How Does Vapor Pressure Cause Water to Boil?

[Chestermiller]

Problem 2:
You have a cylinder with a massless, frictionless piston (axis of cylinder is vertical). There is 1 liter of liquid water in the cylinder at 20 C, and 1 liter of head space containing a mixture of water vapor and air. The cylinder and piston are enclosed in a room containing air at a pressure of 100 kPa. The system is in thermodynamic equilibrium. In this problem, we are going to be neglecting the effects of gravity on the contents of the cylinder, so that the variation of pressure within the cylinder is going to be considered negligible compared to the total pressure.

What is the pressure exerted by the piston on the gas mixture in the head space? What is the pressure throughout the cylinder? What is the equilibrium vapor pressure of water at 20 C? What is the partial pressure of water vapor in the head space? What is the partial pressure of the air in the head space? What is the pressure throughout the liquid water? From the ideal gas law, how many moles of gas mixture are in the head space?

 

[Biker]

Problem 2:
You have a cylinder with a massless, frictionless piston (axis of cylinder is vertical). There is 1 liter of liquid water in the cylinder at 20 C, and 1 liter of head space containing a mixture of water vapor and air. The cylinder and piston are enclosed in a room containing air at a pressure of 100 mPa. The system is in thermodynamic equilibrium. In this problem, we are going to be neglecting the effects of gravity on the contents of the cylinder, so that the variation of pressure within the cylinder is going to be considered negligible compared to the total pressure.

What is the pressure exerted by the piston on the gas mixture in the head space? What is the pressure throughout the cylinder? What is the equilibrium vapor pressure of water at 20 C? What is the partial pressure of water vapor in the head space? What is the partial pressure of the air in the head space? What is the pressure throughout the liquid water? From the ideal gas law, how many moles of gas mixture are in the head space?

1) It should be 100 KPa which is 10^5Pa
2) As you said we are going to neglect gravity here. So it is will be the same
3) 3158.1885 Pa
4)
A bit of problem here.. I could just do 3158.1885/10^5 and get it but where does this get place in this situation?
he only place that the "vapor pressure - temperature" relation must be satisfied is at the interface between the vapor and liquid. The vapor at the piston face is "superheated," in that its pressure is less than the equilibrium vapor pressure at the system temperature.
5) ^^
6)Hmm think it should be 100 KPa
7)
10^5 * 0.01 = n 8.3 * (273+25)
n = 0.404 moles

 

[Chestermiller]

1) It should be 100mPa which is 10^8 Pa
2) As you said we are going to neglect gravity here. So it is will be the same
3) 3158.1885 Pa
4)
A bit of problem here.. I could just do 3158.1885/10^8 and get it but where does this get place in this situation?
he only place that the "vapor pressure - temperature" relation must be satisfied is at the interface between the vapor and liquid. The vapor at the piston face is "superheated," in that its pressure is less than the equilibrium vapor pressure at the system temperature.
5) ^^
6)Hmm think it should be 100 mPa
7)
10^8 * 0.01 = n 8.3 * (273+25)
n = 404.3 moles
Which is a lot XD

Uh oh. I meant for the external pressure to be only 100 kPa, not 100 mPa. Can you please edit your answer, and I will edit my question. Sorry for the error.

Chet

 

[Biker]

Uh oh. I meant for the external pressure to be only 100 kPa, not 100 mPa. Can you please edit your answer, and I will edit my question. Sorry for the error.

Chet

Done.

 

[Chestermiller]

1) It should be 100 KPa which is 10^5Pa
2) As you said we are going to neglect gravity here. So it is will be the same
3) 3158.1885 Pa

In post #15, you gave the correct value of 2338.8 Pa for the equilibrium vapor pressure of water at 20 C.

4) and 5) ^^
A bit of problem here.. I could just do 3158.1885/10^5 and get it but where does this get place in this situation?
the only place that the "vapor pressure - temperature" relation must be satisfied is at the interface between the vapor and liquid. The vapor at the piston face is "superheated," in that its pressure is less than the equilibrium vapor pressure at the system temperature.

In a mixture of ideal gases, each gas exerts a partial pressure as if the other gases were not even present. Certainly, at the interface with the liquid water, the partial pressure of the water vapor is equal to the equilibrium vapor pressure, 2338.8 Pa. Since we are neglecting gravitational effects, the partial pressure of the water vapor throughout the head space is 2338.8 Pa. So, at the piston face, it will also be equal to2338.8 Pa. Since the total pressure is 100 kPa, and the partial pressure of the water vapor in the head space is 2.3388 kPa, the partial pressure of the air in the head space must be 97.66 kPa.

6)Hmm think it should be 100 KPa

This is correct. So, even through the partial pressure of the water vapor is equal to the equilibrium vapor pressure 2.3388 kPa, the pressure in the liquid water is 100 kPa.

7)
10^5 * 0.01 = n 8.3 * (273+25)
n = 0.404 moles

Correct.Next questions:
1. Given the partial pressures of water vapor and air in the head space, what are the mole fractions of water vapor and air?
2. How many moles of water are in the head space? How many grams of water are in the head space?
3. How many moles of air are in the head space? How many grams of air are in the head space?
4. How many grams of water total are in the container, assuming that the density of the liquid is 1000 gm/liter?