Q.The value of Henry's constant $K_H$ is _____________.

Concept: Henry's Law relates the partial pressure of a gas to its molar concentration (or mole fraction) in solution.

Henry's Law is written as $p = K_H \cdot x$, where $p$ is the partial pressure of the gas, $x$ is its mole fraction in solution, and $K_H$ is Henry's constant.

Rearranging: $x = \frac{p}{K_H}$. For a fixed partial pressure, a larger $K_H$ means a smaller mole fraction in solution — that is, lower solubility. Conversely, a smaller $K_H$ allows more gas to dissolve, meaning higher solubility. …

Henry's Law connects the partial pressure of a gas above a liquid to its concentration (or mole fraction) in the liquid at equilibrium. The law is usually written as

where $p$ is the partial pressure of the gas, $x$ is its mole fraction in solution, and $K_H$ is Henry's constant for that particular gas–solvent pair at a given temperature.

The key insight is to understand what $K_H$ means physically. Rearranging the equation gives

This tells us that for a fixed partial pressure $p$, a larger $K_H$ produces a smaller mole fraction $x$ in solution. In other words, you need more pressure to dissolve the same amount of gas when $K_H$ is large. That's the signature of a gas that doesn't want to dissolve easily—low solubility.

Conversely, a gas with high solubility dissolves readily even at low pressure, which corresponds to a small $K_H$.

Let's walk through the options:

1. Option (i): greater for gases with higher solubility.

   If a gas is highly soluble, a small pressure suffices to dissolve a large amount, so $x$ is large for small $p$. That makes $K_H = p/x$ small, not large. This contradicts the claim.

2. Option (ii): greater for gases with lower solubility.

   A poorly soluble gas requires high pressure to achieve even a modest mole fraction in solution. The ratio $p/x$ is therefore large, meaning $K_H$ is large. This matches our physical reasoning perfectly. …

Concept: Henry's Law and Solubility of Gases

Henry's Law states that at a constant temperature, the amount of gas dissolved in a liquid is directly proportional to the partial pressure of that gas above the liquid.

Mathematically:

where:

• $P$ = partial pressure of the gas
• $K_H$ = Henry's constant
• $x$ = mole fraction of the gas in the solution (measure of solubility)

Method: Direct Proportionality Analysis

Steps:

1. Identify the relationship

   From Henry's Law: $P = K_H \cdot x$

   Rearranging: $K_H = \frac{P}{x}$

2. Interpret the variables

   • $x$ (mole fraction) represents solubility — higher $x$ means more gas dissolved.
   • $K_H$ is in the denominator of the solubility expression.

3. Apply the inverse logic …

Let’s break this down step-by-step.

The Concept: Henry’s Law

Henry’s law states:

At constant temperature, the solubility of a gas in a liquid is directly proportional to the partial pressure of the gas above the liquid.

Mathematically:

Where:

• $p$ = partial pressure of the gas above the liquid
• $x$ = mole fraction of the gas in the liquid (a measure of solubility)
• $K_H$ = Henry’s constant (depends on the gas, solvent, and temperature)

The Key Relationship

From the equation:

• For a fixed pressure $p$, higher $K_H$ means lower $x$ (lower solubility).
• Lower $K_H$ means higher $x$ (higher solubility).

✓ Conclusion: $K_H$ is greater for gases with lower solubility.

So the correct answer is (ii).

Common Mistakes Students Make

✗ Mistake 1: Confusing direct and inverse proportionality

• What they think: “If solubility is high, $K_H$ should be high.”
• Why it’s wrong: They misread the equation $p = K_H x$. For fixed $p$, $K_H$ and $x$ are inversely related.
• How to avoid: Always rearrange the formula: $x = p / K_H$. Then ask: “If $K_H$ increases, what happens to $x$?” — it decreases.

✗ Mistake 2: Thinking $K_H$ is constant for all gases

• What they think: “Henry’s constant is a constant, so it’s the same for every gas.”
• Why it’s wrong: $K_H$ is specific to each gas–solvent pair and varies with temperature. It is not universal.
• How to avoid: Remember: “Constant” in Henry’s law means constant for a given gas and solvent at a given temperature, not across all gases.

✗ Mistake 3: Ignoring the effect of temperature

• What they think: “$K_H$ doesn’t change.” …