For a binary liquid solution of A and B. `P_A^0`=pure vapour pressure of A . `P_B^0`=pure vapour pressure of B. `X_A`=mole fraction of A in liquid phase.`Y_A`=mole fraction of A in vapour phase.
`{:("Column I","Column II"),((A)P_A^0gtP_B^0"[Ideal liquid solution]",(p)X_A=Y_A),((B)"Azeotropic mixture",(q)X_AltY_A),(( C)"Equimolar ideal mixture of A & B with "P_A^0ltP_B^0,(r)X_BltY_B),((D)"Equimolar ideal mixture of A & B with "P_A^0=P_B^0,(s)Y_BgtY_A),(,(t)X_B=Y_B):}`

Explanation

To solve the problem, we need to match the statements in Column I with the corresponding statements in Column II based on the properties of a binary liquid solution of components A and B.

### Step-by-Step Solution:

1. **Understanding the Properties of the Components**:
- Given that \( P_A^0 > P_B^0 \), it indicates that component A is more volatile than component B. This means that in the vapor phase, the mole fraction of A will be higher than in the liquid phase.

**Hint**: Remember that higher vapor pressure indicates higher volatility.

2. **Analyzing the First Statement (A)**:
- For an ideal liquid solution where \( P_A^0 > P_B^0 \), we can conclude that \( X_A < Y_A \). This means that the mole fraction of A in the liquid phase (X_A) is less than the mole fraction of A in the vapor phase (Y_A).

**Hint**: Relate volatility to mole fractions in liquid and vapor phases.

3. **Analyzing the Second Statement (B)**:
- An azeotropic mixture has the same composition in both the liquid and vapor phases. Therefore, \( X_A = Y_A \).

**Hint**: Azeotropes have equal mole fractions in both phases.

4. **Analyzing the Third Statement (C)**:
- For an equimolar ideal mixture of A and B where \( P_A^0 < P_B^0 \), it implies that component B is more volatile. Thus, we can conclude that \( X_B < Y_B \) and \( Y_B > Y_A \).

**Hint**: Consider how the volatility affects the mole fractions in both phases.

5. **Analyzing the Fourth Statement (D)**:
- For an equimolar ideal mixture of A and B where \( P_A^0 = P_B^0 \), the mole fractions in both phases will be equal, i.e., \( X_A = Y_A \) and \( X_B = Y_B \).

**Hint**: Equal vapor pressures lead to equal mole fractions.

### Final Matching:

- **(A)**: \( P_A^0 > P_B^0 \) → **(q)**: \( X_A < Y_A \)
- **(B)**: Azeotropic mixture → **(p)**: \( X_A = Y_A \)
- **(C)**: Equimolar ideal mixture of A & B with \( P_A^0 < P_B^0 \) → **(r)**: \( X_B < Y_B \)
- **(D)**: Equimolar ideal mixture of A & B with \( P_A^0 = P_B^0 \) → **(t)**: \( X_B = Y_B \)

### Summary of Matches:
- A → q
- B → p
- C → r
- D → t