To find the vapor pressure of the solution, we need to 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 ethyl ether (Xā) in the solution can be calculated by dividing the moles of ethyl ether by the total moles of both components:
Xā = moles of ethyl ether / total moles
Xā = 0.100 / (0.100 + 0.841)
Xā = 0.100 / 0.941
Xā ā 0.106
The mole fraction of ethyl alcohol (Xā) can be calculated similarly:
Xā = moles of ethyl alcohol / total moles
Xā = 0.841 / (0.100 + 0.841)
Xā = 0.841 / 0.941
Xā ā 0.894
Now, we can calculate the vapor pressure of the solution using Raoult's Law:
P_solution = Pā * Xā + Pā * Xā
where Pā = vapor pressure of ethyl ether and Pā = vapor pressure of ethyl alcohol.
Plugging in the values:
P_solution = (375 torr * 0.106) + (20.0 torr * 0.894)
P_solution = 39.75 torr + 17.88 torr
P_solution ā 57.63 torr
Therefore, the vapor pressure of the solution at 20Ā°C is approximately 57.63 torr.