Heptane and octane form an ideal solution. At 373 K, the vapour pressures 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?

To find the vapor pressure of a mixture of heptane and octane, we can use Raoult's Law, which states that the vapor pressure of a component in a mixture is equal to the vapor pressure of the pure component multiplied by its mole fraction in the mixture. Let's break this down step by step.

Step 1: Calculate Moles of Each Component

First, we need to determine the number of moles of heptane and octane in the mixture. The molar mass of heptane (C7H16) is approximately 100.2 g/mol, and for octane (C8H18), it is about 114.2 g/mol.

• Moles of Heptane:

  Using the formula: moles = mass / molar mass

  For heptane: moles = 26.0 g / 100.2 g/mol ≈ 0.259 moles

• Moles of Octane:

  For octane: moles = 35.0 g / 114.2 g/mol ≈ 0.307 moles

Step 2: Calculate Total Moles in the Mixture

Next, we add the moles of both components to find the total number of moles in the mixture.

Total moles = moles of heptane + moles of octane = 0.259 + 0.307 ≈ 0.566 moles

Step 3: Determine Mole Fractions

Now, we can calculate the mole fractions of each component in the mixture.

• Mole Fraction of Heptane (X_heptane):

  X_heptane = moles of heptane / total moles = 0.259 / 0.566 ≈ 0.458

• Mole Fraction of Octane (X_octane):

  X_octane = moles of octane / total moles = 0.307 / 0.566 ≈ 0.542

Step 4: Apply Raoult's Law

According to Raoult's Law, the vapor pressure of the mixture (P_total) can be calculated as follows:

P_total = (X_heptane * P_heptane) + (X_octane * P_octane)

Where:

• P_heptane = 105.2 kPa
• P_octane = 46.8 kPa

Substituting the values we calculated:

P_total = (0.458 * 105.2 kPa) + (0.542 * 46.8 kPa)

Step 5: Calculate the Total Vapor Pressure

Now, we perform the calculations:

• For heptane: 0.458 * 105.2 ≈ 48.2 kPa
• For octane: 0.542 * 46.8 ≈ 25.4 kPa

Adding these together gives:

P_total ≈ 48.2 kPa + 25.4 kPa ≈ 73.6 kPa

Final Result

The vapor pressure of the mixture of 26.0 g of heptane and 35 g of octane at 373 K is approximately 73.6 kPa. This calculation illustrates how the individual contributions of each component in a mixture can be combined to determine the overall vapor pressure, showcasing the practical application of Raoult's Law in real-world scenarios.