To determine the mole ratio of benzene (C6H6) to n-octane in the vapor above the solution, we need to consider the vapor pressure of each component and their relative amounts in the solution.
Here's how we can approach this problem step by step:
Step 1: Calculate the masses of benzene and n-octane in the solution.
- Assume we have 100 grams of the solution.
- The solution is 15.0% benzene by mass, so the mass of benzene can be calculated as:
Mass of benzene = 15.0 grams (100 grams)
- Similarly, the mass of n-octane can be calculated as:
Mass of n-octane = 85.0 grams (100 grams)
Step 2: Convert the masses of benzene and n-octane to moles.
- First, we need to calculate the molecular weight of benzene and n-octane.
Molecular weight of benzene (C6H6) = 6(12.01 g/mol) + 6(1.01 g/mol) = 78.11 g/mol
Molecular weight of n-octane (C8H18) = 8(12.01 g/mol) + 18(1.01 g/mol) = 114.23 g/mol
- Now, we can convert the masses to moles using the molecular weights:
Moles of benzene = Mass of benzene / Molecular weight of benzene
= 15.0 g / 78.11 g/mol
Moles of n-octane = Mass of n-octane / Molecular weight of n-octane
= 85.0 g / 114.23 g/mol
Step 3: Calculate the mole ratio of benzene to n-octane.
- The mole ratio of benzene to n-octane can be determined by dividing the moles of benzene by the moles of n-octane:
Mole ratio of benzene to n-octane = Moles of benzene / Moles of n-octane
For example, if we calculate the moles and mole ratio using the given masses and molecular weights, we would have:
Moles of benzene = 15.0 g / 78.11 g/mol ≈ 0.192 mol
Moles of n-octane = 85.0 g / 114.23 g/mol ≈ 0.743 mol
Mole ratio of benzene to n-octane = 0.192 mol / 0.743 mol ≈ 0.258
Therefore, the mole ratio of benzene to n-octane in the vapor above the solution is approximately 0.258.