Heptane and octane form an ideal solution. At 373 K, the vapour pressure of the two liquid components are 105.2 kPa and 46.8 kPa respectively, what will be the vapour pressure of a mixture of 26.0 g of heptane and 35 g of octane ?

Options

A. 7.308 kPa
B. 73.08 kPa
C. 730.8 kPa
D. 7308 kPa

Explanation

To find the vapor pressure of a mixture of heptane and octane, we can use Raoult's Law and Dalton's Law. Here’s a step-by-step solution:

### Step 1: Calculate the number of moles of heptane and octane.

**Heptane:**
- Given mass of heptane = 26.0 g
- Molar mass of heptane (C7H16) = 100 g/mol

\[ \text{Number of moles of heptane} = \frac{\text{mass}}{\text{molar mass}} = \frac{26.0 \, \text{g}}{100 \, \text{g/mol}} = 0.26 \, \text{mol} \]

**Octane:**
- Given mass of octane = 35.0 g
- Molar mass of octane (C8H18) = 114 g/mol

\[ \text{Number of moles of octane} = \frac{35.0 \, \text{g}}{114 \, \text{g/mol}} \approx 0.307 \, \text{mol} \]

### Step 2: Calculate the total number of moles in the mixture.

\[ \text{Total moles} = \text{moles of heptane} + \text{moles of octane} = 0.26 \, \text{mol} + 0.307 \, \text{mol} \approx 0.567 \, \text{mol} \]

### Step 3: Calculate the mole fraction of heptane and octane.

**Mole fraction of heptane (X_A):**

\[ X_A = \frac{\text{moles of heptane}}{\text{total moles}} = \frac{0.26}{0.567} \approx 0.459 \]

**Mole fraction of octane (X_B):**

\[ X_B = \frac{\text{moles of octane}}{\text{total moles}} = \frac{0.307}{0.567} \approx 0.541 \]

### Step 4: Calculate the partial pressures of heptane and octane using Raoult's Law.

**Partial pressure of heptane (P_A):**

\[ P_A = X_A \times P^0_A = 0.459 \times 105.2 \, \text{kPa} \approx 48.34 \, \text{kPa} \]

**Partial pressure of octane (P_B):**

\[ P_B = X_B \times P^0_B = 0.541 \times 46.8 \, \text{kPa} \approx 25.34 \, \text{kPa} \]

### Step 5: Calculate the total vapor pressure of the mixture.

\[ P_{\text{total}} = P_A + P_B = 48.34 \, \text{kPa} + 25.34 \, \text{kPa} \approx 73.68 \, \text{kPa} \]

### Final Answer:
The vapor pressure of the mixture of 26.0 g of heptane and 35.0 g of octane at 373 K is approximately **73.68 kPa**.

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