Question

Vapour pressure of pure A = 100 torr, moles = 2; vapour pressure of pure B = 80 torr, moles = 3. Total vapour pressure of the mixture is

• A. 440 torr
• B. 460 torr
• C. 180 torr
• D. 88 torr

Answer 1

Answer: (D)

88 torr

Answer 2

Here's how to calculate the total vapor pressure of the mixture:

1. Calculate Mole Fractions in Liquid Phase:

   Total moles of the mixture ($n_{total}$) = Moles of A ($n_A$) + Moles of B ($n_B$)

   $n_{total} = 2 \text{ moles} + 3 \text{ moles} = 5 \text{ moles}$

   Mole fraction of A ($X_A$) = $\frac{n_A}{n_{total}} = \frac{2}{5} = 0.4$

   Mole fraction of B ($X_B$) = $\frac{n_B}{n_{total}} = \frac{3}{5} = 0.6$

2. Calculate Partial Pressures in Vapor Phase (Raoult's Law):

   According to Raoult's Law, the partial pressure of a component in an ideal solution is given by $P_i = X_i P_i^0$, where $P_i^0$ is the vapor pressure of the pure component.

   Partial pressure of A ($P_A$) = $X_A \cdot P_A^0 = 0.4 \times 100 \text{ torr} = 40 \text{ torr}$

   Partial pressure of B ($P_B$) = $X_B \cdot P_B^0 = 0.6 \times 80 \text{ torr} = 48 \text{ torr}$

3. Calculate Total Vapor Pressure (Dalton's Law of Partial Pressures):

   The total vapor pressure of the mixture ($P_{total}$) is the sum of the partial pressures of its components.

   $P_{total} = P_A + P_B = 40 \text{ torr} + 48 \text{ torr} = 88 \text{ torr}$