Question

At a given temperature and pressure nitrogen gas is more soluble in water than helium gas. Which one of them has a higher value of ${{\text{K}}_{\text{H}}}$ ?

Answer 1

To solve this question, it is required to have knowledge about the solubility of gas and the factors it depends on. According to Henry’s law, the solubility of gas depends upon the pressure of the gas and the Henry’s constant, i.e. ${{\text{K}}_{\text{H}}}$.

Complete step by step answer:
As we know, at a specific temperature, Henry’s law states that the solubility of a gas in a liquid is directly proportional to the pressure of the gas above it. The proportionality is replaced by a constant known as Henry’s constant. It can be written as:
${\text{Solubility = }}{{\text{K}}_{\text{H}}} \times {{\text{P}}_{\text{g}}}$ where ${{\text{P}}_{\text{g}}}$ is the pressure of gas. (Eq. 1)
In the question, it is given that the temperature and pressure is constant. This means that, according to Henry’s law the solubility of the gas will only be dependent upon Henry’s constant, i.e. ${{\text{K}}_{\text{H}}}$ . So, the Eq. 1 can be rewritten as:
${\text{Solubility }} \propto {\text{ }}{{\text{K}}_{\text{H}}}$
It is given in the question that, the solubility of nitrogen gas is higher than the solubility of helium gas in water. So, this means that Henry's constant for nitrogen gas will be more than that for helium gas.
$\therefore$ The ${{\text{K}}_{\text{H}}}$ value will be higher for nitrogen gas than it will be for helium gas.

Note: If there are two gases in the mixture, then the solubility of the gas will also be dependent on the amount of gas present, i.e. the mole fraction of the gas. But since in this question, the gases are separate, i.e. there is no mention of a mixture of gases. So, the solubility of the gas will only depend on its pressure and Henry’s constant.