toluene = T
benzene = B
moles T = grams/molar mass
moles B = grams/molar mass
mole fraction B = moles B/total moles.
mole fraction T = moles T/total moles.
PB = XB*Po
PT = XT*Po
Total pressure = PB + PT.
benzene = B
moles T = grams/molar mass
moles B = grams/molar mass
mole fraction B = moles B/total moles.
mole fraction T = moles T/total moles.
PB = XB*Po
PT = XT*Po
Total pressure = PB + PT.
Step 1: Calculate the moles of benzene (C6H6) and toluene (C6H5CH3).
Moles of benzene = Mass of benzene / Molar mass of benzene
Molar mass of benzene (C6H6) = (6 * atomic mass of carbon) + (6 * atomic mass of hydrogen)
= (6 * 12.01 g/mol) + (6 * 1.01 g/mol)
= 78.11 g/mol
Moles of benzene = 66.73 g / 78.11 g/mol
Similarly, calculate the moles of toluene:
Molar mass of toluene (C6H5CH3) = (6 * atomic mass of carbon) + (5 * atomic mass of hydrogen) + (3 * atomic mass of carbon)
= (6 * 12.01 g/mol) + (5 * 1.01 g/mol) + (3 * 12.01 g/mol)
= 92.14 g/mol
Moles of toluene = 63.26 g / 92.14 g/mol
Step 2: Calculate the mole fraction of each component:
Mole fraction of benzene = Moles of benzene / Total moles of both components
Mole fraction of toluene = Moles of toluene / Total moles of both components
Step 3: Calculate the partial pressures of each component:
Partial pressure of benzene = Mole fraction of benzene * Vapor pressure of benzene
Partial pressure of toluene = Mole fraction of toluene * Vapor pressure of toluene
Step 4: Calculate the total vapor pressure:
Total vapor pressure = Partial pressure of benzene + Partial pressure of toluene
Now, using the given values:
Given:
Mass of benzene (C6H6) = 66.73 g
Mass of toluene (C6H5CH3) = 63.26 g
Vapor pressure of benzene at 20°C = 75 Torr
Vapor pressure of toluene at 20°C = 22 Torr
Step 1:
Moles of benzene = 66.73 g / 78.11 g/mol ≈ 0.8533 mol
Moles of toluene = 63.26 g / 92.14 g/mol ≈ 0.6863 mol
Step 2:
Mole fraction of benzene = 0.8533 mol / (0.8533 mol + 0.6863 mol) ≈ 0.554
Mole fraction of toluene = 0.6863 mol / (0.8533 mol + 0.6863 mol) ≈ 0.446
Step 3:
Partial pressure of benzene = 0.554 * 75 Torr ≈ 41.55 Torr
Partial pressure of toluene = 0.446 * 22 Torr ≈ 9.79 Torr
Step 4:
Total vapor pressure = 41.55 Torr + 9.79 Torr ≈ 51.34 Torr
Therefore, the vapor pressure above the solution is approximately 51.34 Torr.