To solve the problem, we will use Raoult's Law and Dalton's Law of partial pressures. Here are the steps to find the total vapor pressure of the mixture and analyze the statements given.
### Step 1: Identify the given data
- Moles of component A (volatile): \( n_A = 1 \)
- Vapor pressure of pure component A: \( P^0_A = 100 \, \text{mm Hg} \)
- Moles of component B (volatile): \( n_B = 3 \)
- Vapor pressure of pure component B: \( P^0_B = 60 \, \text{mm Hg} \)
- Total vapor pressure of the mixture: \( P = 75 \, \text{mm Hg} \)
### Step 2: Calculate the total number of moles in the mixture
The total number of moles in the mixture is:
\[
n_{total} = n_A + n_B = 1 + 3 = 4 \, \text{moles}
\]
### Step 3: Calculate the mole fractions of components A and B
The mole fraction of component A (\( X_A \)) and component B (\( X_B \)) can be calculated as follows:
\[
X_A = \frac{n_A}{n_{total}} = \frac{1}{4} = 0.25
\]
\[
X_B = \frac{n_B}{n_{total}} = \frac{3}{4} = 0.75
\]
### Step 4: Apply Raoult's Law to find the partial pressures
According to Raoult's Law, the partial pressures of components A and B are given by:
\[
P_A = P^0_A \cdot X_A = 100 \, \text{mm Hg} \cdot 0.25 = 25 \, \text{mm Hg}
\]
\[
P_B = P^0_B \cdot X_B = 60 \, \text{mm Hg} \cdot 0.75 = 45 \, \text{mm Hg}
\]
### Step 5: Calculate the total vapor pressure of the mixture
The total vapor pressure \( P \) of the mixture is the sum of the partial pressures:
\[
P = P_A + P_B = 25 \, \text{mm Hg} + 45 \, \text{mm Hg} = 70 \, \text{mm Hg}
\]
### Step 6: Compare the calculated total vapor pressure with the given total vapor pressure
The calculated total vapor pressure is \( 70 \, \text{mm Hg} \), which is less than the given total vapor pressure of \( 75 \, \text{mm Hg} \). This indicates a positive deviation from Raoult's Law.
### Step 7: Analyze the statements
1. **Positive deviation from Raoult's Law**: Correct, as \( 70 \, \text{mm Hg} < 75 \, \text{mm Hg} \).
2. **Boiling point has been lowered**: Correct, since the vapor pressure is higher than expected, indicating a lower boiling point.
3. **Force of attraction between AB smaller than between AA or BB**: Correct, as the mixture exhibits positive deviation, indicating weaker interactions between A and B compared to A-A or B-B interactions.
### Conclusion
All statements are correct, so the answer is that all of the above statements are true.
---
