Total vapour pressure of mixture of 1 mole of volaile components A (`P_(a^(%)`)=100 mm Hg) and 3 mole of volatile component B(`P_B^(@) =80 mm Hg`) is 90 mm Hg. For such case:

Options

A. There is positive deviation from Rsoult's law
B. boiling point has been lowered
C. force of attraction between A and B is weaker than that between A and A or betweenB and B
D. All the above statement are correct

Answer

To solve the problem step by step, we need to find the total vapor pressure of a mixture of two volatile components A and B and analyze the deviation from Raoult's law.

### Step 1: Identify the given data
- Moles of component A (n_A) = 1 mole
- Vapor pressure of pure component A (P_A^0) = 100 mm Hg
- Moles of component B (n_B) = 3 moles
- Vapor pressure of pure component B (P_B^0) = 80 mm Hg
- Total vapor pressure of the mixture (P_total) = 90 mm Hg

### Step 2: Calculate the total number of moles in the mixture
Total moles (n_total) = n_A + n_B = 1 + 3 = 4 moles

### Step 3: Calculate the mole fractions of components A and B
- Mole fraction of A (X_A) = n_A / n_total = 1 / 4 = 0.25
- Mole fraction of B (X_B) = n_B / n_total = 3 / 4 = 0.75

### Step 4: Calculate the ideal vapor pressure of the mixture (P_ideal)
Using Raoult's law, the ideal vapor pressure (P_ideal) can be calculated as:
\[ P_{ideal} = P_A^0 \cdot X_A + P_B^0 \cdot X_B \]
Substituting the values:
\[ P_{ideal} = (100 \, \text{mm Hg} \cdot 0.25) + (80 \, \text{mm Hg} \cdot 0.75) \]
Calculating:
\[ P_{ideal} = 25 \, \text{mm Hg} + 60 \, \text{mm Hg} = 85 \, \text{mm Hg} \]

### Step 5: Compare P_ideal with P_total
We have:
- P_ideal = 85 mm Hg
- P_total = 90 mm Hg

Since P_total > P_ideal, this indicates a positive deviation from Raoult's law.

### Step 6: Analyze the implications of positive deviation
1. **Boiling Point**: The boiling point of the solution is lowered because the total vapor pressure is higher than expected for an ideal solution.
2. **Forces of Attraction**: The forces of attraction between A and B are weaker than those between A and A or B and B, leading to the positive deviation.

### Conclusion
Based on the analysis:
- The solution exhibits positive deviation from Raoult's law.
- The boiling point is lowered.
- The forces of attraction between A and B are weaker than those between A and A or B and B.

Thus, the correct answer is option D.