Relative Lowering of Vapour Pressure — Core Principles

Core Principles

Vapour pressure is the pressure exerted by the vapour in equilibrium with its liquid phase. When a non-volatile solute is added to a pure solvent, it occupies some surface area, reducing the number of solvent molecules that can escape into the vapour phase.

This leads to a decrease in the solvent's vapour pressure, known as 'lowering of vapour pressure'. The 'relative lowering of vapour pressure' (RLVP) is the ratio of this lowering to the vapour pressure of the pure solvent.

According to Raoult's Law, for ideal dilute solutions, RLVP is directly equal to the mole fraction of the solute ($X_{solute}$). Mathematically, it's expressed as $rac{P^0 - P_s}{P^0} = X_{solute}$, where $P^0$ is the vapour pressure of the pure solvent and $P_s$ is the vapour pressure of the solution.

This property is colligative, meaning it depends only on the number of solute particles, not their identity, and is crucial for determining the molar mass of unknown non-volatile solutes.

Important Differences

vs Elevation of Boiling Point (EBP)

Aspect	This Topic	Elevation of Boiling Point (EBP)
Definition	Relative Lowering of Vapour Pressure (RLVP) is the fractional decrease in the vapour pressure of a solvent upon addition of a non-volatile solute.	Elevation of Boiling Point (EBP) is the increase in the boiling point of a solvent upon addition of a non-volatile solute.
Direct Cause	Reduced number of solvent molecules at the liquid surface available for evaporation.	Lowering of vapour pressure, which means a higher temperature is needed for the solution's vapour pressure to reach atmospheric pressure.
Formula	$rac{P^0 - P_s}{P^0} = X_{solute}$ (or $i cdot X_{solute}$)	$Delta T_b = K_b cdot m$ (or $i cdot K_b cdot m$)
Concentration Term	Mole fraction ($X_{solute}$)	Molality ($m$)
Measurement	Requires precise measurement of vapour pressures of pure solvent and solution.	Requires precise measurement of boiling points of pure solvent and solution.
Relationship	RLVP is the fundamental colligative property from which EBP (and others) are derived.	EBP is a direct consequence of RLVP; a lower vapour pressure implies a higher boiling point.

Both Relative Lowering of Vapour Pressure (RLVP) and Elevation of Boiling Point (EBP) are colligative properties, meaning they depend on the number of solute particles, not their identity. However, they describe different observable phenomena and use different concentration units in their primary formulas. RLVP quantifies the fractional decrease in vapour pressure due to a non-volatile solute, expressed in terms of mole fraction. EBP quantifies the increase in boiling temperature, expressed in terms of molality. Fundamentally, RLVP is the root cause for EBP; a solution with lower vapour pressure needs to be heated to a higher temperature to achieve the same vapour pressure as the pure solvent at its boiling point.