Question: 81. 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?
(1) The solution shows positive deviation.
(2) The solution shows negative deviation.
(3) The solution is ideal.
(4) The solution has volume greater than the sum of individual volumes.
Answer: Option (2)
Explanation:
For an ideal solution, the vapour pressure is given by Raoult’s law:
P_{\text{ideal}} = X_X P_X^{\circ} + X_Y P_Y^{\circ}The total number of moles is 5 + 10 = 15.
The mole fractions are:
X_X = \frac{5}{15} = \frac{1}{3} X_Y = \frac{10}{15} = \frac{2}{3}Using Raoult’s law:
P_{\text{ideal}} = \frac{1}{3} \times 63 + \frac{2}{3} \times 78 P_{\text{ideal}} = 21 + 52 = 73 \text{ torr}The observed vapour pressure of the solution is 70 \text{ torr},
which is less than the ideal vapour pressure 73 \text{ torr}.
When the vapour pressure of a solution is lower than that predicted by Raoult’s law,
the solution shows negative deviation.
This occurs due to stronger intermolecular attraction between unlike molecules.
Therefore, the correct statement is that the solution shows negative deviation from Raoult’s law.