The Compleat Distiller

THE COMPLEAT DISTILLER 98
Antoine Equation
The Clausius-Clapeyron equation is a very useful tool, but to use it, you need to know the vapour
pressure P 0 at a temperature T 0 , and the LHV of that substance H. For our purposes, this is not as
difficult as it seems, because P 0 is 760mm.Hg (1000 mbar) at the boiling point T 0 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:
Log 10 P= A - B / (T + C)
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 ºC 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 ºC, 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.
Equilibrium Curves
You now have enough information to work out what happens when you heat a mix of ethanol and
water and send the vapor through a reflux column, by combining Raoult's and Dalton's laws with either
the Clausius-Clapeyron or the Antoine equations. The following demonstration uses the Clausius-
Clapeyron equation.
We know from Raoult that P TOTAL = P 1 + P 2 = X 1 P 1 * + X 2 P 2 *
And we know from mol fractions that X 1 + X 2 = 1 so X 1 = (P TOTAL - P 2 *) / (P 1 * - P 2 *) Eqn 1
As P 1 = X 1 P* and also (from Dalton) P 1 = Y 1 P TOTAL so Y 1 = X 1 P* / P TOTAL Eqn 2
We can calculate P 1 * and P 2 * from Clausius-Clapeyron log e (Pn*/P 0 ) = H(1/T 0 - 1/T) / R Eqn 3
P 0 and T 0 are the pressures and temperatures of the pure liquids at their boiling points, something we
already know for water and ethanol, and P TOTAL is atmospheric pressure
These results show why it's important to keep the pressure constant, and also indicate what happens if
you operate at higher or lower pressures. Equation 2 shows that raising the pressure lowers the yield of
vapor, and that lowering the pressure (eg. vacuum distillation) increases it. We've seen many designs
for stills that operate under high pressure in the hope that this will increase the yield. Not only is that
practice dangerous, the equations show that it's based on ignorance.