Calculate the vapor pressure of a solution of 0.39 mol of cholesterol in 5.4 mol of toluene at 32oC. Pure toluene has a vapor pressure of 41 torr at 32oC.
Isn't this Raoult's law? http://www.ausetute.com.au/raoult.html
Pressure= 5.4/(5.4+.39) * 41torr
To calculate the vapor pressure of a solution of two components, we can use Raoult's law, which states that the vapor pressure of a component in a solution is equal to the product of its mole fraction and the vapor pressure of the pure component.
First, we need to calculate the mole fraction of cholesterol and toluene in the solution.
Step 1: Calculate the total moles of the solution:
Total moles = moles of cholesterol + moles of toluene
Total moles = 0.39 mol + 5.4 mol
Total moles = 5.79 mol
Step 2: Calculate the mole fraction of cholesterol and toluene:
Mole fraction of cholesterol = moles of cholesterol / total moles
Mole fraction of cholesterol = 0.39 mol / 5.79 mol
Mole fraction of cholesterol = 0.0674
Mole fraction of toluene = moles of toluene / total moles
Mole fraction of toluene = 5.4 mol / 5.79 mol
Mole fraction of toluene = 0.9326
Step 3: Calculate the vapor pressure of the solution using Raoult's law:
Vapor pressure of the solution = (Mole fraction of cholesterol) * (Vapor pressure of cholesterol) + (Mole fraction of toluene) * (Vapor Pressure of toluene)
Given:
Vapor pressure of cholesterol = 0 (Cholesterol does not have appreciable vapor pressure at this temperature)
Vapor pressure of toluene = 41 torr
Vapor pressure of the solution = (0.0674) * (0) + (0.9326) * (41 torr)
Vapor pressure of the solution = 0 + 38.23 torr
Therefore, the vapor pressure of the solution is approximately 38.23 torr at 32°C.
To calculate the vapor pressure of a solution, we can use Raoult's Law. According to Raoult's Law, 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.
The mole fraction of the solvent (toluene) can be calculated by dividing the number of moles of the solvent by the total number of moles in the solution.
Given:
Number of moles of cholesterol (solute) = 0.39 mol
Number of moles of toluene (solvent) = 5.4 mol
Vapor pressure of pure toluene = 41 torr
Step 1: Calculate the total number of moles in the solution.
Total moles = moles of cholesterol + moles of toluene
Total moles = 0.39 mol + 5.4 mol
Total moles = 5.79 mol
Step 2: Calculate the mole fraction of toluene.
Mole fraction of toluene = moles of toluene / total moles
Mole fraction of toluene = 5.4 mol / 5.79 mol
Mole fraction of toluene ≈ 0.932
Step 3: Apply Raoult's Law to calculate the vapor pressure of the solution.
Vapor pressure of the solution = mole fraction of toluene * vapor pressure of pure toluene
Vapor pressure of the solution = 0.932 * 41 torr
Vapor pressure of the solution ≈ 38.012 torr
Therefore, the vapor pressure of the solution of 0.39 mol of cholesterol in 5.4 mol of toluene at 32°C is approximately 38.012 torr.