Vapour Pressure of Solutions of Solids in Liquids — Revision Notes

⚡ 30-Second Revision

Vapour Pressure Lowering — $P_A < P_A^0$ for solution with non-volatile solute.
Raoult's Law — $P_A = x_A P_A^0$
Lowering of VP — $Delta P = P_A^0 - P_A$
Relative Lowering of VP — $\frac{Delta P}{P_A^0} = \frac{P_A^0 - P_A}{P_A^0} = x_B$
Mole Fraction of Solute — $x_B = \frac{n_B}{n_A + n_B}$
Molar Mass Determination (dilute soln) — $\frac{P_A^0 - P_A}{P_A^0} \approx \frac{w_B M_A}{M_B w_A}$
Colligative Property — Depends on number of solute particles, not nature.
Non-volatile Solute — Does not vaporize significantly.

2-Minute Revision

The vapour pressure of a solution containing a non-volatile solid solute is always lower than that of the pure solvent at the same temperature. This occurs because the solute particles occupy a portion of the liquid surface, reducing the number of solvent molecules that can escape into the vapour phase.

Raoult's Law quantifies this: the vapour pressure of the solvent in the solution ($P_A$) is directly proportional to its mole fraction ($x_A$) in the solution, given by $P_A = x_A P_A^0$. The lowering of vapour pressure ($Delta P = P_A^0 - P_A$) is a colligative property, meaning it depends only on the number of solute particles.

The relative lowering of vapour pressure ($rac{Delta P}{P_A^0}$) is equal to the mole fraction of the solute ($x_B$). This relationship is crucial for determining the molar mass of unknown non-volatile solutes, especially in dilute solutions where approximations can be made.

Remember to account for the van't Hoff factor ($i$) for electrolytic solutes.

5-Minute Revision

To thoroughly revise the vapour pressure of solutions with non-volatile solutes, start by solidifying the core concept: the presence of non-volatile solute particles at the liquid surface physically obstructs some solvent molecules from escaping into the vapour phase, thereby reducing the rate of evaporation and leading to a lower equilibrium vapour pressure.

This is a dynamic equilibrium shift. Quantitatively, Raoult's Law states $P_A = x_A P_A^0$, where $P_A$ is the solution's vapour pressure, $x_A$ is the solvent's mole fraction, and $P_A^0$ is the pure solvent's vapour pressure.

The absolute lowering of vapour pressure is $Delta P = P_A^0 - P_A$. The most important form is the relative lowering of vapour pressure, $rac{Delta P}{P_A^0} = x_B$, which equals the mole fraction of the solute.

This equation highlights that vapour pressure lowering is a colligative property, dependent on the number of solute particles. For practical applications, particularly in determining the molar mass ($M_B$) of an unknown non-volatile solute, we use the expanded form for dilute solutions: $rac{P_A^0 - P_A}{P_A^0} = \frac{w_B M_A}{M_B w_A}$, where $w$ represents mass and $M$ represents molar mass, with subscripts A for solvent and B for solute.

Practice numerical problems involving these formulas, ensuring correct calculation of mole fractions and careful unit handling. Also, be prepared for conceptual questions on ideal vs. non-ideal solutions and the effect of electrolytes (using the van't Hoff factor, $i$, to modify $x_B$ to $i cdot x_B$).

Prelims Revision Notes

Vapour Pressure of Solutions (Non-volatile Solute)

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Definition — Vapour pressure of a solution with a non-volatile solute is *lower* than that of the pure solvent at the same temperature.

* Reason: Solute particles occupy surface area, reducing solvent evaporation rate.

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Raoult's Law (for non-volatile solute)

* The partial vapour pressure of the solvent in solution ($P_A$) is directly proportional to its mole fraction ($x_A$) in the solution. * Formula: $P_A = x_A P_A^0$ * $P_A$: Vapour pressure of solvent in solution * $x_A$: Mole fraction of solvent * $P_A^0$: Vapour pressure of pure solvent

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Lowering of Vapour Pressure ($Delta P$)

* $Delta P = P_A^0 - P_A$ * Substitute Raoult's Law: $Delta P = P_A^0 - x_A P_A^0 = P_A^0 (1 - x_A)$ * Since $x_A + x_B = 1$, then $1 - x_A = x_B$ (mole fraction of solute). * So, $Delta P = x_B P_A^0$

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Relative Lowering of Vapour Pressure

* Ratio of lowering of VP to pure solvent VP: $\frac{Delta P}{P_A^0} = \frac{P_A^0 - P_A}{P_A^0}$ * Key Result: $\frac{P_A^0 - P_A}{P_A^0} = x_B$ (Relative lowering of VP equals mole fraction of solute).

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Mole Fraction Calculations

* $x_A = \frac{n_A}{n_A + n_B}$ (solvent) * $x_B = \frac{n_B}{n_A + n_B}$ (solute) * $n = \frac{\text{mass}}{\text{molar mass}}$

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Molar Mass Determination of Solute ($M_B$)

* Using $\frac{P_A^0 - P_A}{P_A^0} = \frac{n_B}{n_A + n_B}$ * For dilute solutions ($n_B ll n_A$): $\frac{P_A^0 - P_A}{P_A^0} \approx \frac{n_B}{n_A} = \frac{w_B/M_B}{w_A/M_A} = \frac{w_B M_A}{M_B w_A}$ * Rearrange to solve for $M_B$: $M_B = \frac{w_B M_A}{w_A} \times \frac{P_A^0}{P_A^0 - P_A}$

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Colligative Property — Vapour pressure lowering depends only on the *number* of solute particles, not their identity.

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Electrolytes — For ionic solutes, use the van't Hoff factor ($i$) to account for dissociation. Effective moles of solute = $i \times n_B$. So, $x_B = \frac{i n_B}{n_A + i n_B}$.

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Ideal Solutions — Obey Raoult's Law over all concentrations. Intermolecular forces A-A, B-B, A-B are similar.

Key Points for NEET:

Master formula application for $P_A$, $x_B$, and $M_B$.
Understand the qualitative effect of adding non-volatile solute.
Be careful with units and calculations.
Remember $P_A^0$ for water at $100^circ C$ is $760,\text{mmHg}$ or $1,\text{atm}$.

Vyyuha Quick Recall

To remember Raoult's Law for non-volatile solutes and its effect: 'VAPOUR LOWERS, SOLUTE SHARES'

VAPOUR LOWERS — Vapour pressure of solution is lower than pure solvent.
SOLUTE SHARES — Solute particles 'share' the surface, reducing solvent escape.
LAW — $P_A = x_A P_A^0$ (Pressure of A = mole fraction of A * pure pressure of A)
RELATIVE — $\frac{Delta P}{P_A^0} = x_B$ (Relative lowering = mole fraction of Solute B)