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5 moles of liquid X and 10 moles of liquid Y make a solution having a vapour pressure of $70\text{ torr}$. The vapour pressures of pure X and Y are $63\text{ torr}$ and $78\text{ torr}$ respectively. Which of the following is true regarding the described solution?
A
The solution shows positive deviation.
B
The solution shows negative deviation.
C
The solution is ideal.
D
The solution has volume greater than the sum of individual volumes.
Explanation
$P_{\text{ideal}} = \chi_X P_X^\circ + \chi_Y P_Y^\circ = \frac{5}{15}(63) + \frac{10}{15}(78) = 21 + 52 = 73\text{ torr}$. Since $P_{\text{obs}} = 70\text{ torr} < P_{\text{ideal}}$, the solution shows negative deviation from Raoult's law.
Detailed Solution
Mole fractions of components: $\chi_X = \frac{5}{5 + 10} = \frac{1}{3}$, $\chi_Y = \frac{10}{15} = \frac{2}{3}$. According to Raoult's law for an ideal solution: $P_{\text{ideal}} = \chi_X P_X^\circ + \chi_Y P_Y^\circ = \left(\frac{1}{3} \times 63\right) + \left(\frac{2}{3} \times 78\right) = 21 + 52 = 73\text{ torr}$. The observed total vapour pressure is $70\text{ torr}$, which is lower than the ideal value ($70\text{ torr} < 73\text{ torr}$). This indicates that intermolecular attractions between X and Y molecules are stronger than X-X and Y-Y interactions, resulting in a negative deviation from Raoult's law.