Q.The vapour pressure of pure water at $298\ \text{K}$ is $23.8\ \text{mm Hg}$. Using the relative lowering of vapour pressure found for the urea solution of the previous example, calculate the actual vapour pressure of that solution.

Colligative properties depend only on the number of solute particles dissolved in a fixed quantity of solvent,

never on their chemical identity; the four studied in this chapter are the relative lowering of vapour pressure,

elevation of boiling point, depression of freezing point, and osmotic pressure, and all four trace back to a

single cause — a non-volatile solute occupies part of the liquid surface, lowering the solvent's vapour pressure.

Applying Raoult's law to just the solvent in a solution of a non-volatile solute gives $p_1 = x_1 p_1^{\circ}$, so

the lowering is $\Delta p = p_1^{\circ}-p_1 = p_1^{\circ}x_2$ (since $x_1+x_2=1$ for a two-component solution).

Dividing by $p_1^{\circ}$ gives the foundational relation, the relative lowering of vapour pressure:

For a dilute solution, $x_2 \approx n_2/n_1$, giving the practically useful approximate form …