A solution is made by mixing 50.0 g C3H6O and 50.0 g of CH3OH. What is the vapor pressure of this solution at 25 degrees C? What is the composition of the vapor expressed as a mole fraction? Assume ideal solution and gas behavior. (At 25 degrees C the vapor pressures of pure acetone and methanol are 271 torr and 143 torr, respectively.)

I calculated the vapor pressure [work shown at end] but I'm confused about the second part of the question. What does it mean to find the composition of the vapor expressed as a mole fraction? It can't be just the mole fraction of 50.0 g C3H6O to 50.0 g CH3OH can it?

Work:
P1= X1 * P*1
50.0 g C3H6O x 1 m/58.09g= .8607 m
50.0 g CH3OH x 1 m/32.05g= 1.560 m
.8607 m C3H6O/2.420 m total= .3556
P1= .3556*143 torr= 50.85 torr

I believe you have used Raoult's Law for a non-volatile solute dissolved in a volatile solvent. In this problem, however, BOTH liquids are volatile and what you have used is not appropriate (although some of the calculation is).
Calculate the mole fraction of acetone (which you have done) and the mole fraction of methanol (which you have done).
Then Pacetone=XacetonePoacetone

Pmethanol=XmethanolPomethanol

The total pressure, then, is
Ptotal=Pacetone + Pmethanol

Let me look to see that all of this copied correctly and I will post the second part of the problem separately.
Check my thinking.

To do the second part, one must realize that the VAPOR will be richer in the more volatile component. The problem is asking you to calculate the mole fractions of the components in the vapor. mole fraction of a component = ratio of partial pressure of component/total pressure. You have just calcualted the total P and you have the partial pressures of each component.

Xaceton=Pacetone/Ptotal

Xmethanol=Pmethanol/Ptotal

Check my thinking.

Ah, I see what you mean now. To find the composition of the vapor expressed as a mole fraction, you need to calculate the mole fraction of each component in the vapor. The mole fraction of a component is the ratio of its partial pressure to the total pressure.

In this case, you have already calculated the partial pressures of acetone and methanol in the vapor:

Pacetone = 50.85 torr (from your calculation)
Pmethanol = ??? (Please calculate this based on the given information)

Next, you'll need to calculate the total pressure of the vapor, which is the sum of the partial pressures of acetone and methanol:

Ptotal = Pacetone + Pmethanol

Once you have the total pressure, you can calculate the mole fractions of acetone and methanol in the vapor:

Xacetone = Pacetone / Ptotal
Xmethanol = Pmethanol / Ptotal

I hope this clarifies the concept of finding the composition of the vapor expressed as a mole fraction. Let me know if you have any other questions!

You are correct in calculating the mole fraction of each component in the vapor. As you mentioned, the mole fraction of a component is calculated by dividing the partial pressure of that component by the total pressure.

In this case, you have already calculated the total pressure to be 50.85 torr.

To find the mole fraction of acetone in the vapor, you would divide the partial pressure of acetone by the total pressure:

X_acetone = P_acetone / P_total = (0.3556 * 143 torr) / 50.85 torr

To find the mole fraction of methanol in the vapor, you would divide the partial pressure of methanol by the total pressure:

X_methanol = P_methanol / P_total = (0.6444 * 143 torr) / 50.85 torr

These calculations will give you the composition of the vapor expressed as mole fractions.

You are correct that the approach you used in your initial calculation is not appropriate for this problem since both liquids, acetone (C3H6O) and methanol (CH3OH), are volatile. But you did make use of the correct equation for Raoult's Law: P1 = X1 * P*1, where P1 is the vapor pressure of the solvent (acetone in this case), X1 is the mole fraction of the solvent, and P*1 is the vapor pressure of the pure solvent.

To answer the second part of the question, you need to calculate the mole fractions of acetone and methanol in the vapor phase. The mole fraction of a component is calculated by dividing the partial pressure of the component by the total pressure. So, in this case:

X_acetone = P_acetone / P_total

X_methanol = P_methanol / P_total

Where P_acetone is the partial pressure of acetone, P_methanol is the partial pressure of methanol, and P_total is the total pressure of the vapor. You have already calculated P_acetone, P_methanol, and P_total in your initial calculation, so you can use those values to find the mole fractions.

Using the values you found:
P_acetone = 50.85 torr
P_methanol = (P_total - P_acetone)
P_total = 50.85 torr + (P_total - 50.85 torr)

Now you can solve for the mole fractions:

X_acetone = (50.85 torr) / P_total
X_methanol = (P_total - 50.85 torr) / P_total

These values will give you the composition of the vapor expressed as mole fractions.