First slide

Theory of dilute solutions

Question

At 20°C, the vapor pressure of 0.1 molal aqueous solutions of urea is 0.03 mm less than that of water, and the vapor pressure of 0.1 molal solutions of KCl is 0.0594 mm less than that of water. The apparent percentage dissociation of KCl in water at the given temperature is (Neglect the moles of solute particles in comparison to the moles of water in both solutions).

Moderate

Solution

$\begin{array}{l} T = 20^{\circ} C 0.1 m solution of urea ΔP = 0.03 mm \\ K Cl \to 0.1 m Δ P = 0.0594 \\ \frac{Δ P}{P} = x_{β} \to 0.1 mole in 1 kg \\ \frac{0.03}{P} = \frac{0.1}{0.1 + 55.5} \\ P = \frac{0.03 \times 55.65}{0.1} = 16.695 \\ \frac{Δ P}{P} = i X_{ρ} \\ \frac{0.0594}{16.695} = i [0.00179] \\ i = 1.987 \end{array}$

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