# Talk:Activity coefficient

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## Deviations from Raoult's Law

Can someone provide information on how activity coefficients demonstrate either positive or negative deviations from Raoult's Law? 171.64.133.56 22:53, 24 February 2006 (UTC)

## Examples; normalisation

This article, which is indirectly referenced from the pH value article, is in desperate need of more explanation. We need an example where the activity coefficient is given as an actual number, not just relative to other activity coefficients.

Am I right in guessing that the normalisation is such that the activity coefficient approaches one as the mixture is diluted?

The article does not currently give a definition of the term.

RandomP 16:16, 19 September 2006 (UTC)

### Article re-written

I hope that the re-write addresses these issues, amongst others.Petergans 10:39, 23 July 2007 (UTC)

## Uncharged species and other corner cases

It would be nice if the article also mentioned how one is to approach:

• the activity coefficients for electrically uncharged species,
• activity of the solvent,
• activity of solids submerged in concentrated electrolytes. —Preceding unsigned comment added by Stan J Klimas (talkcontribs) 20:27, 21 October 2007 (UTC)
Activity coefficients for carbohydrates is an active field of research. Try Google on "activity coefficient carbohydrate". I remember this also being discussed in an ancient text book but can't remember the authors for sure. Were they perhaps Robinson and Stokes?Petergans 11:27, 25 October 2007 (UTC)
Thank you. Indeed, e.g.: "Temperature dependence of water activity in aqueous solutions of sucrose", Food Chemistry, Volume 96, Issue 3, June 2006, Pages 346-370, 3rd International Workshop on Water in Foods.
"-15 to +150 °C, sucrose concentrations up to 98% wt. The isotherms of water activity coefficient exhibit a characteristic minimum at about 96% wt. sucrose which is then followed by a dramatic increase to values well exceeding 1". Stan J. Klimas 21:44, 28 October 2007 (UTC)
A link for this mentioned article from Food Chemistry: [1].--85.121.32.1 (talk) 13:06, 18 July 2016 (UTC)

### Ternary solutions - electrolyte - non-electrolyte interaction

Info on this aspects (related to those from above) should be mentioned with examples of practical importance refering to sugar - electrolytes solution of medical use and salting in and salting-out.--188.26.22.131 (talk) 15:11, 25 September 2012 (UTC)

A link for this case [2].--85.121.32.1 (talk) 13:09, 18 July 2016 (UTC)
An analysis of ternary systems at WP:RD/S Wikipedia:Reference_desk/Science#Ternary_ideal_mixture_obtained_from_non-ideal_binaries.--82.137.9.237 (talk) 12:31, 25 October 2017 (UTC)
Link update for the above sources at RefDesk Archives: Wikipedia:Reference_desk/Archives/Science/2017_October_21#Ternary_ideal_mixture_obtained_from_non-ideal_binaries.--82.137.8.95 (talk) 15:05, 29 October 2017 (UTC)

A simple example of a non-ideal mixture between two liquids A and B. In this example, the attraction between A and B molecules is similar to between B and B, but the A-A interaction (red arrows) is very unfavorable (repulsive) by comparison. At higher concentration of A, the A-A interactions become more frequent, so the activity coefficient of A (free energy per molecule of A) goes up.

I want to add this animation. (See right.) It's supposed to be very very basic textbook chemistry. Please let me know if you see any problems or can suggest improvements (big or small). Thanks! --Steve (talk) 03:15, 7 September 2010 (UTC)

I like the sequence of images but I'm not sure they work well as an animation. It is hard to compare the change from frame to frame. However it might work better as a series of four panels side by side, showing the progression of the concentration. I do think it is important to illustrate more WP articles! Also you may find the same or similar graphics useful on the activity (chemistry) article. David Hollman (Talk) 07:09, 7 September 2010 (UTC)
I agree the animation is too fast. More fundamentally, the chemistry is not quite right. If we are dealing with ions, as previous discussions suggested, there are three kinds of particle involved: cation, anion and solvent. Activity coefficients of ionic substances are principally affected by cation-anion interactions. In Debye–Hückel theory each ion is at the centre of a spherical cloud of ions of the opposite charge. The activity coefficient depends on the radius of the cloud. This is satisfactory only for ions of low charge in rather dilute solutions.
At higher concentrations ion pair formation (look it up) is important.The monopole electric field is quite long range. The animation suggests interactions only at close range, but interactions can and do occur also with intervening solvent molecules. This is because solvent molecules like water are dipolar and so assist interactions, e.g. Na+(Oδ-Hδ+2)Cl-.
For high concentrations, might I suggest that the animation shows just two ions from a dissolved salt, such as Na+ and Cl-, in a sea of solvent molecules, with interactions of different strengths (at closer distances as concentration increases) shown by an arrow of different length? The solvent molecules will be arranged in an idealized array, like a crystal lattice based on hexagonal close packing. Ions can simply exchange sites with solvent molecules in this idealized structure. Petergans (talk) 08:24, 8 September 2010 (UTC)
Petergans -- These are not ions. What is there in the image or caption that makes you infer that A or B is ionic?? When I look at the image and caption, I find it 100% clear that A and B are neutral. It's unclear to you? Why? Of course I could change the caption to "...two liquids of neutral molecules A and B..." or something to dispel all doubts.
(I'll think about your ion-related suggestions as the basis for a possible different illustration at some point.)
Petergans and David -- I'll try slowing the animation or changing it to a four-panel image, and see how it looks. I'm worried that with multi-panels the figure would be too big, but don't know til I try! --Steve (talk) 15:25, 8 September 2010 (UTC)
More frames would help. It might be easier to use a proper drawing program like inkscape to generate the base image. you can, I believe, animate with synfig, but I have never tried, so I cannot tell you how good it is. User A1 (talk) 17:32, 8 September 2010 (UTC)
From a scientific perspective, I think ions come up as your animation would be fundamentally wrong for molecular species, which are downright complex. In any case, it is not the mean distance between A that defines anything, this would only be true in a 1D system, it is the frequency of a particular orientation group that is more important. User A1 (talk) 17:33, 8 September 2010 (UTC)
I don't actually think increasing the number of frames would help, because it isn't simulating motion; its showing four different concentrations of the solution in order to make a comparison. If it were slowed down, that might help, but I'm still not sure that would allow a useful comparison among the frames. The 4-panel idea (I was thinking horizontal since the existing frames are vertical) may take up space, but personally I think a valuable image is worth it. Thanks for being open to all this feedback Steve! David Hollman (Talk) 17:45, 8 September 2010 (UTC)
The activity coefficient of a solute such as sucrose in water depends primarily on changes in solute-solvent and solvent-solvent interactions. The probability that two solute molecules come close to each other is very small, except in exceedingly concentrated solutions. The ratio of water to solute molecules is about 55/x where x is the molar concentration. Thus even in a 0.1M solution, which is quite concentrated in regard to activity coefficients, the ratio is about 550:1 (8.23:1). It was the fact of your A molecules coming into contact with each other that made me think it was an ionic interaction. Petergans (talk) 18:28, 8 September 2010 (UTC)

OK, my new plan is to re-do the figure for the specific example of the acetone-chloroform mixture. I can base it on real data. I'll show from very-dilute chloroform up to a 50-50 (mole%) mixture.

Petergans, you can look at the data and you'll see that in this case 0.1M is not "quite concentrated in regard to activity coefficients": The solution only becomes noticeably non-ideal at 20-30 mole%.

The idea (as I understand it) is very simple, and taught in freshman chemistry courses: The activity coefficient goes down (negative deviation from Raoult's law) because the attraction between acetone and chloroform is stronger than the attraction between acetone/acetone or chloroform/chloroform. I think this is easy to depict, although obviously I need to change some things compared to the most-recent figure above.

User A1, would you describe the non-ideality of acetone-chloroform mixtures as "downright complex"? Why? I understood that it was basic freshman chemistry, and found this simple description in several textbooks, my own chemistry course, and not to mention on wikipedia (Raoult's law). Also, can you please define the term "orientation group"? I've never heard it used in chemistry. Thanks!

Thanks for all the feedback all of you!! :-) --Steve (talk) 00:23, 9 September 2010 (UTC)

That makes it much much clearer. The animation should go into the thermodynamics section. A small extension of the text relating to Raoult's law regarding this specific system would be welcome. As the data are available perhaps the Raoult's law diagram could be included in the animation in place of the activity coefficient plot. I would also like to see the activity of both A and B, not just A. Petergans (talk) 09:18, 9 September 2010 (UTC)
A small point: would mol fraction be a better variable for the x axis? Petergans (talk) 12:25, 9 September 2010 (UTC)
Hi SByrnes, with regards to the orientation group, look at figures 7, (acetone-chloroform) 10 (acetone-methanol) and 14 (methanol-chloroform) from this paper. The Radial distribution function can aid in determining the preferred groupings for molecules. In the chloroform-acetone system, the acetone oxygen atom likes to rest between the hydrogens of chloroform in a little bunch. It is this preferred orientation group that gives you the reduced free energy. The more of these that can be promoted (by altering the concentration), the more stable the overall system, roughly speaking. User A1 (talk) 11:17, 9 September 2010 (UTC)

## Conventions- symmetric and asymmetric

The two conventions and their mutual conversion should be described.--188.26.22.131 (talk) 15:00, 25 September 2012 (UTC)

## Higher concentrations ionic solutions

It would be useful to include aspects concerning higher concentration ionic solutions activity coefficients and how is the deviation from ideality separated from the total dissociation assumed by lower concentration theories like that of Debye - Huckel.--188.26.22.131 (talk) 09:48, 19 August 2013 (UTC)

You are right. In fact Davies equation, Bromley equation, SIT theory and Pitzer equation all address this issue, but have not been linked here. I am too busy at the moment to attend to this. Petergans (talk) 10:36, 19 August 2013 (UTC)

The article should specify the connection between conductivity (electrolytic) and the thermodynamic activity coeffient.--188.26.22.131 (talk) 12:58, 9 September 2014 (UTC)

## lg or log_10

lg and log_10 are symbols for the same thing: decadic logarithm. Please use in your article either lg or log_10, but not both together.

## Undissociated electrolyte

The article does not address the determination of this quantity for the undissociated part or fraction of a dissolved ionic compound. The activity coefficient of an electrolyte as a measurable quantity cannot be defined in terms of unmeasurable quantities like individual activity coefficient of the ions.--82.137.13.174 (talk) 08:41, 20 July 2016 (UTC)

Concentrated solution statistical part: ${\displaystyle ln\gamma _{s}={\frac {h-\nu }{\nu }}ln(1+{\frac {br}{55.5}})-{\frac {h}{\nu }}ln(1-{\frac {br}{55.5}})+{\frac {br(r+h-\nu )}{55.5(1+{\frac {br}{55.5}})}}}$--82.137.11.178 (talk) 23:32, 14 August 2016 (UTC)

## Link to ion transport number

What is the connection of this quantity to ion transport number?--82.137.11.146 (talk) 14:17, 7 September 2016 (UTC)

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