Relative Lowering of Vapour Pressure — Revision Notes

⚡ 30-Second Revision

Vapour Pressure ($P^0$) — Pressure of vapour above pure liquid.
Lowering of Vapour Pressure ($Delta P$) — $P^0 - P_s$.
Relative Lowering of Vapour Pressure (RLVP) — $rac{P^0 - P_s}{P^0}$.
Raoult's Law (for non-volatile solute) — $rac{P^0 - P_s}{P^0} = X_{solute}$.
Mole Fraction of Solute ($X_{solute}$) — $rac{n_{solute}}{n_{solute} + n_{solvent}}$.
Colligative Property — Depends on number of solute particles, not their nature.
Van't Hoff Factor ($i$) — For electrolytes, $rac{P^0 - P_s}{P^0} = i cdot X_{solute}$.

2-Minute Revision

Relative Lowering of Vapour Pressure (RLVP) is a colligative property, meaning it depends solely on the number of solute particles, not their identity. When a non-volatile solute is added to a pure solvent, it reduces the number of solvent molecules at the liquid surface, thereby decreasing the rate of evaporation.

This leads to a lower equilibrium vapour pressure for the solution ($P_s$) compared to the pure solvent ($P^0$). The difference, $P^0 - P_s$, is the lowering of vapour pressure. The relative lowering is defined as $rac{P^0 - P_s}{P^0}$.

According to Raoult's Law, for ideal dilute solutions, this relative lowering is equal to the mole fraction of the solute ($X_{solute}$). For electrolytes that dissociate or associate, the van't Hoff factor ($i$) must be included, modifying the formula to $rac{P^0 - P_s}{P^0} = i cdot X_{solute}$.

This property is crucial for determining the molar mass of unknown non-volatile solutes and forms the basis for understanding other colligative properties.

5-Minute Revision

Relative Lowering of Vapour Pressure (RLVP) is one of the four colligative properties, which are characteristics of solutions that depend on the concentration of solute particles, irrespective of their chemical nature.

The phenomenon begins with the concept of vapour pressure: in a closed system, a pure liquid establishes an equilibrium with its vapour, exerting a specific pressure ($P^0$). When a non-volatile solute is dissolved in this liquid, its particles occupy a portion of the liquid's surface.

This physical obstruction reduces the number of solvent molecules that can escape into the vapour phase, thus decreasing the rate of evaporation. Consequently, the equilibrium vapour pressure above the solution ($P_s$) becomes lower than that of the pure solvent ($P^0$).

The 'lowering' is $P^0 - P_s$. The 'relative lowering' is the ratio of this lowering to the pure solvent's vapour pressure: $rac{P^0 - P_s}{P^0}$.

Raoult's Law provides the quantitative basis, stating that for an ideal solution with a non-volatile solute, the vapour pressure of the solution is $P_s = P^0 cdot X_{solvent}$, where $X_{solvent}$ is the mole fraction of the solvent.

From this, we derive the key RLVP equation: $rac{P^0 - P_s}{P^0} = X_{solute}$, where $X_{solute}$ is the mole fraction of the solute. This equation highlights that RLVP is directly proportional to the mole fraction of the solute, confirming its colligative nature.

For solutions where the solute undergoes dissociation (like NaCl, $i=2$) or association, the effective number of particles changes, and the van't Hoff factor ($i$) must be incorporated: $rac{P^0 - P_s}{P^0} = i cdot X_{solute}$.

RLVP is widely used for determining the molar mass of unknown non-volatile substances. Remember that this law applies best to dilute, ideal solutions. Deviations occur in concentrated or non-ideal solutions.

Prelims Revision Notes

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Vapour Pressure ($P^0$) — Pressure exerted by solvent vapour in equilibrium with liquid at a given temperature.
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Effect of Non-Volatile Solute — Reduces surface area for solvent evaporation $implies$ lowers vapour pressure of solution ($P_s < P^0$).
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Lowering of Vapour Pressure ($Delta P$) — $Delta P = P^0 - P_s$.
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Relative Lowering of Vapour Pressure (RLVP) — $rac{P^0 - P_s}{P^0}$. This is a colligative property.
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Raoult's Law (for non-volatile solute) — $P_s = P^0 cdot X_{solvent}$.
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RLVP Formula — $rac{P^0 - P_s}{P^0} = X_{solute}$.

* $X_{solute} = \frac{n_{solute}}{n_{solute} + n_{solvent}}$. * $n_{solute} = \frac{\text{mass of solute}}{\text{molar mass of solute}} = \frac{w_2}{M_2}$. * $n_{solvent} = \frac{\text{mass of solvent}}{\text{molar mass of solvent}} = \frac{w_1}{M_1}$.

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For Dilute Solutions (Approximation) — $X_{solute} approx \frac{n_{solute}}{n_{solvent}}$. So, $rac{P^0 - P_s}{P^0} approx \frac{n_{solute}}{n_{solvent}}$. Use with caution, exact formula is preferred.
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Van't Hoff Factor ($i$) — For electrolytes (solutes that dissociate/associate):

* $rac{P^0 - P_s}{P^0} = i cdot X_{solute}$. * $i = \frac{\text{observed colligative property}}{\text{calculated colligative property (assuming no dissociation/association)}}$. * For NaCl, $i=2$; for CaCl$_2$, $i=3$; for non-electrolytes (glucose, urea), $i=1$.

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Applications — Primarily used for determining the molar mass of unknown non-volatile solutes.
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Key Conceptual Points

* RLVP depends *only* on the number of solute particles, not their nature. * RLVP is the fundamental colligative property; all others (EBP, DFP, OP) are consequences of it. * Applicable to ideal dilute solutions. Deviations occur in concentrated or non-ideal solutions.

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Comparison — Higher $X_{solute}$ (or $i cdot X_{solute}$) $implies$ greater RLVP $implies$ lower $P_s$ $implies$ higher boiling point $implies$ lower freezing point $implies$ higher osmotic pressure.

Vyyuha Quick Recall

Really Low Vapour Pressure Equals Xtra Solute Moles. (RLVP = $X_{solute}$)