Vapor Pressure, Equillibrium, and Increasing Pressure

Question

I'm trying to make sure my understanding of vapor pressure and transients is correct.

Let's assume I have a thermally-controlled sealed environment which started out as the regular air (i.e. atmospheric gasses and their respective ratios) with no gaseous water or ethanol at 101.325 kPa, 30 C. This container will maintain a temperature of 30 C after the start of this experiment.

Inside this environment there are two containers which can be remotely opened.

When I open the first container, exposing the pure water inside with a saturation vapor pressure (First question: is that the right term?) of 4.2455 kPa (from Wikipedia) and wait until it reaches equilibrium (100% humidity), does this mean this is the new state of the container?

• Pressure: 101.325 + 4.2455 = 105.5705 kPa

• Partial-Pressure of H2O: 4.2455 kPa

Then I open the second container, exposing pure isopropyl alcohol inside with a saturation vapor pressure of 10.555 kPa (from WolframAlpha) and wait until it reaches equilibrium again, does this mean this is the new state of the container?

• Pressure: 101.325 + 4.2455 + 10.555 = 116.1255 kPa

• Partial-Pressure of H2O: 4.2455 kPa

• Partial-Pressure of Ethanol: 10.555 kPa

So, in the end, the pressure of the vessel increased each time a new liquid was introduced.

In this hypothetically-ideal environment, would the pressures simply rise until it reached that perfectly equilibrium? If so, I expect in a real environment the pressure would rise but there would always be a cold spot somewhere which caused the vapor pressure (in that specific area) to drop, leading to water condensing, leading to the partial pressure being lower as the air mixes, leading to more evaporation; is this correct?

Some notes:

• Assume that there is enough of each liquid to reach equilibrium without running out of liquid.

• The sealed environment effectively adds energy to counteract the heat of vaporization of each liquid, and also prevents the gasses from releasing/absorbing energy into/from the external environment or from changing due to pressure changes. It is essentially a magic make-everything-this-one-temperature machine.

Answer 1

There are a couple of gotchas' with the problem.

The volumes of the liquids and gases are specified. So 1 drop of water in a million gallon tank of dry air isn't going to be enough water to reach saturation.

You stated that "This container will maintain a temperature of 30 C after the start of this experiment." However the problem statement doesn't explicitly state that the contents of the container will be in thermal equilibrium with the container. That does seem to be a reasonable interpretation however. (If the evaporation had taken place adiabatically, then the liquid and gas would have to cool to account for the evaporation.)

There is another significant factor here. The water would absorb ethanol, and the ethanol would absorb water. You can't really figure this out without knowing all the volumes, or at least the relative volumes.

Now if you assume that there is enough liquid to saturate the gas phase, that the system (gas phase and liquid phase) absorbs heat from outside the system, then the vapor pressure of the liquid at $30\ ^\circ\mathrm{C}$ is added to the internal pressure of the gas phase before the evaporation takes place.