5 moles of liquid X and 10 moles of liquid Y make a solution having a total vapour pressure 70 torr. The vapour pressures of pure X and pure Y are 64 torr and 76 torr respectively.Calculate the expected pressure.

Options

A. 70 torr
B. 80 torr
C. 72 torr
D. 82 torr

Answer

To solve the problem, we will use Raoult's Law, which states that the vapor pressure of a solution is equal to the sum of the partial pressures of each component in the solution.

### Step-by-Step Solution:

1. **Identify the Given Data:**
- Moles of liquid X (n_X) = 5 moles
- Moles of liquid Y (n_Y) = 10 moles
- Vapor pressure of pure X (P°_X) = 64 torr
- Vapor pressure of pure Y (P°_Y) = 76 torr
- Total vapor pressure of the solution (P_total) = 70 torr (not needed for calculation but provided)

2. **Calculate the Total Moles of the Solution:**
\[ n_{total} = n_X + n_Y = 5 + 10 = 15 \text{ moles} \]

3. **Calculate the Mole Fraction of Each Component:**
- Mole fraction of X (χ_X):
\[ χ_X = \frac{n_X}{n_{total}} = \frac{5}{15} = \frac{1}{3} \]
- Mole fraction of Y (χ_Y):
\[ χ_Y = \frac{n_Y}{n_{total}} = \frac{10}{15} = \frac{2}{3} \]

4. **Calculate the Partial Pressure of Each Component Using Raoult's Law:**
- Partial pressure of X (P_X):
\[ P_X = χ_X \cdot P°_X = \left(\frac{1}{3}\right) \cdot 64 \text{ torr} = \frac{64}{3} \text{ torr} \approx 21.33 \text{ torr} \]
- Partial pressure of Y (P_Y):
\[ P_Y = χ_Y \cdot P°_Y = \left(\frac{2}{3}\right) \cdot 76 \text{ torr} = \frac{152}{3} \text{ torr} \approx 50.67 \text{ torr} \]

5. **Calculate the Total Vapor Pressure of the Solution:**
\[ P_{total} = P_X + P_Y = 21.33 \text{ torr} + 50.67 \text{ torr} = 72 \text{ torr} \]

### Final Answer:
The expected pressure of the solution is **72 torr**.

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