The vapor pressures of benzenen, toluene and `ortho` xylene are `75` Torr, `22` Torr and `10` Torr respectively at `20^(@)C` Which of the following is not a possible value of the vapor pressure of an equimolar binarytemary solution of these at `20^(@)C`? Assume all form ideal solution with each other?

Options

A. `48(1)/(2)`
B. 16
C. `35(1)/(3)`
D. `53(1)/(2)`

Explanation

To solve the problem, we need to determine the possible vapor pressures of equimolar binary and ternary solutions formed from benzene, toluene, and ortho xylene, given their individual vapor pressures at 20°C.

### Step-by-Step Solution:

1. **Identify the Given Vapor Pressures:**
- Vapor pressure of benzene (P_benzene) = 75 Torr
- Vapor pressure of toluene (P_toluene) = 22 Torr
- Vapor pressure of ortho xylene (P_xylene) = 10 Torr

2. **Calculate the Vapor Pressure of Equimolar Binary Mixtures:**
- For an equimolar binary mixture, the mole fraction of each component is 0.5.

**Binary Mixture of Benzene and Toluene:**
\[ P_{total} = P_benzene \cdot x_{benzene} + P_toluene \cdot x_{toluene} \]
\[ P_{total} = 75 \cdot 0.5 + 22 \cdot 0.5 = 37.5 + 11 = 48.5 \text{ Torr} \]

**Binary Mixture of Benzene and Ortho Xylene:**
\[ P_{total} = P_benzene \cdot x_{benzene} + P_xylene \cdot x_{xylene} \]
\[ P_{total} = 75 \cdot 0.5 + 10 \cdot 0.5 = 37.5 + 5 = 42.5 \text{ Torr} \]

**Binary Mixture of Toluene and Ortho Xylene:**
\[ P_{total} = P_toluene \cdot x_{toluene} + P_xylene \cdot x_{xylene} \]
\[ P_{total} = 22 \cdot 0.5 + 10 \cdot 0.5 = 11 + 5 = 16 \text{ Torr} \]

3. **Calculate the Vapor Pressure of Equimolar Ternary Mixture:**
- For an equimolar ternary mixture, the mole fraction of each component is \( \frac{1}{3} \).

\[ P_{total} = P_benzene \cdot x_{benzene} + P_toluene \cdot x_{toluene} + P_xylene \cdot x_{xylene} \]
\[ P_{total} = 75 \cdot \frac{1}{3} + 22 \cdot \frac{1}{3} + 10 \cdot \frac{1}{3} \]
\[ P_{total} = 25 + \frac{22}{3} + \frac{10}{3} = 25 + 10.67 + 3.33 = 39 \text{ Torr} \approx 35.33 \text{ Torr} \]

4. **Determine Possible Vapor Pressures:**
- The possible vapor pressures from the calculations are:
- 48.5 Torr (Benzene + Toluene)
- 42.5 Torr (Benzene + Ortho Xylene)
- 16 Torr (Toluene + Ortho Xylene)
- 35.33 Torr (Ternary mixture)

5. **Identify the Incorrect Value:**
- The question asks for a value that is **not** possible. If we consider the calculated values and any other options provided, we can conclude that any value outside the range of 16 Torr to 48.5 Torr would be incorrect.

### Conclusion:
Based on the calculations, the value of 53.5 Torr is not a possible vapor pressure for the equimolar binary or ternary solution of benzene, toluene, and ortho xylene.