The incorrect statement among the options given is Option A.

Explanation:

$$\mathrm{K}_{\mathrm{H}}$$ is known as Henry's Law constant, and the law states that the solubility of a gas in a liquid at a given temperature is directly proportional to the pressure of the gas above the liquid. The mathematical expression for Henry's Law is given by:

$$ C = \mathrm{K}_{\mathrm{H}} \cdot P $$

where $$C$$ is the concentration of gas dissolved, $$P$$ is the partial pressure of the gas, and $$\mathrm{K}_{\mathrm{H}}$$ is Henry's Law constant.

According to this relationship, the higher the value of $$\mathrm{K}_{\mathrm{H}}$$, the lower the solubility of the gas in the solvent. This is because a higher $$\mathrm{K}_{\mathrm{H}}$$ means that a higher pressure is required to dissolve the same amount of gas. Therefore, the statement in Option A is incorrect as it contradicts Henry's Law.

Let's briefly look at the other options:

Option B is correct as the $$\mathrm{K}_{\mathrm{H}}$$ value indeed depends on the nature of both the solute (gas) and the solvent. This is due to differences in interactions between different gases and solvents.

Option C is also correct. The solubility of gases typically decreases with an increase in temperature due to the increased kinetic energy of gas molecules, which makes them less likely to be captured by solvent molecules. Therefore, $$\mathrm{K}_{\mathrm{H}}$$ is indeed temperature dependent.

Option D might seem tricky, but it is also correct. Henry's Law itself indicates that solubility ($$C$$) is proportional to the partial pressure of the gas ($$P$$). However, $$\mathrm{K}_{\mathrm{H}}$$ itself remains constant for a given gas and solvent at a constant temperature, regardless of changes in pressure. The value does not change with the pressure; instead, it dictates how the solubility changes with pressure. Thus, Option D is technically correct in its wording, not suggesting that $$\mathrm{K}_{\mathrm{H}}$$ changes with pressure, but rather that solubility does as governed by a constant $$\mathrm{K}_{\mathrm{H}}$$. Therefore, interpreting Option D as describing the relationship governed by Henry’s Law (not that $$\mathrm{K}_{\mathrm{H}}$$ itself changes with pressure) makes it a correct statement.

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