The total pressure exerted in ideal binary solution is given by `P=P_(A)^(@)X_(A)+P_(B)^(@)X_(B)` where `P_(A)^(@)&P_(B)^(@)` are the respective vapour pressure of pure components and `X_(A)&X_(B)` are their mole fraction in liquid phase. And composition of the vapour phase is determined with the help of Datton's law partial pressure: `Y_(A)=(P_(A)^(@)X_(A))/(P)`
If total pressure exerted in an ideal binary solution is given by `P=(5400)/(60+30Y_(A))mm` of Hg.
The more volatile liquid is:

Options

A. liquid A
B. liquid B
C. both are same
D. it depends on the amount of A and B

Answer

To solve the problem, we need to determine which of the two liquids in the ideal binary solution is more volatile. We will use the given equation for total pressure and apply Dalton's law of partial pressures.

### Step-by-Step Solution:

1. **Understand the Given Equation**:
The total pressure \( P \) in an ideal binary solution is given by:
\[ P = P_A^0 X_A + P_B^0 X_B \]
where \( P_A^0 \) and \( P_B^0 \) are the vapor pressures of the pure components A and B, and \( X_A \) and \( X_B \) are their mole fractions in the liquid phase.

2. **Composition of Vapor Phase**:
The composition of the vapor phase is given by Dalton's law:
\[ Y_A = \frac{P_A^0 X_A}{P} \]
where \( Y_A \) is the mole fraction of component A in the vapor phase.

3. **Substituting Total Pressure**:
We are given the total pressure as:
\[ P = \frac{5400}{60 + 30Y_A} \text{ mm of Hg} \]

4. **Finding \( P_A^0 \)**:
To find \( P_A^0 \), we set \( Y_A = 1 \) (which means only component A is present):
\[ P_A^0 = \frac{5400}{60 + 30 \cdot 1} = \frac{5400}{90} = 60 \text{ mm of Hg} \]

5. **Finding \( P_B^0 \)**:
Now, to find \( P_B^0 \), we set \( Y_A = 0 \) (which means only component B is present):
\[ P_B^0 = \frac{5400}{60 + 30 \cdot 0} = \frac{5400}{60} = 90 \text{ mm of Hg} \]

6. **Comparing Vapor Pressures**:
Now we compare the vapor pressures:
- \( P_A^0 = 60 \text{ mm of Hg} \)
- \( P_B^0 = 90 \text{ mm of Hg} \)

Since \( P_B^0 > P_A^0 \), liquid B has a higher vapor pressure than liquid A.

7. **Conclusion**:
The liquid with the higher vapor pressure is more volatile. Therefore, liquid B is the more volatile liquid.

### Final Answer:
The more volatile liquid is **B**.