Compression of gases that liquefies

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Discussion Overview

The discussion revolves around the behavior of a gas mixture under compression in a closed system containing water and a gas, referred to as gas A. Participants explore the implications of phase transitions, partial pressures, and the application of Raoult's and Henry's laws in determining the changes in the system's pressures as the mixture is compressed to a specified pressure of 2 atm.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant describes a scenario where gas A is added to water at 298K, resulting in a total pressure of 1 atm, and questions how the partial pressures of A and water change when the mixture is compressed to 2 atm.
  • Another participant questions whether the described situation leads to a stable final state, emphasizing that the final pressure must equal 2 atm.
  • There is a repeated inquiry about whether gas A undergoes a phase transition at 1.5 atm and how this affects the mixture.
  • Participants discuss the miscibility of the liquid phases of A and water and whether Raoult's law and Henry's law can be applied to calculate their partial pressures.
  • One participant expresses uncertainty about how to determine the amount of gas A that dissolves in water and how the pressures change as the system is compressed.
  • Another participant points out the potential misuse of terminology regarding compression and pressurization, suggesting a need for clarification on the energy of compression and the assumptions regarding the process (adiabatic or isothermal).
  • There is a discussion about the assumptions of ideal gas behavior for the gas phase and the implications for the liquid phase, questioning the applicability of Raoult's law and Henry's law.
  • One participant expresses confusion about how the system's pressures can equal 2 atm given the phase transition pressures of A and water.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the behavior of the system under the specified conditions. There are multiple competing views regarding the application of phase laws, the behavior of the gases and liquids, and the implications of the specified pressures.

Contextual Notes

Participants express uncertainty regarding the assumptions made about the behavior of the gas and liquid phases, particularly in relation to ideal versus non-ideal mixtures. There is also ambiguity about how to quantify the changes in partial pressures as the system is compressed.

  • #31
sgstudent said:
I don't see where there will be a point like that though.

I thought of this nA/L*1.5+(1-nA/L)*0.031=1.3 but I can't seem to think of the other equation to solve the simultaneous equations though. Could I get a nudge in the right direction?
Your Roault's law equation is correct, but I'm going to write it in terms of the liquid mole fraction of water x, rather than the liquid mole fraction of A. I hope that's OK with you:
$$0.031x+1.5(1-x)=P\tag{1}$$where P is the total pressure.

OVERALL MASS BALANCE:
The number of moles of liquid L plus the number of moles of vapor V must be equal to the total number of moles of water in the container (21) plus the total number of moles of A in the container (133.53). So,
$$L+V=154.53\tag{2}$$

MASS BALANCE ON WATER:
The number of moles of water in the liquid phase (Lx) plus the number of moles of water in the vapor phase (##\frac{0.031x}{P}V##) must be equal to the total number of moles of water in the container (21):
$$Lx+\frac{0.031x}{P}V=21\tag{3}$$

We have liquid in the cylinder with vapor in the head space, and we increase the pressure P in the cylinder by forcing a piston down on the top of the vapor. We would like to determine whether there is a certain pressure beyond which all the vapor has been squeezed into the liquid, and only liquid remains below the piston. Our game plan is to choose a sequence of increasing values for P and solve for the mole fraction of water in the liquid x, and the number of moles of liquid L and vapor V. The calculation goes like this:

1. Choose a value for P
2. Solve Eqn. 1 for the corresponding value of x
3. Substitute the values for P and x into equation 3
4. Solve Eqns. 2 and 3 simultaneously for L and V

I would like you to carry out this procedure for values of P equal to 1.0, 1.1, 1.2, 1.25, and 1.3 atm. Then make a graph of x vs P and a second graph of L and V vs P.
 
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  • #32
Chestermiller said:
Your Roault's law equation is correct, but I'm going to write it in terms of the liquid mole fraction of water x, rather than the liquid mole fraction of A. I hope that's OK with you:
$$0.031x+1.5(1-x)=P\tag{1}$$where P is the total pressure.

OVERALL MASS BALANCE:
The number of moles of liquid L plus the number of moles of vapor V must be equal to the total number of moles of water in the container (21) plus the total number of moles of A in the container (133.53). So,
$$L+V=154.53\tag{2}$$

MASS BALANCE ON WATER:
The number of moles of water in the liquid phase (Lx) plus the number of moles of water in the vapor phase (##\frac{0.031x}{P}V##) must be equal to the total number of moles of water in the container (21):
$$Lx+\frac{0.031x}{P}V=21\tag{3}$$

We have liquid in the cylinder with vapor in the head space, and we increase the pressure P in the cylinder by forcing a piston down on the top of the vapor. We would like to determine whether there is a certain pressure beyond which all the vapor has been squeezed into the liquid, and only liquid remains below the piston. Our game plan is to choose a sequence of increasing values for P and solve for the mole fraction of water in the liquid x, and the number of moles of liquid L and vapor V. The calculation goes like this:

1. Choose a value for P
2. Solve Eqn. 1 for the corresponding value of x
3. Substitute the values for P and x into equation 3
4. Solve Eqns. 2 and 3 simultaneously for L and V

I would like you to carry out this procedure for values of P equal to 1.0, 1.1, 1.2, 1.25, and 1.3 atm. Then make a graph of x vs P and a second graph of L and V vs P.
Prof chestermiller, could I continue on with this on the next weekend as my midterms are next week and this chapter isn't tested. Just wanted to let you know that I haven't ghosted you for this problem.
 
  • #33
sgstudent said:
Prof chestermiller, could I continue on with this on the next weekend as my midterms are next week and this chapter isn't tested. Just wanted to let you know that I haven't ghosted you for this problem.
Certainly you can continue at your convenience.
 

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