Q & A: vapor pressure in a container

Hi, This problem is very important for my research. I am an Electrical Engineer. I need to know the TOTAL pressure inside a CLOSED chamber with certain amount of water inside (chamber and water volume known). Next, I heat this chamber to 95 or 100 deg C and have to calculate the pressure. From Dalton’s law, total pressure is sum of partial pressures = P due to water vapor + P due to air AT THAT TEMPERATURE. I am calculating P due to air at different temperatures using P/T = const. (as chamber volume is constant) But the vapor pressure equations do not include volume of vessel or water. Does it mean that vapor pressure 1L of water is same in a 10L container and a 1000L container?(both closed) Am I calculating the pressure inside the chamber the right way? any ideas?
- pradeep
TX

Your key question is very clearly stated: "Does it mean that vapor pressure 1L of water is same in a 10L container and a 1000L container?(both closed)"

The answer is yes, so long as the liquid water is not completely converted to vapor. Here’s one way to understand that. The vapor pressure is maintained by an equilibrium between the vapor and the liquid- equal rates of molecules flying off the liquid surface and reentering it. The balance of those rates depends only on the temperature and the vapor pressure near the surface, not on how much liquid or vapor there may be below or above the surface.

Perhaps a more fundamental way to see the same result would be in terms of the chemical potentials of the water in the liquid and the vapor, which must be equal in equilibrium and which again are determined by local properties, not overall sizes.

Of course, in a very big, hot container the calculated vapor pressure will exceed what could be obtained from all of the water you put in. In that case just treat the water as another gas with a fixed number of molecules.

Mike W.

(published on 10/22/2007)

How could I know that whether all the liquids are completely converted into vapor or there is still some liquid in the container. I have a closed container of 60 mL and I do wanna load different amounts of water (10,20,30,40 and 50 mL)at room temperature and then heat to 250C. Thx.
- JAHID FERDOUS
Columbia, SC, USA

What you want is a phase diagram showing the concentration of vapor vs. temperature for water. Then you could check whether at 250°C the concentration corresponding to 10 gm/ 60mL is in the vapor phase. I don't think it is, so I think you will still have some liquid left even in that case. Unfortunately, in my quick search I found only pressure vs temperature diagrams. Conversion of pressure to gas concentration is not as simple here as using the ideal gas law, because it doesn't work at very high densities.

If you have a pressure gauge, you will see a dramatic change in the temperature-dependence of the pressure if the liquid is used up.

I do hope you understand that the pressures here are high, so there is a real safety issue.

Mike W.

(published on 05/20/2010)