Draw a suitable diagram to express the relationship for ideal solutions of `A` and `B` between vapour pressure and mole fractions of components at constant temperature

Answer

To solve the problem of drawing a suitable diagram to express the relationship for ideal solutions of components A and B between vapor pressure and mole fractions at constant temperature, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Components**: We have two components, A and B. Each component has a vapor pressure when pure, denoted as \( P_A^0 \) for component A and \( P_B^0 \) for component B.

2. **Define Mole Fractions**: The mole fractions of components A and B are defined as:
- \( X_A \) = mole fraction of component A
- \( X_B \) = mole fraction of component B
- Note that \( X_A + X_B = 1 \)

3. **Set Up the Axes**:
- On the y-axis, plot the vapor pressure (P).
- On the x-axis, plot the mole fraction of component A (\( X_A \)). Since \( X_B = 1 - X_A \), the x-axis will range from 0 to 1.

4. **Plot Vapor Pressures**:
- At \( X_A = 1 \) (pure A), the vapor pressure is \( P_A^0 \).
- At \( X_A = 0 \) (pure B), the vapor pressure is \( P_B^0 \).

5. **Draw Partial Pressure Lines**:
- Draw a straight line from the point (1, \( P_A^0 \)) to the point (0, 0) representing the partial pressure of component A, which can be expressed as:
\[ P_A = X_A \cdot P_A^0 \]
- Draw another straight line from the point (0, \( P_B^0 \)) to the point (1, 0) representing the partial pressure of component B, which can be expressed as:
\[ P_B = X_B \cdot P_B^0 \]

6. **Total Vapor Pressure**:
- The total vapor pressure (\( P_T \)) is the sum of the partial pressures of A and B:
\[ P_T = P_A + P_B = X_A \cdot P_A^0 + (1 - X_A) \cdot P_B^0 \]
- This relationship can be represented as a straight line that starts from \( P_A^0 \) when \( X_A = 1 \) and ends at \( P_B^0 \) when \( X_A = 0 \).

7. **Label the Diagram**:
- Clearly label the axes, the lines for \( P_A \), \( P_B \), and \( P_T \), and the points where the lines intersect the axes.

### Final Diagram:
- You should have a graph with:
- Y-axis labeled as "Vapor Pressure (P)"
- X-axis labeled as "Mole Fraction of A (\( X_A \))"
- A line for \( P_A \) starting from \( P_A^0 \) and going to the origin.
- A line for \( P_B \) starting from \( P_B^0 \) and going to the origin.
- A line for \( P_T \) that connects \( P_A^0 \) and \( P_B^0 \).