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 partial pressure of each component in a solution is equal to the vapor pressure of the pure component multiplied by its mole fraction in the solution.
First, let's calculate the mole fraction of ethyl ether (Xether) and ethyl alcohol (Xalcohol) in the solution.
Mole fraction (X) is calculated using the equation:
X = moles of component / total moles of all components
Given:
moles of ethyl ether = 0.100 mole
moles of ethyl alcohol = 0.841 mole
Total moles of all components = moles of ethyl ether + moles of ethyl alcohol
= 0.100 mole + 0.841 mole
= 0.941 mole
Now, let's calculate the mole fractions:
Xether = moles of ethyl ether / total moles of all components
= 0.100 mole / 0.941 mole
≈ 0.106
Xalcohol = moles of ethyl alcohol / total moles of all components
= 0.841 mole / 0.941 mole
≈ 0.894
Now, we can use Raoult's law to calculate the vapor pressure of the solution.
Vapor pressure of the solution (Psolution) = Xether * Pether + Xalcohol * Palcohol
Given:
Pether = 375 torr (vapor pressure of ethyl ether)
Palcohol = 20.0 torr (vapor pressure of ethyl alcohol)
Psolution = 0.106 * 375 torr + 0.894 * 20.0 torr
≈ 39.75 torr + 17.88 torr
≈ 57.63 torr
Therefore, the vapor pressure of the solution at 20°C (assuming ideal behavior) is approximately 57.63 torr.