A solution is made by adding 0.100 mole of ethyl ether to 0.841 mole of ethyl alcohol. If the vapor pressure of ethyl ether and ethyl alcohol at 20oC are 375 torr and 20.0 torr, respectively, the vapor pressure of the solution at 20oC (assuming ideal behavior) is:
Answer
To find the vapor pressure of the solution, we can use Raoult's law which states that the vapor pressure of a solution is equal to the mole fraction of the solvent multiplied by the vapor pressure of the pure solvent.
Step 1: Calculate the mole fraction of ethyl ether (solvent).
Mole fraction (X_ether) = Moles of ether / Total moles
Moles of ether = 0.100 mol
Moles of alcohol = 0.841 mol
Total moles = 0.100 mol + 0.841 mol = 0.941 mol
X_ether = 0.100 mol / 0.941 mol ≈ 0.1063
Step 2: Calculate the mole fraction of ethyl alcohol (solvent).
X_alcohol = 1 - X_ether
X_alcohol = 1 - 0.1063 = 0.8937
Step 3: Use Raoult's law to calculate the vapor pressure of the solution.
P_solution = (X_ether * P_ether) + (X_alcohol * P_alcohol)
Given:
P_ether = 375 torr
P_alcohol = 20.0 torr
P_solution = (0.1063 * 375 torr) + (0.8937 * 20.0 torr)
P_solution = 39.844 torr + 17.874 torr
P_solution ≈ 57.718 torr
Therefore, the vapor pressure of the solution at 20°C is approximately 57.718 torr.
To determine the vapor pressure of the solution, we can use Raoult's law, which states that the vapor pressure of a component in a solution is equal to the product of the mole fraction of that component in the solution and its pure vapor pressure.
First, we need to calculate the mole fraction of ethyl ether and ethyl alcohol in the solution.
Mole fraction of ethyl ether (Xether) = moles of ethyl ether / total moles of the solution
= 0.100 / (0.100 + 0.841)
Mole fraction of ethyl alcohol (Xalcohol) = moles of ethyl alcohol / total moles of the solution
= 0.841 / (0.100 + 0.841)
Now, we can calculate the vapor pressure of the solution using Raoult's law:
Vapor pressure of the solution = (Xether * Pure vapor pressure of ethyl ether) + (Xalcohol * Pure vapor pressure of ethyl alcohol)
Substituting the given values:
Vapor pressure of the solution = (Xether * 375 torr) + (Xalcohol * 20.0 torr)
Now, let's calculate the values:
Xether = 0.100 / (0.100 + 0.841) ≈ 0.106
Xalcohol = 0.841 / (0.100 + 0.841) ≈ 0.894
Vapor pressure of the solution = (0.106 * 375 torr) + (0.894 * 20.0 torr)
Vapor pressure of the solution = 39.75 torr + 17.88 torr
Vapor pressure of the solution = 57.63 torr
Therefore, the vapor pressure of the solution at 20°C (assuming ideal behavior) is approximately 57.63 torr.
total moles = mol ether + mol EtOH
Xether = moles ether/total mols
XEtOH = moles EtOH/total moles
pether = Xether*Po ether
pEtOH = XEtOH*Po EtOH
Total vapor pressure above the solution = pether + pEtOH.