Calculate the vapor pressure of a solution of 0.48 mol of cholesterol in 6.0 mol of toluene at 32°C. Pure toluene has a vapor pressure of 41 torr at 32°C. (Assume ideal behavior.)
Xtoluene = mols toluene/total mols
Psoln = Xtoluene*Potoluene
To calculate the vapor pressure of a solution, you can use Raoult's law, which states that the vapor pressure of a solvent above a solution is equal to the mole fraction of the solvent multiplied by the vapor pressure of the pure solvent.
First, let's calculate the mole fraction of the solvent (toluene) in the solution. The mole fraction (X) is the ratio of moles of the solvent to the total moles of all components in the solution.
Moles of toluene = 6.0 mol
Moles of cholesterol = 0.48 mol
Total moles of the components = Moles of toluene + Moles of cholesterol = 6.0 mol + 0.48 mol = 6.48 mol
Mole fraction of toluene (X) = Moles of toluene / Total moles of the components
= 6.0 mol / 6.48 mol
≈ 0.926
Now, we can calculate the vapor pressure of the solution using Raoult's law.
Vapor pressure of solution = Mole fraction of solvent (X) x Vapor pressure of pure solvent
Vapor pressure of solution = 0.926 x 41 torr
≈ 37.93 torr
Therefore, the vapor pressure of the solution of 0.48 mol of cholesterol in 6.0 mol of toluene at 32°C is approximately 37.93 torr.