Vapour Pressure of Liquid Solutions — Revision Notes

⚡ 30-Second Revision

Vapour Pressure (VP) — Pressure by vapour in equilibrium with liquid.
Raoult's Law (Non-volatile solute) — $P_s = X_{solvent} P_{solvent}^0$.
Relative Lowering of VP — $\frac{P_{solvent}^0 - P_s}{P_{solvent}^0} = X_{solute}$.
Raoult's Law (Volatile solutes) — $P_A = X_A P_A^0$, $P_B = X_B P_B^0$.
Total VP — $P_{total} = P_A + P_B = X_A P_A^0 + X_B P_B^0$.
Ideal Solution — Obeys Raoult's Law, $\Delta H_{mixing} = 0$, $\Delta V_{mixing} = 0$, A-B forces similar to A-A, B-B.
Positive Deviation — $P_{total} > P_{ideal}$, A-B forces < A-A/B-B, $\Delta H_{mixing} > 0$, $\Delta V_{mixing} > 0$. (e.g., Ethanol + Water)
Negative Deviation — $P_{total} < P_{ideal}$, A-B forces > A-A/B-B, $\Delta H_{mixing} < 0$, $\Delta V_{mixing} < 0$. (e.g., Acetone + Chloroform)
Azeotropes — Constant boiling mixtures, cannot be separated by fractional distillation.

- Minimum Boiling Azeotrope: From large positive deviation. - Maximum Boiling Azeotrope: From large negative deviation.

2-Minute Revision

Vapour pressure is the pressure exerted by a vapour in equilibrium with its liquid. For a pure liquid, it increases with temperature. When a non-volatile solute is added, the vapour pressure of the solution decreases, a phenomenon explained by Raoult's Law: $P_s = X_{solvent} P_{solvent}^0$. The relative lowering of vapour pressure, $\frac{P_{solvent}^0 - P_s}{P_{solvent}^0}$, is equal to the mole fraction of the solute ($X_{solute}$), a key colligative property used to find molar mass.

For solutions with two volatile components, each contributes to the total vapour pressure according to its mole fraction and pure vapour pressure: $P_{total} = X_A P_A^0 + X_B P_B^0$. Ideal solutions strictly follow Raoult's Law, with no heat or volume change on mixing, and similar intermolecular forces.

Non-ideal solutions deviate. Positive deviations occur when solute-solvent interactions are weaker, leading to higher vapour pressure, positive \Delta H_{mixing} and \Delta V_{mixing}. Negative deviations occur when solute-solvent interactions are stronger, leading to lower vapour pressure, negative \Delta H_{mixing} and \Delta V_{mixing}.

Significant deviations can form azeotropes, which are constant boiling mixtures (minimum boiling from positive deviation, maximum boiling from negative deviation) that cannot be separated by simple distillation.

5-Minute Revision

Let's quickly review the critical aspects of vapour pressure of liquid solutions for NEET. Firstly, remember that vapour pressure is the equilibrium pressure of vapour above a liquid. For pure liquids, it's temperature-dependent.

When we introduce a non-volatile solute, the vapour pressure of the solvent is lowered. This is quantitatively described by Raoult's Law: $P_s = X_{solvent} P_{solvent}^0$. A direct consequence is the relative lowering of vapour pressure, $\frac{P_{solvent}^0 - P_s}{P_{solvent}^0} = X_{solute}$, which is a colligative property and often used to determine the molar mass of an unknown solute.

For example, if pure water has a VP of 20 mmHg and a solution has 18 mmHg, the relative lowering is $(20-18)/20 = 0.1$, so the mole fraction of solute is 0.1.

When both components are volatile, each contributes to the total vapour pressure. Raoult's Law states $P_A = X_A P_A^0$ and $P_B = X_B P_B^0$. The total pressure is $P_{total} = P_A + P_B$. For instance, if $P_A^0 = 100$ mmHg and $P_B^0 = 200$ mmHg, and $X_A = 0.5$, then $P_{total} = (0.5 \times 100) + (0.5 \times 200) = 50 + 100 = 150$ mmHg.

Solutions are classified as ideal or non-ideal. Ideal solutions obey Raoult's Law perfectly, with \Delta H_{mixing} = 0 and \Delta V_{mixing} = 0, implying similar intermolecular forces (e.g., benzene-toluene).

Non-ideal solutions deviate. Positive deviations occur when A-B interactions are weaker than A-A and B-B, leading to higher vapour pressure, \Delta H_{mixing} > 0, and \Delta V_{mixing} > 0 (e.g., ethanol-water).

Negative deviations occur when A-B interactions are stronger, resulting in lower vapour pressure, \Delta H_{mixing} < 0, and \Delta V_{mixing} < 0 (e.g., acetone-chloroform).

Finally, remember azeotropes. These are constant boiling mixtures formed by non-ideal solutions. Minimum boiling azeotropes arise from large positive deviations (e.g., 95.6% ethanol-water), having a boiling point lower than either pure component. Maximum boiling azeotropes arise from large negative deviations (e.g., 68% nitric acid-water), having a boiling point higher than either pure component. Crucially, azeotropes cannot be separated by simple fractional distillation.

Prelims Revision Notes

1
Vapour Pressure (VP) — Pressure exerted by vapour in equilibrium with liquid at a given temperature. Increases with temperature.
2
Raoult's Law for Non-Volatile Solute — When a non-volatile solute is added to a volatile solvent, the vapour pressure of the solution ($P_s$) is directly proportional to the mole fraction of the solvent ($X_{solvent}$) and the vapour pressure of the pure solvent ($P_{solvent}^0$). Formula: $P_s = X_{solvent} P_{solvent}^0$.
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Lowering of Vapour Pressure — $P_{solvent}^0 - P_s$.
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Relative Lowering of Vapour Pressure — $\frac{P_{solvent}^0 - P_s}{P_{solvent}^0} = X_{solute}$. This is a colligative property, dependent only on the number of solute particles. Used to calculate molar mass of non-volatile solutes.
5
Raoult's Law for Volatile Solute Mixtures — For a binary solution of volatile liquids A and B, the partial vapour pressure of each component is $P_A = X_A P_A^0$ and $P_B = X_B P_B^0$. The total vapour pressure is $P_{total} = P_A + P_B = X_A P_A^0 + X_B P_B^0$.
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Composition of Vapour Phase — The mole fraction of a component in the vapour phase ($Y_A$) can be calculated using Dalton's Law of Partial Pressures: $Y_A = \frac{P_A}{P_{total}}$.
7
Ideal Solutions

* Obey Raoult's Law over the entire concentration range. * Intermolecular forces (A-B) are similar to (A-A) and (B-B). * $\Delta H_{mixing} = 0$ (no heat change). * $\Delta V_{mixing} = 0$ (no volume change). * Examples: Benzene + Toluene, n-Hexane + n-Heptane.

1
Non-Ideal Solutions (Deviations from Raoult's Law)

* Positive Deviation: * A-B intermolecular forces are weaker than A-A and B-B. * Molecules escape more easily, so $P_{total} > (X_A P_A^0 + X_B P_B^0)$. * $\Delta H_{mixing} > 0$ (endothermic).

* $\Delta V_{mixing} > 0$ (volume expansion). * Examples: Ethanol + Water, Acetone + Ethanol, Carbon Disulphide + Acetone. * Negative Deviation: * A-B intermolecular forces are stronger than A-A and B-B.

* Molecules escape less easily, so $P_{total} < (X_A P_A^0 + X_B P_B^0)$. * $\Delta H_{mixing} < 0$ (exothermic). * $\Delta V_{mixing} < 0$ (volume contraction). * Examples: Acetone + Chloroform, Nitric acid + Water, Acetic acid + Pyridine.

1
Azeotropes (Constant Boiling Mixtures)

* Liquid mixtures that boil at a constant temperature without changing composition. * Cannot be separated by fractional distillation. * Minimum Boiling Azeotropes: Formed by solutions showing large positive deviations (e.g., 95.6% ethanol in water, boils below pure ethanol or water). * Maximum Boiling Azeotropes: Formed by solutions showing large negative deviations (e.g., 68% nitric acid in water, boils above pure nitric acid or water).

Vyyuha Quick Recall

For deviations from Raoult's Law:

Positive Deviation: People Drink Ethanol & Water (Ethanol + Water). They feel Weaker (A-B forces weaker), get Hot ($\Delta H_{mixing} > 0$), and Volume Increases ($\Delta V_{mixing} > 0$). Their Vapour Pressure is High.

Negative Deviation: No Drinking Acetone & Chloroform (Acetone + Chloroform). They feel Stronger (A-B forces stronger), get Cold ($\Delta H_{mixing} < 0$), and Volume Decreases ($\Delta V_{mixing} < 0$). Their Vapour Pressure is Low.