solution is made by adding 0.100 mole of ethyl ether to 0.350 mole of ethyl alcohol. If the vapor pressure of ethyl ether and ethyl alcohol at 20°C are 375 torr and 20.0 torr, respectively, the vapor pressure of the solution at 20°C (assuming ideal behavior) is:
Pether = Xether*Po ether
Palc = Xalc*Po alc
Ptotal = pether + palc
I assume you know how to get Xether and Xalc. Xether = mols ether/total mols.
Xalc = mols alc/total mols.
To determine the vapor pressure of the solution, we need to use Raoult's law, which states that the vapor pressure of a component in a mixture is proportional to its mole fraction in the mixture.
First, we need to find the mole fraction of each component in the mixture. The mole fraction of a component is calculated by dividing the number of moles of that component by the total number of moles of all components.
Given:
- Moles of ethyl ether (C2H5-O-C2H5) = 0.100 mol
- Moles of ethyl alcohol (C2H5-OH) = 0.350 mol
Total moles = 0.100 mol + 0.350 mol = 0.450 mol
Mole fraction of ethyl ether = Moles of ethyl ether / Total moles
= 0.100 mol / 0.450 mol
= 0.222
Mole fraction of ethyl alcohol = Moles of ethyl alcohol / Total moles
= 0.350 mol / 0.450 mol
= 0.778
Now, we can use Raoult's law to find the vapor pressure of the solution.
P solution = X ether * P ether + X alcohol * P alcohol
where:
- P solution is the vapor pressure of the solution
- X ether is the mole fraction of ethyl ether in the solution
- P ether is the vapor pressure of ethyl ether
- X alcohol is the mole fraction of ethyl alcohol in the solution
- P alcohol is the vapor pressure of ethyl alcohol
Plugging in the values:
P solution = (0.222 * 375 torr) + (0.778 * 20.0 torr)
= 83.25 torr + 15.56 torr
= 98.81 torr
Therefore, the vapor pressure of the solution at 20°C, assuming ideal behavior, is 98.81 torr.