Question

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

• A. The solution shows negative deviation.
• B. The solution is ideal.
• C. The solution has volume greater than the sum of individual volumes.
• D. The solution shows positive deviation.

Hint:

A solution exhibits negative deviation when its vapor pressure is lower than expected based on Raoult's law. This occurs when the intermolecular forces between the components of the solution are stronger than between the components and the solvent.

Answer 1

The Correct Option is A

Raoult's law predicts the vapor pressure of an ideal solution using the formula: \[ P_{\text{solution}} = X_X P_X^0 + X_Y P_Y^0 \]. In this equation, \( P_{\text{solution}} \) represents the solution's vapor pressure, \( X_X \) and \( X_Y \) are the mole fractions of components X and Y, and \( P_X^0 \) and \( P_Y^0 \) are the vapor pressures of pure X and Y, respectively. Given Moles of X = 5, Moles of Y = 10, \( P_X^0 = 63 \, \text{torr} \), and \( P_Y^0 = 78 \, \text{torr} \). The total moles are 5 + 10 = 15. The mole fractions are calculated as: \[ X_X = \frac{5}{15} = \frac{1}{3}, \quad X_Y = \frac{10}{15} = \frac{2}{3} \]. Applying Raoult's law yields: \[ P_{\text{solution}} = \left(\frac{1}{3}\right)(63) + \left(\frac{2}{3}\right)(78) \] \[ P_{\text{solution}} = 21 + 52 = 73 \, \text{torr} \]. The provided vapor pressure is 70 torr, which is less than the calculated 73 torr. This indicates negative deviation from Raoult's law. Consequently, the solution exhibits negative deviation. Therefore, the correct answer is (1) The solution shows negative deviation.