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.