5 moles of liquid X and 10 moles of liquid Y make a solution having a vapour pressure of 70 torr. The vapour pressures of pure X and Y are 63 torr and 78 torr respectively. Which of the following is true regarding the described solution?

Solution & Explanation

\textbf{Answer:} (D) The solution shows negative deviation. \textbf{Solution:} Mole fractions: $x_X = \frac{5}{15} = \frac{1}{3}$, $x_Y = \frac{10}{15} = \frac{2}{3}$. If ideal, by Raoult's law: $P_{ideal} = p_X^\circ x_X + p_Y^\circ x_Y = 63 \times \frac{1}{3} + 78 \times \frac{2}{3} = 21 + 52 = 73$ torr. Observed $P = 70$ torr $< 73$ torr. Since the observed vapour pressure is \textbf{less} than the ideal value, the solution shows \textbf{negative deviation} from Raoult's law.