By lookup of the CRC Handbook, I could obtain the vapor pressure of water or mercury as a function of temperature. For example, it is $138~\mathrm{Pa}$ at $400~\mathrm K$ for mercury.

Now I want to use the vapor pressure to calculate the vapor density with the equation of state of ideal gas $p=\rho R_\text{spe} T=\rho \frac{R_\text{g}}{M} T$, where $p$ takes the value of vapor pressure, $T$ is the corresponding temperature at saturation in $K$, the specific gas constant $R_\text{spe}$ of vapor is given by the universal gas constant $R_\text{g}$ divided by the molar mass $M$ with $R_\text{g}=8.3145~\mathrm{J/(mol\cdot K)}$ and $M=200.59~\mathrm{g/mol}$ for mercury for example. Then the vapor density $\rho$ at saturation could be calculated readily.

My question is whether or not I can still use the classical ideal gas law at such a low pressure, for example $\sim100$ Pa for mercury or $10$ -$100~\mathrm{ Pa}$ for water vapor?

  • $\begingroup$ The ideal gas approximation actually works even better at low pressure. $\endgroup$ – valerio Oct 5 '16 at 7:58
  • $\begingroup$ For water, besides the look-up tables, there are functions of temperature that are useful across a very broad range of temperatures. $\endgroup$ – Jon Custer Oct 5 '16 at 12:37
  • $\begingroup$ @JonCuster, you meant the vapor density as a function of equilibrium temperature? And where is it? Thanks. $\endgroup$ – jsxs Oct 6 '16 at 1:43
  • $\begingroup$ Google is your friend. I found several references searching on 'saturated water vapor pressure calculation' - the Engineering Toolbox gives expressions for both the vapor pressure and density of water. $\endgroup$ – Jon Custer Oct 6 '16 at 13:02

As you can see from the following picture [source], the ideal gas approximation actually becomes better at low pressure:

enter image description here

You can also see from the picture that the validity of the approximation also depends on the gas you are considering. If you want a better approximation, I would suggest you use the van der Waals equation. You can find the values of the constants to plug into the formula here.


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