Relative Lowering of Vapour Pressure | Colligative Properties Class 12

Relative Lowering of Vapour Pressure

Colligative Properties | Solutions Class 12 Chemistry

1. Concept of Vapour Pressure Lowering

When a non-volatile solute (like sugar, urea, salt) is added to a volatile solvent (like water), the vapour pressure of the solution becomes lower than that of the pure solvent.

                    Why? The non-volatile solute particles occupy part of the liquid surface, reducing the surface area available for solvent molecules to escape into the vapour phase.
                

2. Derivation from Raoult's Law

According to Raoult's Law for non-volatile solutes, the vapour pressure of the solution ($P_s$) is directly proportional to the mole fraction of the solvent ($\chi_1$).

$$ P_s = P^\circ \chi_1 $$

Since $\chi_1 + \chi_2 = 1$ (where $\chi_2$ is solute mole fraction):

$$ P_s = P^\circ (1 - \chi_2) $$ $$ P_s = P^\circ - P^\circ \chi_2 $$ $$ P^\circ \chi_2 = P^\circ - P_s $$

$$ \frac{P^\circ - P_s}{P^\circ} = \chi_2 $$

Here:

$P^\circ - P_s$ = Lowering of Vapour Pressure (Not Colligative).
$\frac{P^\circ - P_s}{P^\circ}$ = Relative Lowering of Vapour Pressure (RLVP) (Is Colligative).
$\chi_2$ = Mole fraction of solute.

3. Determination of Molar Mass ($M_2$)

We can determine the molar mass of the solute using RLVP.

$$ \frac{P^\circ - P_s}{P^\circ} = \chi_2 = \frac{n_2}{n_1 + n_2} $$

For dilute solutions ($n_2 \ll n_1$), we can approximate $n_1 + n_2 \approx n_1$.

$$ \frac{P^\circ - P_s}{P^\circ} = \frac{n_2}{n_1} = \frac{w_2/M_2}{w_1/M_1} $$

$$ M_2 = \frac{w_2 \times M_1 \times P^\circ}{w_1 \times (P^\circ - P_s)} $$

Where $w_1, w_2$ are masses and $M_1, M_2$ are molar masses of solvent and solute respectively.

4. Ostwald-Walker Dynamic Method

This is an experimental method to determine RLVP. Dry air is passed successively through:

Solution bulbs (Loss in mass $\propto P_s$).
Pure Solvent bulbs (Loss in mass $\propto P^\circ - P_s$).
Calcium Chloride guard tube (Gain in mass $\propto P^\circ$).

Result: $\frac{\text{Loss in Solvent Mass}}{\text{Total Loss}} \approx \text{RLVP}$.

Practice Quiz

Test your understanding of RLVP.

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