## Antoine Equation

The Clausius-Clapeyron equation is a very useful tool, but to use it, you need to know the vapour pressure P0 at a temperature T0, and the LHV of that substance H. For our purposes, this is not as difficult as it seems, because P0 is 760mm.Hg (1000 mbar) at the boiling point T0 of the substance, and the LHV is in the table above.

There are several other methods of calculating vapor pressure. One of the easiest to use is the Antoine equation, and it has some advantages. It is more accurate than the Clausius-Clapeyron equation over specific temperature ranges and it doesn't require you to look up the vapor pressure or LHV, because these are incorporated into parameters for each substance. The Antoine equation is:

Where P is the vapor pressure and T is the temperature, and A, B and C are parameters for the particular substance.

If you'd like to try using this simple equation, here are the parameters for water and the first two alcohols. These parameters require that temperature be in degrees Celsius.

 Substance Temp. Range °C A B C Water 1 - 100 8.190447 1730.630 233.426 Methyl alcohol 15 - 84 8.205910 1582.271 239.726 Ethyl alcohol 20 - 93 8.236515 1592.864 226.184

When you use the Antoine equation to find the vapor pressure of water at the boiling point of pure ethanol, 78.32 °C, the result is 436 mbar, which is closer to the actual measured pressure.

The difference is that the Clausius-Clapeyron equation is derived from the theoretical behavior of a "perfect gas", while the Antoine equation's parameters are based on careful measurements and experimentation. Since the results of the two equations fall within 2% of one another, you can use either one quite comfortably for practical matters.