# How do I calculate the pressure of a known liquid in a sealed container heated above boiling point?

If I have water in a sealed container heated to say 150 degrees, how do I determine the amount of pressure being generated in the container? What about for other liquids? I have searched extensively and cannot figure this out.

I was looking for a formula of sorts, but for example reasons let's say a 5000 ml container with 4500 ml of water in it, with the rest of the space air, heated to 150 degrees Celsius.

• First we would need to know how much water per volume in the sealed container. Also we would need to know if any air is in the container or not. If we knew those things, then the next step is to consult steam tables (either equilibrium or superheated) to determine all the thermodynamic properties of the steam at the right temperature and bulk density. Feb 15, 2015 at 17:27

Note: for convenience, "gas" refers to any gas at a temperature beyond its boiling point; "vapor" refers to any gas evaporated from its liquid state, also implying that the liquid itself is below its boiling point, such as the 150 degrees water in your example.

Dalton's law of partial pressure would come in handy here. The law states that the partial pressure generated by each type of gas particles sum up to the total pressure in a sealed container. The partial pressure of "gasses" can directly be calculated using the ideal gas law. Of course the partial pressure of "gasses" is 0Pa if there is no gas but only vapor in your container.

Now the partial pressure of the vapor of liquids. In a sealed container, if left to attain dynamic equilibrium (which is the steady state in this case) the partial pressure of the vapor of any liquid would be equal to its equilibrium vapor pressure, which is a function of temperature only. Though not excessively accurate, the Antoine equation can be used to estimate this:
$\log P = A- {B \over C+T}$
where P is the equilibrium vapor pressure, A, B and C are substance-specific constants and T is the thermodynamic temperature of the substance. The three substance-specific constants can be checked up on the internet, or provided by other sources, whereas conducting experiments can be a last resort (as it is a very tedious experiment that you need the whole curve of the function to approximate the constants).

If the liquid in question is a mixture of more than one liquid substance, then you'd need a third law - Raoult's law to determine the partial vapor pressure of each component of the mixture:
$p_i = p_i^\star x_i$
where $p_i$ is the partial vapor pressure of component $i$ of the mixture, $p_i^\star$ is the equilibrium vapor pressure of a pure sample of component $i$(in itself, not in a mixture), and $x_i$ is the mole fraction of $i$ in the liquid.
At dynamic equilibrium, combining Dalton's law of partial pressure and Raoult's law yields the expression for total vapor pressure:
$p_{total} = \sum p_i^\star x_i$

Since steam (water vapor) is the most common working fluid in external-combustion engines, steam tables, as mentioned by Curt F above, are widely used and will show the relationship more accurately than the ideal gas law, "PV=nRT", http://en.wikipedia.org/wiki/Ideal_gas_law. See http://www.wolframalpha.com/examples/SteamTables.html, http://www.efunda.com/materials/water/steamtable_sat.cfm or http://www.tlv.com/global/TI/calculator/steam-table-pressure.html for an online steam table.

• DrMoishe, what about for other liquids such as organics? Water was just an example of convenience. Will the ideal gas law alone allow me calculate the pressures that will build up in a tank if I heat a liquid beyond its boiling point? I ask because I feel as if the ideal gas law would be come unapplicable when the pressure is so much that more water cannot evaporate. Is there simply not straightforward way/formula to calculate how much pressure would build up in a container at certain temperatures? Feb 15, 2015 at 19:04
• There are additional factors not included in the ideal gas equation, such as van der Waals force, en.wikipedia.org/wiki/Van_der_Waals_force. In theory, if you know all the forces acting on a substance, you can calculate its pressure/volume/temperature relationship, but in practice the formula is derived empirically. Tables are available for many substances such as CO2 and NH3. J. Willard Gibbs, en.wikipedia.org/wiki/Josiah_Willard_Gibbs, was one of the first to explore chemical thermodynamics; you might want to read his work. Feb 15, 2015 at 22:26

There are various empirically derived equations which are used to predict pressure given a temperature. As already mentioned the Antoine equation is for vapor pressure but can be used (although extrapolation should never be preferred to interpolation, and most empirical equations list the range of temperatures they are applied to (and derived from). These equations all require experimentally determined parameters and are essentially "curve fitting". (but see discussion on Van der Waals equation of state) Note that the ideal gas law rarely has accuracy to +/- 1% and occasionally as bad as 5% error...if I recall, the fit for CO2 near STP is in the "not so good" category for the IGL. Wikipedia discusses several alternatives to the IGL and The Handbook of Chemistry and Physics has tables for some of them (at least it used to, I don't have access to the most recent editions), as does Perry's Handbook of Chemical Engineering.

• Welcome to Chemistry.SE! Take the tour to get familiar with this site. Mathematical expressions and equations can be formatted using $\LaTeX$ syntax. For more information in general have a look at the help center. At the moment this reads more like a comment than an actual answer - could you elaborate a little more. With a bit more rep, you will be able to post comments on any question/answer. Jun 24, 2016 at 6:18