## Monday, September 23, 2013

### Getting Activity Coefficients for Mixtures

In last week’s  blog I talked about non-ideal solution mixtures that can go far afield of the predictions of vapor pressure over a mixture from Raoult's Law.    The fix for this situation was to modify Raoult’s Law to include an activity coefficient (AC):

VPM = (VPP)(MF)(AC)

VPM = vapor pressure of the compound of interest over the mixture
VPP = vapor pressure of pure compound
MF =  mole fraction of the compound

The thermodynamic AC can be very large (>1000) as in the case of benzene coming out of water or pretty close to one (1.0) as in the case of the mixture of compounds with similar structures like methanol in ethanol or a mixture of aromatics hydrocarbons.

So how do we come up with a numeric AC is for a compound of interest in a mixture of chemicals?   Well there are models, of course.    In this case there are relatively complicated physical-chemical models that use the structural characteristics of the molecules in the mixture to estimate the AC values of each component.  Here again we needed someone to do the computing coding so we would not have to wade through all the math.  We need a dedicated user-friendly program.  I think that the most useful one that I have found over the years of looking has been:  UNIFACAL.exe.    This little program (1.7mb) can do wonders.   The screen shot below shows what I mean:

Notice that there are places for 6 mixture components.   I have put the two component (binary) system that I talked about in the last blog:  1.7 grams (solubility limit) of benzene in 1 liter of water.   UNIFACAL comes with a modest database of benzene, chlorobenzene, ethylbenzene, toluene and water.   It is is a relatively simple matter to add compounds using the database.  For example, I added ethanol by adding up 1 x CH3 group, 1 x CH2 group, and 1 x OH group.   You will find it is even easier than it sounds once you know the structure of the chemical you want to add and move to actually put it into the UNIFACAL Database.    All the halogens are in the database, along with some silicon, sulfur and nitrogen containing moieties.

Notice that the AC of benzene in this aqueous mixture is predicted to be over 2400 which is essentially the full expression of the vapor pressure (VPP) of pure benzene.   The reasons for this are discussed in the previous blog.

The latest version of this program was written and has been shared as freeware since 1998 by Bruce Choy and Danny D. Reible from The University of Sydney Australia and Louisiana State University and we owe them a debt of gratitude for their generosity.

Another way to estimate vapor pressure of compounds in water is to use Henry's Law Constant (HLC).
Henry's Law is simply a variation on Raoutl's Law.   It says that the amount of a mixture's component vapor in the equilibrium head-space will be a constant proportion to the amount of that component dissolved in the liquid mixture.  This constant ratio is called Henry's Law Constant (HLC) and if one knows the concentration in water and the HLC then he or she can calculate the concentration (i.e., vapor pressure) in the headspace.   Remember that the saturation  head-space concentration is convertible to the partial pressure which is the vapor pressure over the mixture (VPM).   We went through this calculation in a previous blog.    Many compounds have published HLC but these, of course, are only for water.   I must say that water is used a lot as a solvent but if you are not dealing with water and have dissimilar organics (e.g., straight and branch chain hydrocarbon and lower alcohol) you need to use the AC approach above.

Note that the AC is a function of concentration (i.e., molefraction) so you need to understand what might happen to the concentration of the evaporating liquid over the time of exposure.   If the time of exposure is pretty short or only a small portion of the evaporating liquid is expected to disappear during the exposure then you do not need to worry about it much; however, if the composition is expected to change significantly during the exposure then you need to account for this.   I usually do this by taking worst case.   That is, what is the worst emission rate that might occur during the exposure and use that for the entire exposure period knowing that it is a purposeful overestimate that still might be useful.  If you cannot live with the overestimation there are other ways to approach the problem but they always require more work.

In the next blog I am going to talk about practical approaches to estimating emission source rates by various means under different circumstances.   If you send me some of the specifics of what has been challenging you I may use it as an example.   Give me as much detail as possible and let me know what I might need to "blind" for reasons of confidentiality.

1. Thank you very much M. Jayjock, very interesting blog.
We have made some works about the use of activity coefficients (AC). Thus, we have published a paper about the use of AC for calculating Vapor Hazard Ratio (VHR) for mixtures used in solvent substitution:
Debia, M.; Bégin, D.; Gérin, M. (2009) Comparative Evaluation of Overexposure Potential Indices used in Solvent Substitution. Annals of Occupational Hygiene 53(4):391-401.

Thank you again,

Maximilien Debia, Ph.D.
Assistant Clinical Professor,
Head of the occupational hygiene laboratory,
Department of environmental and Occupational Health.
maximilien.debia@umontreal.ca

2. Great, Mike. Many thanks. Note the link you give above is broken.
It is now https://unifac-calculator.software.informer.com/

It took me a few years to realize you covered this in your Blog! I will be referring others to this in any training models I do on partial vapor pressures from mixtures.

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