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

• runningman19
In summary, the problem at hand involves a system containing 3 moles of methanol and 7 moles of water at 25 degrees celsius. As the temperature is raised, the mole fraction of methanol in the gas phase reaches 40%. Using the Txy diagram, the initial mole fraction of methanol in the liquid phase at 25 C can be determined. By heating the solution and holding the total pressure constant at 1 atm, the temperature at which a vapor phase begins to form can be found, along with the mole fraction of methanol in the initial vapor. At a certain temperature, the mole fraction of methanol in the vapor phase will be 40%, corresponding to a mole fraction of 0.1 in
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: yaPa=xaP*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.

runningman19 said:

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: yaPa=xaP*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?

Chestermiller said:
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

runningman19 said:
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 %.

1. What is a Txy diagram?

A Txy diagram is a graphical representation of the equilibrium between two components in a liquid-vapor system at a constant temperature (T) and pressure. It shows the composition of the liquid and vapor phases in equilibrium at different pressures.

2. How do I read a Txy diagram?

The x-axis of a Txy diagram represents the mole fraction of one component, while the y-axis represents the mole fraction of the other component. The diagonal line on the graph is called the "tie line" and represents the compositions of the liquid and vapor phases in equilibrium. The points where the tie line intersects with the curved lines, called "vapor-liquid equilibrium curves," indicate the compositions of the vapor and liquid phases at that particular pressure.

3. How do I use a Txy diagram to solve a problem?

To solve a Txy diagram problem, you first need to determine the pressure and temperature at which the system is in equilibrium. Then, locate the point on the graph where the corresponding pressure intersects with the vapor-liquid equilibrium curve. This point will give you the compositions of the liquid and vapor phases in equilibrium. You can then use these compositions to calculate other properties of the system, such as the relative amounts of each component.

4. What is the significance of the critical point on a Txy diagram?

The critical point on a Txy diagram represents the temperature and pressure at which the liquid and vapor phases of a system become indistinguishable. Above the critical point, the liquid and vapor phases merge into a single phase known as the supercritical fluid. The critical point is important because it marks the maximum pressure and temperature at which the system can exist in two distinct phases.

5. How does the Txy diagram change with different components?

The shape and position of the Txy diagram can vary depending on the components involved in the system. The critical point, vapor-liquid equilibrium curves, and tie lines will all be different for different components. Additionally, the azeotrope (a mixture of components that cannot be separated by distillation) may appear at different compositions on the graph for different systems.

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