Xether = mols ether/total mols.
Xethanol = mols ethanol/total mols.
pether = Xether*Poether
pethanol = Xethanol*Poethanol.
Totol P = pether + pethanol.
Xethanol = mols ethanol/total mols.
pether = Xether*Poether
pethanol = Xethanol*Poethanol.
Totol P = pether + pethanol.
The mole fraction of ethyl ether can be calculated using the formula:
Mole fraction of ethyl ether = Moles of ethyl ether / Total moles of both components
Mole fraction of ethyl ether = 0.100 moles / (0.100 moles + 0.500 moles)
Mole fraction of ethyl ether = 0.100 / 0.600
Mole fraction of ethyl ether = 0.1667
Now we can calculate the vapor pressure of the solution using Raoult's law:
Vapor pressure of the solution = Mole fraction of ethyl ether * Vapor pressure of ethyl ether + Mole fraction of ethyl alcohol * Vapor pressure of ethyl alcohol
Vapor pressure of the solution = 0.1667 * 375 torr + 0.8333 * 20.0 torr
Calculating the above expression:
Vapor pressure of the solution = (0.1667 * 375) + (0.8333 * 20.0)
Vapor pressure of the solution = 62.5 + 16.67
Vapor pressure of the solution = 79.17 torr
Therefore, the vapor pressure of the solution at 20oC (assuming ideal behavior) is 79.17 torr.
The mole fraction of a component can be calculated by dividing the number of moles of that component by the total number of moles in the solution.
Given:
Moles of ethyl ether (C4H10O) = 0.100 mol
Moles of ethyl alcohol (C2H6O) = 0.500 mol
Vapor pressure of ethyl ether (C4H10O) = 375 torr
Vapor pressure of ethyl alcohol (C2H6O) = 20.0 torr
Step 1: Calculate the mole fraction of ethyl ether (C4H10O):
Mole fraction of C4H10O = moles of C4H10O / total moles in solution
Mole fraction of C4H10O = 0.100 mol / (0.100 mol + 0.500 mol)
Mole fraction of C4H10O = 0.100 mol / 0.600 mol
Mole fraction of C4H10O = 0.1667
Step 2: Calculate the mole fraction of ethyl alcohol (C2H6O):
Mole fraction of C2H6O = moles of C2H6O / total moles in solution
Mole fraction of C2H6O = 0.500 mol / (0.100 mol + 0.500 mol)
Mole fraction of C2H6O = 0.500 mol / 0.600 mol
Mole fraction of C2H6O = 0.8333
Step 3: Calculate the vapor pressure of the solution using Raoult's Law:
Vapor pressure of solution = (mole fraction of C4H10O) * (vapor pressure of C4H10O) + (mole fraction of C2H6O) * (vapor pressure of C2H6O)
Vapor pressure of solution = (0.1667) * (375 torr) + (0.8333) * (20.0 torr)
Vapor pressure of solution = 62.5 torr + 16.7 torr
Vapor pressure of solution = 79.2 torr
Therefore, the vapor pressure of the solution at 20 oC (assuming ideal behavior) is 79.2 torr.