The total vapour pressure of a mixture of 1 mole of A (`P_A = 200 mm Hg`) and 3 mole of B (`P_B= 360` mm Hg) is 350 mm Hg. Then

Options

A. There is no deviation from Raoult's law
B. There is positive deviation from Raoult's law
C. There is negative deviation from Raoult's law
D. Molecular masses of A and B are also required

Answer

To solve the problem, we need to calculate the total vapor pressure of the mixture of components A and B using Raoult's law and compare it with the given total vapor pressure.

### Step-by-Step Solution:

1. **Identify the Moles and Vapor Pressures**:
- Moles of A (n_A) = 1
- Moles of B (n_B) = 3
- Vapor pressure of pure A (P_A) = 200 mm Hg
- Vapor pressure of pure B (P_B) = 360 mm Hg
- Given total vapor pressure (P_total) = 350 mm Hg

2. **Calculate the Total Moles in the Mixture**:
\[ n_{total} = n_A + n_B = 1 + 3 = 4 \text{ moles} \]

3. **Calculate the Mole Fractions**:
- Mole fraction of A (\(X_A\)):
\[ X_A = \frac{n_A}{n_{total}} = \frac{1}{4} = 0.25 \]
- Mole fraction of B (\(X_B\)):
\[ X_B = \frac{n_B}{n_{total}} = \frac{3}{4} = 0.75 \]

4. **Calculate the Partial Pressures**:
- Partial pressure of A (\(P_A^{\text{partial}}\)):
\[ P_A^{\text{partial}} = P_A \times X_A = 200 \, \text{mm Hg} \times 0.25 = 50 \, \text{mm Hg} \]
- Partial pressure of B (\(P_B^{\text{partial}}\)):
\[ P_B^{\text{partial}} = P_B \times X_B = 360 \, \text{mm Hg} \times 0.75 = 270 \, \text{mm Hg} \]

5. **Calculate the Total Vapor Pressure**:
\[ P_{total}^{\text{calculated}} = P_A^{\text{partial}} + P_B^{\text{partial}} = 50 \, \text{mm Hg} + 270 \, \text{mm Hg} = 320 \, \text{mm Hg} \]

6. **Compare with Given Total Vapor Pressure**:
- Given \(P_{total} = 350 \, \text{mm Hg}\)
- Calculated \(P_{total}^{\text{calculated}} = 320 \, \text{mm Hg}\)

7. **Determine the Deviation**:
Since \(P_{total}^{\text{calculated}} < P_{total}\), this indicates a positive deviation from Raoult's law.

### Conclusion:
The total vapor pressure calculated (320 mm Hg) is less than the given total vapor pressure (350 mm Hg), indicating a positive deviation from Raoult's law.