Benzene (C6H6) and toluene (C5H5CH3) form nearly ideal solutions. At 20°C the vapor pressure of benzene is 74.7 Torr and that of toluene is 22.3 Torr. a) Find the equilibrium partial pressures above a solution of 100.0 g benzene and 100.0 g toluene. b) Find the mole fractions in the vapor phase that is in equilibrium with the solution in part a).
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To find the equilibrium partial pressures above the solution, we need to use Raoult's Law, which states that the vapor pressure of a component in an ideal solution is directly proportional to its mole fraction in the solution.
a) Let's calculate the mole fractions of benzene (C6H6) and toluene (C5H5CH3) in the solution:
Molar mass of benzene (C6H6) = 12.01 g/mol x 6 + 1.01 g/mol x 6 = 78.11 g/mol
Molar mass of toluene (C5H5CH3) = 12.01 g/mol x 7 + 1.01 g/mol x 8 = 92.14 g/mol
Number of moles of benzene (C6H6) = 100.0 g / 78.11 g/mol = 1.28 mol
Number of moles of toluene (C5H5CH3) = 100.0 g / 92.14 g/mol = 1.09 mol
Total number of moles in the solution = moles of benzene + moles of toluene
= 1.28 mol + 1.09 mol = 2.37 mol
Mole fraction of benzene (C6H6) = 1.28 mol / 2.37 mol = 0.54
Mole fraction of toluene (C5H5CH3) = 1.09 mol / 2.37 mol = 0.46
Now, we can use Raoult's Law to calculate the equilibrium partial pressures:
Partial pressure of benzene = Mole fraction of benzene x Vapor pressure of benzene
= 0.54 x 74.7 Torr = 40.338 Torr
Partial pressure of toluene = Mole fraction of toluene x Vapor pressure of toluene
= 0.46 x 22.3 Torr = 10.238 Torr
Therefore, the equilibrium partial pressures above the solution of 100.0 g benzene and 100.0 g toluene are:
Partial pressure of benzene = 40.338 Torr
Partial pressure of toluene = 10.238 Torr
b) To find the mole fractions in the vapor phase that is in equilibrium with the solution, we can use Dalton's Law of partial pressures, which states that the total pressure of a mixture of ideal gases is the sum of the partial pressures of each component.
Total pressure above the solution = Partial pressure of benzene + Partial pressure of toluene
= 40.338 Torr + 10.238 Torr = 50.576 Torr
The mole fraction of benzene in the vapor phase can be calculated using its partial pressure:
Mole fraction of benzene in vapor phase = Partial pressure of benzene / Total pressure above the solution
= 40.338 Torr / 50.576 Torr = 0.797
The mole fraction of toluene in the vapor phase can be calculated using its partial pressure:
Mole fraction of toluene in vapor phase = Partial pressure of toluene / Total pressure above the solution
= 10.238 Torr / 50.576 Torr = 0.203
Therefore, the mole fractions in the vapor phase that are in equilibrium with the solution are:
Mole fraction of benzene = 0.797
Mole fraction of toluene = 0.203