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Q1.36:
100 g of liquid A (molar mass 140 g \(mol^{-1}\)) was dissolved in 1000 g of liquid B (molar mass 180 g \(mol^{-1}\)). The vapour pressure of pure liquid B was found to be 500 torr. Calculate the vapour pressure of pure liquid A and its vapour pressure in the solution if the total vapour pressure of the solution is 475 Torr.

Solution :

Step 1: Calculating the Number of Moles of Components

To determine the mole fraction of each component, we first calculate the number of moles ($n$) for solute A and solvent B using the formula $n = \frac{\text{mass}}{\text{molar mass}}$.

  • For liquid A: $n_A = \frac{100\text{ g}}{140\text{ g mol}^{-1}} \approx 0.7143\text{ mol}$
  • For liquid B: $n_B = \frac{1000\text{ g}}{180\text{ g mol}^{-1}} \approx 5.5556\text{ mol}$

Step 2: Calculating Mole Fractions ($x$)

The mole fraction of a component is defined as the ratio of its moles to the total moles in the mixture [$x_i = \frac{n_i}{n_A + n_B}$].

Total moles ($n_T$) = $0.7143 + 5.5556 = 6.2699\text{ mol}$

  • $x_A = \frac{0.7143}{6.2699} \approx 0.1139$
  • $x_B = \frac{5.5556}{6.2699} \approx 0.8861$

Step 3: Calculating Vapour Pressure of Pure Liquid A ($P_A^\circ$)

According to Raoult's Law, the total vapour pressure of the solution ($P_T$) is the sum of partial pressures of individual components: $P_T = P_A^\circ x_A + P_B^\circ x_B$ [Per Raoult's Law for ideal solutions].

Given: $P_T = 475\text{ Torr}$, $P_B^\circ = 500\text{ Torr}$.

Substituting the values into the equation:

$475 = (P_A^\circ \times 0.1139) + (500 \times 0.8861)$

$475 = (P_A^\circ \times 0.1139) + 443.05$

$P_A^\circ \times 0.1139 = 475 - 443.05 = 31.95$

$P_A^\circ = \frac{31.95}{0.1139} \approx 280.51\text{ Torr}$

Step 4: Calculating Vapour Pressure of A in the Solution ($P_A$)

The partial pressure of component A in the solution is given by $P_A = P_A^\circ x_A$ [Definition of partial pressure].

$P_A = 280.51 \times 0.1139 \approx 31.95\text{ Torr}$

Visual Representation of Partial Pressures

Mole Fraction of A Pressure (Torr) Solution Point (x=0.11, P=475)

Final Solution: The vapour pressure of pure liquid A is 280.51 Torr, and its vapour pressure in the solution is 31.95 Torr.


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