ increases with temperature). This

explains why warmer water holds less dissolved oxygen, stressing aquatic life, and why gas solubility calculations

in this chapter always specify a fixed temperature. …