Q.[Note: two or more options may be correct] Which of the following factor(s) affect the solubility of a gaseous solute in the fixed volume of liquid solvent?

The key idea is Henry’s Law: at constant temperature, the solubility of a gas in a liquid is directly proportional to the partial pressure of the gas above the liquid. Solubility also depends on the nature of the solute (different gases have different Henry’s constants) and on temperature (solubility of gases generally decreases as temperature rises).

Reasoning steps:

1. Nature of solute — Henry’s constant $k_H$ is specific to each gas–solvent pair, so solubility varies with the gas.
2. Temperature — For most gases, dissolution is exothermic; increasing temperature shifts equilibrium toward the gas phase, reducing solubility.
3. Pressure — From Henry’s law $C = k_H P$, solubility increases linearly with partial pressure at fixed $T$. …

The key to this question is understanding Henry’s Law, which governs the solubility of gases in liquids. Henry’s Law states that at a constant temperature, the concentration (or solubility) of a gas in a liquid is directly proportional to the partial pressure of that gas above the liquid. Mathematically:

where $C$ is the solubility (often in mol/L), $P$ is the partial pressure of the gas, and $k_H$ is the Henry’s law constant — which depends on the nature of the gas and the solvent, and on temperature.

So, solubility is not a fixed number; it changes with three things: the identity of the gas and liquid (nature), the temperature, and the pressure. The question asks: which factors affect solubility in a fixed volume of liquid solvent? That means the solvent volume is constant, but the solute gas can vary.

Let’s examine each factor:

1. Nature of solute (a) — Different gases have different $k_H$ values. For example, $CO_2$ is much more soluble in water than $O_2$ at the same temperature and pressure. So the nature of the gaseous solute definitely affects solubility. This factor is always relevant.

2. Temperature (b) — For most gases, solubility in liquids decreases as temperature increases (think of a warm soda going flat faster). Henry’s constant $k_H$ changes with temperature. So temperature always affects solubility.

3. Pressure (c) — According to Henry’s Law, solubility is directly proportional to pressure. If you increase the pressure of the gas above the liquid, more gas dissolves. So pressure also affects solubility.

Now, the question is tricky because it says “in the fixed volume of liquid solvent” — that just means the amount of liquid doesn’t change, but it doesn’t restrict which variables are held constant. The options list combinations of factors under different conditions:

• (i) says (a) and (c) at constant T — that is, nature and pressure matter when temperature is fixed. That’s true, but it ignores temperature itself as a factor.
• (ii) says (a) and (b) at constant P — nature and temperature matter when pressure is fixed. That’s also true, but it ignores pressure.
• (iii) says (b) and (c) only — temperature and pressure matter, but it leaves out nature of solute. That’s false because different gases have different solubilities even at same T and P.
• (iv) says (c) only — only pressure matters. That’s false because nature and temperature also matter. …

Concept: Factors Affecting Solubility of a Gas in a Liquid (Henry’s Law)

The solubility of a gas in a liquid depends on three main factors:

• Nature of solute and solvent (intermolecular forces) — affects Henry's constant $k_H$
• Temperature (solubility decreases with increase in temperature for gases) — also affects $k_H$
• Pressure (solubility increases with increase in pressure, as per Henry’s Law)

Method: Direct Application of Henry’s Law + Factual Recall

Steps:

1. Recall Henry’s Law At constant temperature, the solubility of a gas in a liquid is directly proportional to the partial pressure of the gas above the liquid:

where $S$ = solubility, $k_H$ = Henry’s constant (depends on nature of gas and solvent, and on temperature), $P$ = pressure.

2. Identify the factors from Henry’s Law

   • Nature of solute → affects $k_H$
   • Pressure → directly affects $S$
   • Temperature → affects $k_H$ (solubility decreases as temperature rises)

3. Evaluate each option as a self-contained true/false statement about which factors matter under the stated constant condition

   • (i) “(a) and (c) at constant T” → At fixed temperature, both the nature of the solute (via $k_H$) and the pressure genuinely affect solubility. True.
   • (ii) “(a) and (b) at constant P” → At fixed pressure, both the nature of the solute and the temperature genuinely affect solubility (through $k_H$). True. …

Here’s a breakdown of the common mistakes students make on this concept — factors affecting the solubility of a gas in a liquid — and how to avoid each.

✗ Mistake 1: Thinking “nature of solute” never matters

Why it happens:

Students memorise “solubility of gas depends on temperature and pressure” and forget that the nature of the gas (its chemical identity) determines how easily it dissolves. For example, $\text{CO}_2$ is much more soluble in water than $\text{O}_2$ at the same $T$ and $P$.

How to avoid:

Remember Henry’s law:

Here, $k_H$ (Henry’s constant) is different for each gas — it depends on the nature of the solute. So nature of solute always matters, regardless of $T$ or $P$.

✗ Mistake 2: Assuming pressure only matters if volume changes

Why it happens:

Students think “fixed volume of liquid” means pressure has no effect. But Henry’s law directly relates solubility to partial pressure of the gas above the liquid — volume of liquid is irrelevant.

How to avoid:

Solubility of a gas is proportional to its partial pressure (not to the container volume). Even in a fixed volume of solvent, increasing $P$ forces more gas molecules into solution.

✗ Mistake 3: Choosing only (b) and (c) — missing (a)

Why it happens:

Students see “temperature and pressure” as the only two factors and ignore the nature of solute. They pick option (iii) without checking if (a) is also correct.

How to avoid:

Always list all three factors mentally:

• Nature of solute ✓ (different gases have different $k_H$)
• Temperature ✓ (solubility decreases as $T$ increases)
• Pressure ✓ (solubility increases as $P$ increases) …