Which of the following plots represents the behavior of an ideal binary liquid solution ?

Options

A. Plot of `1//P_("total,")` against `y_A` is linear
B. Plot of `1//P_("total,")` against `y_B` is non - linear
C. Plot of `P_("total,")` against `y_A` is linear
D. Plot of `P_("total,")` against `y_B` is linear (Here, `y_A and y_B` are the mole fraction of components A and B in vapour )

Answer

To determine which plot represents the behavior of an ideal binary liquid solution, we need to analyze the relationships between the mole fractions of the components in the vapor phase and the total pressure.

### Step-by-Step Solution:

1. **Understanding the Variables**:
- Let \( Y_A \) be the mole fraction of component A in the vapor phase.
- Let \( Y_B \) be the mole fraction of component B in the vapor phase.
- The total pressure \( P_{total} \) is the sum of the partial pressures of A and B.

2. **Using Raoult's Law**:
- According to Raoult's Law, the vapor pressure of a component in an ideal solution is directly proportional to its mole fraction in the liquid phase.
- For component A:
\[ P_A = P_{0A} \cdot X_A \]
where \( P_{0A} \) is the vapor pressure of pure A and \( X_A \) is the mole fraction of A in the liquid phase.
- For component B:
\[ P_B = P_{0B} \cdot X_B \]
where \( P_{0B} \) is the vapor pressure of pure B and \( X_B \) is the mole fraction of B in the liquid phase.

3. **Relating Vapor and Liquid Phase**:
- The total vapor pressure can be expressed as:
\[ P_{total} = P_A + P_B = P_{0A} \cdot X_A + P_{0B} \cdot X_B \]
- Since \( X_A + X_B = 1 \), we can express \( X_B \) as \( 1 - X_A \).

4. **Expressing \( Y_A \) and \( Y_B \)**:
- The mole fraction of A in the vapor phase \( Y_A \) can be expressed as:
\[ Y_A = \frac{P_A}{P_{total}} = \frac{P_{0A} \cdot X_A}{P_{total}} \]
- Similarly, for B:
\[ Y_B = \frac{P_B}{P_{total}} = \frac{P_{0B} \cdot X_B}{P_{total}} \]

5. **Plotting the Relationship**:
- If we plot \( Y_A \) against \( P_{total} \) or \( 1/P_{total} \), we find that the relationship is linear. This is because both \( Y_A \) and \( Y_B \) behave linearly with respect to the total pressure in an ideal solution.

6. **Identifying the Correct Plot**:
- The plot that shows a linear relationship between \( Y_A \) and \( 1/P_{total} \) is the correct representation of an ideal binary liquid solution.

### Conclusion:
The correct answer is the plot of \( 1/P_{total} \) against \( Y_A \) which is linear.