Total vapour pressure of mixture of `1` mol of volatile component `A(P_(A^(@))=100mmHg)` and `3` mol of volatile component `B(P_(B^(@)=80 mmHg)` is `75mm`. For such case:

Options

A. there is positive deviation from Raoult's low
B. boiling point has been lowered
C. force of attraction between `A` and `B` is maller than that between `A` and `A` between `B` and `B`
D. All the above statements are correct.

Explanation

To solve the problem, we need to analyze the given information about the volatile components A and B, their vapor pressures, and the total vapor pressure of the mixture.

### Step-by-Step Solution:

1. **Identify the Given Data:**
- Moles of component A, \( n_A = 1 \)
- Moles of component B, \( n_B = 3 \)
- Vapor pressure of pure component A, \( P_{A}^0 = 100 \, \text{mmHg} \)
- Vapor pressure of pure component B, \( P_{B}^0 = 80 \, \text{mmHg} \)
- Total vapor pressure of the mixture, \( P_{total} = 75 \, \text{mmHg} \)

2. **Calculate the Mole Fractions:**
- Total moles in the mixture, \( n_{total} = n_A + n_B = 1 + 3 = 4 \)
- Mole fraction of component A, \( \chi_A = \frac{n_A}{n_{total}} = \frac{1}{4} \)
- Mole fraction of component B, \( \chi_B = \frac{n_B}{n_{total}} = \frac{3}{4} \)

3. **Calculate the Ideal Vapor Pressure:**
- Using Raoult's Law, the ideal vapor pressure of the mixture \( P_{ideal} \) can be calculated as:
\[ P_{ideal} = P_{A}^0 \cdot \chi_A + P_{B}^0 \cdot \chi_B \]
- Substituting the values:
\[ P_{ideal} = (100 \, \text{mmHg} \cdot \frac{1}{4}) + (80 \, \text{mmHg} \cdot \frac{3}{4}) \]
\[ P_{ideal} = 25 \, \text{mmHg} + 60 \, \text{mmHg} = 85 \, \text{mmHg} \]

4. **Compare Actual and Ideal Vapor Pressures:**
- Given that the actual vapor pressure \( P_{total} = 75 \, \text{mmHg} \) is less than the ideal vapor pressure \( P_{ideal} = 85 \, \text{mmHg} \), we can conclude that there is a positive deviation from Raoult's Law.

5. **Conclusion:**
- Since the actual vapor pressure is less than the ideal vapor pressure, this indicates a positive deviation from Raoult's Law. Therefore, the correct answer is that there is a positive deviation from Raoult's law.