At `100^@C` vapour pressure of heptane and octane are respectively 105.2 and 46.8 kPa. Calculate the vapour pressure of 60 grams of the mixture of two liquids, in which the mass of octane is 35g.

Answer

To solve the problem of calculating the vapor pressure of a mixture of heptane and octane at 100°C, we will follow these steps:

### Step 1: Identify the given data
- Vapor pressure of heptane (Pₐ⁰) = 105.2 kPa
- Vapor pressure of octane (Pᵦ⁰) = 46.8 kPa
- Mass of octane (mᵦ) = 35 g
- Total mass of the mixture (m_total) = 60 g

### Step 2: Calculate the mass of heptane
To find the mass of heptane, we subtract the mass of octane from the total mass of the mixture:
\[ mₐ = m_{total} - mᵦ = 60 \, \text{g} - 35 \, \text{g} = 25 \, \text{g} \]

### Step 3: Calculate the molar masses
- Molar mass of heptane (C₇H₁₆) = 100 g/mol
- Molar mass of octane (C₈H₁₈) = 114 g/mol

### Step 4: Calculate the number of moles of each component
Using the formula:
\[ \text{Number of moles} = \frac{\text{mass}}{\text{molar mass}} \]
- For heptane:
\[ nₐ = \frac{mₐ}{Mₐ} = \frac{25 \, \text{g}}{100 \, \text{g/mol}} = 0.25 \, \text{mol} \]
- For octane:
\[ nᵦ = \frac{mᵦ}{Mᵦ} = \frac{35 \, \text{g}}{114 \, \text{g/mol}} \approx 0.307 \, \text{mol} \]

### Step 5: Calculate the total number of moles
\[ n_{total} = nₐ + nᵦ = 0.25 \, \text{mol} + 0.307 \, \text{mol} \approx 0.557 \, \text{mol} \]

### Step 6: Calculate the mole fractions
- Mole fraction of heptane (Xₐ):
\[ Xₐ = \frac{nₐ}{n_{total}} = \frac{0.25}{0.557} \approx 0.449 \]
- Mole fraction of octane (Xᵦ):
\[ Xᵦ = \frac{nᵦ}{n_{total}} = \frac{0.307}{0.557} \approx 0.551 \]

### Step 7: Apply Raoult's Law to find the vapor pressure of the mixture
According to Raoult's Law:
\[ P_{solution} = Pₐ⁰ \cdot Xₐ + Pᵦ⁰ \cdot Xᵦ \]
Substituting the values:
\[ P_{solution} = (105.2 \, \text{kPa} \cdot 0.449) + (46.8 \, \text{kPa} \cdot 0.551) \]
Calculating each term:
\[ P_{solution} = 47.16 \, \text{kPa} + 25.77 \, \text{kPa} \approx 72.93 \, \text{kPa} \]

### Final Answer
The vapor pressure of the mixture is approximately **72.93 kPa**.

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