The vapor pressures of benzenen, toluene and `a` xylene are `70` Torr, `20` 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. `45`
B. 15
C. `33(1)/(3)`
D. `54(3)/(2)`

Explanation

To solve the problem, we need to determine the possible vapor pressures of an equimolar ternary solution of benzene, toluene, and xylene at 20°C. The vapor pressures of the individual components are given as follows:

- Vapor pressure of benzene (P_benzene) = 70 Torr
- Vapor pressure of toluene (P_toluene) = 20 Torr
- Vapor pressure of xylene (P_xylene) = 10 Torr

### Step-by-Step Solution:

1. **Understanding the Equimolar Ternary Mixture:**
In an equimolar ternary mixture, the mole fraction of each component is equal. Since there are three components (benzene, toluene, and xylene), the mole fraction (X) of each will be:
\[ X_{benzene} = X_{toluene} = X_{xylene} = \frac{1}{3} \]

2. **Calculating the Total Vapor Pressure:**
The total vapor pressure (P_total) of an ideal solution can be calculated using Raoult's Law:
\[ P_{total} = X_{benzene} \cdot P_{benzene} + X_{toluene} \cdot P_{toluene} + X_{xylene} \cdot P_{xylene} \]
Substituting the values:
\[ P_{total} = \left(\frac{1}{3} \cdot 70\right) + \left(\frac{1}{3} \cdot 20\right) + \left(\frac{1}{3} \cdot 10\right) \]

3. **Calculating Each Component's Contribution:**
- Contribution from benzene:
\[ \frac{1}{3} \cdot 70 = \frac{70}{3} \approx 23.33 \text{ Torr} \]
- Contribution from toluene:
\[ \frac{1}{3} \cdot 20 = \frac{20}{3} \approx 6.67 \text{ Torr} \]
- Contribution from xylene:
\[ \frac{1}{3} \cdot 10 = \frac{10}{3} \approx 3.33 \text{ Torr} \]

4. **Adding the Contributions:**
Now, we add these contributions together:
\[ P_{total} = \frac{70}{3} + \frac{20}{3} + \frac{10}{3} = \frac{100}{3} \text{ Torr} \approx 33.33 \text{ Torr} \]

5. **Identifying Possible Values:**
The possible vapor pressure values for the equimolar ternary mixture must lie between the lowest and highest vapor pressures of the individual components, which are 10 Torr (xylene) and 70 Torr (benzene). Therefore, the possible range for the vapor pressure of the ternary mixture is:
\[ 10 \text{ Torr} < P_{total} < 70 \text{ Torr} \]

6. **Finding the Not Possible Value:**
From the options provided, we need to identify which value does not fall within the range of 10 Torr to 70 Torr. The calculated total vapor pressure of the equimolar ternary mixture is approximately 33.33 Torr. Any value outside the range of 10 to 70 Torr is not possible.

### Conclusion:
The value that is not a possible vapor pressure for the equimolar ternary solution is the one that exceeds 70 Torr or is below 10 Torr. Based on the calculations, the answer is the value that does not match the calculated total pressure.