An aqueous solution containing liquid `A(M.Wt.=128) 64%` by weight has a vapour pressure of `145mm`. Find the vapour pressure A. If that of water is `155mm` at the same temperature.

Options

A. `205mm`
B. `2.05mm`
C. `1.05mm`
D. `105mm`

Explanation

To find the vapor pressure of liquid A (denoted as \( P_{A0} \)), we will use Raoult's law, which relates the vapor pressure of a solution to the vapor pressures of its components and their mole fractions.

### Step-by-Step Solution:

1. **Identify the Given Data:**
- Weight percentage of liquid A = 64%
- Vapor pressure of the solution (\( P_t \)) = 145 mm Hg
- Vapor pressure of water (\( P_{B0} \)) = 155 mm Hg
- Molecular weight of A = 128 g/mol
- Molecular weight of water (B) = 18 g/mol

2. **Calculate the Weight of Components:**
- Assume the total weight of the solution is 100 g.
- Weight of A = 64 g
- Weight of water (B) = 100 g - 64 g = 36 g

3. **Calculate Moles of Each Component:**
- Moles of A = \( \frac{\text{Weight of A}}{\text{Molecular weight of A}} = \frac{64 \text{ g}}{128 \text{ g/mol}} = 0.5 \text{ mol} \)
- Moles of water = \( \frac{\text{Weight of water}}{\text{Molecular weight of water}} = \frac{36 \text{ g}}{18 \text{ g/mol}} = 2 \text{ mol} \)

4. **Calculate Total Moles in the Solution:**
- Total moles = Moles of A + Moles of water = \( 0.5 + 2 = 2.5 \text{ mol} \)

5. **Calculate Mole Fractions:**
- Mole fraction of A (\( X_A \)) = \( \frac{\text{Moles of A}}{\text{Total moles}} = \frac{0.5}{2.5} = 0.2 \)
- Mole fraction of water (\( X_B \)) = \( 1 - X_A = 1 - 0.2 = 0.8 \)

6. **Apply Raoult's Law:**
- According to Raoult's law, the total vapor pressure of the solution is given by:
\[ P_t = P_{A0} \cdot X_A + P_{B0} \cdot X_B \]
- Substitute the known values:
\[ 145 = P_{A0} \cdot 0.2 + 155 \cdot 0.8 \]

7. **Calculate \( P_{A0} \):**
- First, calculate \( 155 \cdot 0.8 \):
\[ 155 \cdot 0.8 = 124 \]
- Now substitute back into the equation:
\[ 145 = P_{A0} \cdot 0.2 + 124 \]
- Rearranging gives:
\[ P_{A0} \cdot 0.2 = 145 - 124 = 21 \]
- Finally, solve for \( P_{A0} \):
\[ P_{A0} = \frac{21}{0.2} = 105 \text{ mm Hg} \]

### Final Answer:
The vapor pressure of liquid A is **105 mm Hg**.

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