Q.$6\ \text{g}$ of urea ($M = 60\ \text{g mol}^{-1}$) is dissolved in $180\ \text{g}$ of water at $298\ \text{K}$. Calculate the relative lowering of vapour pressure of the 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 …