What is the vapor pressure in Torr above a solution prepared by mixing 66.73g of benzene C6H6 with 63.26g toluene C6H5CH3 at 20 Celsius. The vapor pressure of pure benzene and toluene at 20celsius are 75 and 22 torr respectively. These compounds form nearly ideal solutions when mixed together.
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.
To calculate the vapor pressure above the solution, we need to first calculate the mole fraction of each component in the mixture using the given masses of benzene and toluene.
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.