At `35^(@)C` the vapour pressure of pure chloroform is `0.359` at atm and that of pure acetone is `0.453` atm. A solution containing 1 mole of chloroform and 4 mole of acetone has a vapour pressure of (in atm)

Options

A. `0.400`
B. `0.812`
C. `0.094`
D. `0.434`

Answer

To find the vapor pressure of the solution containing 1 mole of chloroform and 4 moles of acetone, we can use Raoult's Law. According to Raoult's Law, the vapor pressure of a solution is equal to the sum of the partial vapor pressures of each component in the solution.

### Step-by-Step Solution:

1. **Identify the Given Data:**
- Vapor pressure of pure chloroform (P°_A) = 0.359 atm
- Vapor pressure of pure acetone (P°_B) = 0.453 atm
- Moles of chloroform (A) = 1 mole
- Moles of acetone (B) = 4 moles

2. **Calculate Total Moles in the Solution:**
\[ \text{Total moles} = \text{Moles of A} + \text{Moles of B} = 1 + 4 = 5 \text{ moles} \]

3. **Calculate the Mole Fraction of Each Component:**
- Mole fraction of chloroform (x_A):
\[ x_A = \frac{\text{Moles of A}}{\text{Total moles}} = \frac{1}{5} = 0.2 \]
- Mole fraction of acetone (x_B):
\[ x_B = \frac{\text{Moles of B}}{\text{Total moles}} = \frac{4}{5} = 0.8 \]

4. **Calculate the Partial Vapor Pressures:**
- Partial vapor pressure of chloroform (P_A):
\[ P_A = x_A \cdot P°_A = 0.2 \cdot 0.359 = 0.0718 \text{ atm} \]
- Partial vapor pressure of acetone (P_B):
\[ P_B = x_B \cdot P°_B = 0.8 \cdot 0.453 = 0.3624 \text{ atm} \]

5. **Calculate the Total Vapor Pressure of the Solution:**
\[ P_{\text{solution}} = P_A + P_B = 0.0718 + 0.3624 = 0.434 \text{ atm} \]

### Final Answer:
The vapor pressure of the solution is **0.434 atm**.

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