A solution is made by adding 0.100 mole of ethyl ether to 0.500 mole of ethyl alcohol. If the vapor pressures of ethyl ether and ethyl alcohol at 20 oC are 375 torr and 20.0 torr, respectively, the vapor pressure of the solution at 20 oC (assuming ideal behavior) is:
To find the vapor pressure of the solution, we need to use Raoult's Law, which states that the vapor pressure of a component in a solution is equal to the mole fraction of that component multiplied by its vapor pressure in its pure state.
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.
To find the vapor pressure of the solution, we can use Raoult's Law, which states that the vapor pressure of a solution is proportional to the mole fraction of each component in the solution.
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.
Xether = mols ether/total mols.
Xethanol = mols ethanol/total mols.
pether = Xether*Poether
pethanol = Xethanol*Poethanol.
Totol P = pether + pethanol.