Solve Txy Diagram Problem: Methanol & Water @ 25°C

[runningman19]

Homework Statement

Hi Everyone,
I am having trouble grasping the concept of Raoult's law, partial pressures etc. One problem in specific is: A system contains 3 moles of methanol and 7 moles of water at 25 degrees celsius. The temperature is raised until there is 40 mol% methanol in the gas phase. How much is left in the liquid phase?
The Txy diagram is attached.
Thanks so much guys,
Nick

2. Homework Equations [/B]
Raoult's Law: y_aP_a=x_aP*_a
Txy diagram attached

The Attempt at a Solution

I believe this problem requires the use of Raoult's law in some form. I have written separate Raoult's law equations for water and methanol in the solution, but neither of these equations is solvable because there are too many unknowns and too few equations.

 

[Chestermiller]

Homework Statement

Hi Everyone,
I am having trouble grasping the concept of Raoult's law, partial pressures etc. One problem in specific is: A system contains 3 moles of methanol and 7 moles of water at 25 degrees celsius. The temperature is raised until there is 40 mol% methanol in the gas phase. How much is left in the liquid phase?
The Txy diagram is attached.
Thanks so much guys,
Nick

2. Homework Equations [/B]
Raoult's Law: y_aP_a=x_aP*_a
Txy diagram attached

The Attempt at a Solution

I believe this problem requires the use of Raoult's law in some form. I have written separate Raoult's law equations for water and methanol in the solution, but neither of these equations is solvable because there are too many unknowns and too few equations.

This is a problem in learning how to use a Txy diagram (not Raoult's law). x is the mole fraction of methanol in the liquid phase and y is the mole fraction methanol in the gas phase. What is the initial mole fraction of methanol in the liquid phase at 25 C? As you heat the solution up (holding the total pressure on the solution constant at 1 atm), at what temperature do you begin to form a vapor phase? What is the mole fraction of methanol in the initial vapor that is formed? At what temperature will there be a mole fraction of 0.4 methanol in the vapor phase? What will be the mole fraction of methanol in the liquid phase at that temperature? At this point, how many total moles of liquid will you have and how many total moles of vapor will you have? How many moles of methanol will remain in the liquid phase?

 

[runningman19]

This is a problem in learning how to use a Txy diagram (not Raoult's law). x is the mole fraction of methanol in the liquid phase and y is the mole fraction methanol in the gas phase. What is the initial mole fraction of methanol in the liquid phase at 25 C? As you heat the solution up (holding the total pressure on the solution constant at 1 atm), at what temperature do you begin to form a vapor phase? What is the mole fraction of methanol in the initial vapor that is formed? At what temperature will there be a mole fraction of 0.4 methanol in the vapor phase? What will be the mole fraction of methanol in the liquid phase at that temperature? At this point, how many total moles of liquid will you have and how many total moles of vapor will you have? How many moles of methanol will remain in the liquid phase?

I think I got it. If you find 0.3 mol% on the x-axis and move up until you hit 0.4 mol% methanol on the vapor curve, you would end up with around 0.1 mol% methanol in the liquid phase. That means at that temperature 0.1 mol% methanol would exist as a liquid.
Thanks

 

[Chestermiller]

I think I got it. If you find 0.3 mol% on the x-axis and move up until you hit 0.4 mol% methanol on the vapor curve, you would end up with around 0.1 mol% methanol in the liquid phase. That means at that temperature 0.1 mol% methanol would exist as a liquid.
Thanks

Almost right. You are asked to find the number of moles of methanol remaining in the liquid phase. To do that, you need to use the "lever rule" to find the total number of moles of liquid remaining. And the mole fraction of methanol in this liquid is 0.1; it's not 0.1 mole %.