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 will use Raoult's Law, which states that the vapor pressure of a solution is equal to the sum of the partial vapor pressures of its components. Here are the steps to solve the problem:

### Step 1: Calculate the mole fractions of chloroform and acetone.
- **Moles of Chloroform (A)** = 1 mole
- **Moles of Acetone (B)** = 4 moles
- **Total moles** = Moles of A + Moles of B = 1 + 4 = 5 moles

Now, we can calculate the mole fractions:
- **Mole fraction of Chloroform (X_A)** = Moles of A / Total moles = 1 / 5 = 0.2
- **Mole fraction of Acetone (X_B)** = Moles of B / Total moles = 4 / 5 = 0.8

### Step 2: Use Raoult's Law to calculate the partial vapor pressures.
Raoult's Law states:
- \( P_A = X_A \cdot P_{A0} \)
- \( P_B = X_B \cdot P_{B0} \)

Where:
- \( P_{A0} \) = Vapor pressure of pure chloroform = 0.359 atm
- \( P_{B0} \) = Vapor pressure of pure acetone = 0.453 atm

Now we calculate the partial pressures:
- **Partial pressure of Chloroform (P_A)**:
\[ P_A = X_A \cdot P_{A0} = 0.2 \cdot 0.359 = 0.0718 \text{ atm} \]

- **Partial pressure of Acetone (P_B)**:
\[ P_B = X_B \cdot P_{B0} = 0.8 \cdot 0.453 = 0.3624 \text{ atm} \]

### Step 3: Calculate the total vapor pressure of the solution.
The total vapor pressure \( P_{solution} \) is the sum of the partial pressures:
\[ P_{solution} = P_A + P_B = 0.0718 + 0.3624 = 0.4342 \text{ atm} \]

### Step 4: Consider the negative deviation from Raoult's Law.
Since chloroform and acetone exhibit negative deviation from Raoult's Law due to hydrogen bonding, the actual vapor pressure will be less than the calculated value. However, we need to choose the closest option from the provided answers.

### Conclusion:
The calculated vapor pressure of the solution is approximately 0.4342 atm. Given the options, the closest value is **0.400 atm**.