The vapour pressure of a liqid solution containing A and B is 99 torr. Colvulate mole % of in vapour phese.
(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 will follow these steps:

### Step 1: Understand the Given Data
We have the following information:
- Total vapor pressure of the solution, \( P_{total} = 99 \, \text{torr} \)
- Vapor pressure of pure A, \( P_{A}^{0} = 100 \, \text{torr} \)
- Vapor pressure of pure B, \( P_{B}^{0} = 80 \, \text{torr} \)

### Step 2: Use Raoult's Law
According to Raoult's Law, the total vapor pressure of a solution can be expressed as:
\[ P_{total} = P_{A}^{0} \cdot x_A + P_{B}^{0} \cdot x_B \]
where \( x_A \) and \( x_B \) are the mole fractions of A and B in the liquid phase, respectively.

Since \( x_A + x_B = 1 \), we can express \( x_A \) as \( 1 - x_B \).

### Step 3: Substitute into the Equation
Substituting \( x_A \) into the equation gives:
\[ P_{total} = P_{A}^{0} \cdot (1 - x_B) + P_{B}^{0} \cdot x_B \]
Substituting the known values:
\[ 99 = 100 \cdot (1 - x_B) + 80 \cdot x_B \]

### Step 4: Simplify the Equation
Expanding the equation:
\[ 99 = 100 - 100x_B + 80x_B \]
Combining like terms:
\[ 99 = 100 - 20x_B \]

### Step 5: Solve for \( x_B \)
Rearranging the equation:
\[ 20x_B = 100 - 99 \]
\[ 20x_B = 1 \]
\[ x_B = \frac{1}{20} \]

### Step 6: Calculate Mole Fraction of B in the Vapor Phase
The mole fraction of B in the vapor phase, \( y_B \), can be calculated using:
\[ y_B = \frac{x_B \cdot P_{B}^{0}}{P_{total}} \]
Substituting the values:
\[ y_B = \frac{\left(\frac{1}{20}\right) \cdot 80}{99} \]
Calculating:
\[ y_B = \frac{4}{99} \]

### Step 7: Convert Mole Fraction to Mole Percentage
To find the mole percentage of B in the vapor phase, we multiply by 100:
\[ \text{Mole percentage of B} = y_B \cdot 100 = \frac{4}{99} \cdot 100 \approx 4.04\% \]

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

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