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
To find the vapor pressure of the solution, we need to apply Raoult's law. According to Raoult's law, the vapor pressure of a component in a solution is directly proportional to its mole fraction.
First, we need to calculate the mole fractions of ethyl ether and ethyl alcohol in the solution.
Mole fraction of ethyl ether (Xether):
Xether = (moles of ethyl ether) / (total moles of both components)
Xether = 0.100 / (0.100 + 0.841)
Mole fraction of ethyl alcohol (Xalcohol):
Xalcohol = (moles of ethyl alcohol) / (total moles of both components)
Xalcohol = 0.841 / (0.100 + 0.841)
Now, we can use the mole fractions to calculate the vapor pressure of the solution.
Vapor pressure of the solution:
Psolution = (Xether * Pvapor_ether) + (Xalcohol * Pvapor_alcohol)
Psolution = (Xether * 375) + (Xalcohol * 20.0)
Substituting the values:
Psolution = (0.100 / (0.100 + 0.841) * 375) + (0.841 / (0.100 + 0.841) * 20.0)
Now, calculate the value:
Psolution = (0.100 / 0.941 * 375) + (0.841 / 0.941 * 20.0)
Psolution = (0.106 * 375) + (0.895 * 20.0)
Psolution = 39.75 + 17.90
Therefore, the vapor pressure of the solution at 20°C is approximately 57.7 torr.