Hi all - I want to calculate vapor pressures from first principles for a class of compounds. In this instance, I am interested in ionic liquids. More generally though, I want to setup a calculation approach for any compound so I can use this technique and resulting tool in the future (...that is, don't say 'reference x has vapor pressure of many ionic liquids' because that doesn't help on with the larger question that I am interested in answering).
I have critical pressure, critical temperature, and Pitzer acentric factors but little else (note, not from measurements but from group contribution methods, "Critical properties of Ionic Liquids. Revisited” , by J. O. Valderrama and R.E. Rojas, IECR (2009)).
First, let me start by stating the obvious that I am an moron - you may have to type slow to me. I think I have a bad definition in my thermodynamic approach or I am doing something wrong. Can you help set me straight?
Second, here is my approach...
For a pure component, at equilibrium, vapor and liquid fugacity must be equal
fL = fv
Pure vapor fugacity is equal to total pressure multiplied by the vapor fugacity coefficient
fv = ϕ(T,P)P
Gas fugacities are calculated using the SRK equation of state (EOS) implemented in Excel with VBA. I have validated my approach extensively with common industrial materials using some process simulators I have had intermittent access to (CHEMCAD and Aspen Plus). I am pretty confident I don't have a flaw with my implementation of the EOS.
For the liquid phase for the pure component, I am calculating the vapor fugacity in equilibrium with the liquid. Or, in other words, I am calculating the vapor fugacity at vapor pressure (...keep in mind that vapor pressure is an unknown and I use an initial guess for vapor pressure). I am using the asterisk below to denote saturation conditions where P* is vapor pressure.
fL = fv* = ϕ(T,P*) P*×exp[VL(P-P*)/(RT)]
The exponential term is the Poynting correction factor with VL as the . The fugacity coefficient was calculated as a vapor fugacity at vapor pressure (where again, my vapor pressure was an initial guess).
Thereafter, my thoughts were to use some optimization technique to solve for vapor pressure that makes objective function, F, equal to zero (or close to it).
minimize F = {ϕ(T,P)P - ϕ(T,P*) P*×exp[VL(P-P*)/(RT)]}2
However, things are breaking down and I get a non-physical result. First, instead of solve the problem I don't know the answer to, I seek to solve the equations for water and compare the predictions to the Antoine equation for water vapor pressure (I am starting at conditions close to ambient). I am not even getting far enough to compare against data though.
Instead, I find the objective function is minimized when P*=P. From this, I infer the non-physical result is due to a non-physical setup. When P*=P, the Poynting correction factor equals one and the objective function, F, becomes.
F = {ϕ(T,P)P - ϕ(T,P*) P*}2
Using Solver in Excel (...even though I am optimizing on variable, Solver is much more robust than Goal Seek), it continues to converge on P = P* which then sets ϕ(T,P)P - ϕ(T,P*). At 300 K, I believe the vapor pressure of water is somewhere around 20 mm Hg without looking it up which is definitely not 760 mm Hg.
Do I have a flaw in my approach? Is it not possible to calculate vapor pressure from critical properties and an EOS?
As I am typing this out, I see I am trying to enforce fv = fv* and equality can be realized numerically if one makes P = P* which is not thermodynamically correct.
Pending vapor pressure can be calculated from an EOS, the next question is accuracy which I will try to evaluate using some common materials of industrial importance. I ultimately want to couple this with the Clausius-Clapeyron equation to try and get enthalpy of vaporization as a function of temperature (then, with an enthalpy latent heat method, I can maybe calculate liquid heat capacity given the ideal heat capacity of the material which I have for ionic liquids from another group contribution method paper - this can be a really powerful technique if I can get it to work).
Thank you all in advance for your time and attention I am hope others can learn from your response while I do the same (...which is another motivation for someone to work through the thermo rather than post a link to some database for ionic liquids).