The vapour pressure of a liquid solution containing A and B is 99 torr. Calculate mole % of B in vapour phase.
(Given : `P_(A^(@)) = 100` torr , `P_(B^(@)) = 80` torr)

Answer

To solve the problem of calculating the mole percentage of component B in the vapor phase of a liquid solution containing A and B, we can follow these steps:

### Step 1: Write Raoult's Law
According to Raoult's Law, the total vapor pressure (P) of a solution is given by:
\[ P = P_{A}^{0} \cdot X_{A} + P_{B}^{0} \cdot X_{B} \]
where:
- \( P_{A}^{0} \) = vapor pressure of pure A = 100 torr
- \( P_{B}^{0} \) = vapor pressure of pure B = 80 torr
- \( X_{A} \) = mole fraction of A
- \( X_{B} \) = mole fraction of B

### Step 2: Express Mole Fractions
Since \( X_{A} + X_{B} = 1 \), we can express \( X_{A} \) in terms of \( X_{B} \):
\[ X_{A} = 1 - X_{B} \]

### Step 3: Substitute into Raoult's Law
Substituting \( X_{A} \) into the equation gives:
\[ P = P_{A}^{0} \cdot (1 - X_{B}) + P_{B}^{0} \cdot X_{B} \]

### Step 4: Substitute Known Values
Now, substituting the known values into the equation:
\[ 99 = 100 \cdot (1 - X_{B}) + 80 \cdot X_{B} \]

### Step 5: Simplify the Equation
Expanding and simplifying the equation:
\[ 99 = 100 - 100X_{B} + 80X_{B} \]
\[ 99 = 100 - 20X_{B} \]

### Step 6: Solve for \( X_{B} \)
Rearranging the equation to solve for \( X_{B} \):
\[ 20X_{B} = 100 - 99 \]
\[ 20X_{B} = 1 \]
\[ X_{B} = \frac{1}{20} \]

### Step 7: Calculate Mole Fraction of B in Vapor Phase
The mole fraction of B in the vapor phase (\( y_{B} \)) can be calculated using:
\[ y_{B} = X_{B} \cdot \frac{P_{B}^{0}}{P} \]
Substituting the values:
\[ y_{B} = \frac{1}{20} \cdot \frac{80}{99} \]

### Step 8: Simplify the Calculation
Calculating \( y_{B} \):
\[ y_{B} = \frac{80}{1980} = \frac{4}{99} \]

### Step 9: Convert to Mole Percentage
To find the mole percentage of B in the vapor phase:
\[ \text{Mole \% of B} = y_{B} \cdot 100 \]
\[ \text{Mole \% of B} = \frac{4}{99} \cdot 100 \approx 4.04\% \]

### Final Answer
The mole percentage of B in the vapor phase is approximately **4%**.

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