# Composite activity coefficients

1. Dec 13, 2008

### tring

In a urine sample (Relman JCI 1961) urine is analyzed. We have a [Na] of 132 mmol/l, K of 62.7 mmol/l, Cl of 182 mmol/l, sulfate of 21.2 mmol/l and some other minor species. The ionic strenght is about 0.22 - now I need to compute the Na+K-Cl-2*SO4. So the ionic strength is higher than 0.1, but how do I aaccount for the many interactions/reactions possible between the species? Can I find a robust common activity coefficient to apply or will I need a separate one for each species?

Best wishes
Troels

2. Dec 14, 2008

### Staff: Mentor

The best approach I can think off will be to use so called Davies equation - it is very similar to the one used in the Debye-Huckel theory. You will find it on this page: Davies equation (and probably on many others).

One coefficient will not work, as it is strongly charge dependent.

Last edited: Dec 14, 2008
3. Dec 14, 2008

### tring

Thanks - I found Davies also here
but as indicated in the complicated theory and e.g. at this site
http://www.calcenstein.com/calc/0328.php
I need to account for the interactions. So here is the SO4-- the main problem, and it will mix with some Na - that Na will have a very different activity coefficient than the Na interaction e.g. with Cl. So when I know the absolute concentrations, how do I partition between all these many possibilities? I hope this is just approximately an understandable question. Thanks again. Best wishes. Troels

Last edited by a moderator: May 3, 2017
4. Dec 14, 2008

### Staff: Mentor

The closest you can get will be the Specific Interaction Theory, which calculates activity coefficients using (experimentally determined) parameters for each specific salt. In most cases that's an overkill - lot of additional work, small differences in the final results. And SIT parameters are published for a relatively small number of ion pairs.

I would either stick to Davies equation (if you need these calculations to be done just once), or - if this is a repeatable problem - I would determine activity coefficients experimentally to use them in all other experiments.

Can you please elaborate on what are you trying to do? If I read your original question properly you are looking for a charge balance of the solution using known concentrations. If so, you don't need activity coefficients at all.

5. Dec 14, 2008

### tring

Thanks again for the answer. I had hoped you wouldn't ask me what I was trying to accomplish, but here goes. What I want to is explore the relationship between the measured strong ion difference in urine (Na+K-Cl-2*SO4 etc) and the apparent SID, had e.g. from eq 1 in the Herman and Booth reference our earlier discussion pointed me to (J Chem Educ 1990, 67: 501-2) which simply states the charge balance at actual pH. This equation is identical to those had from PA Stewart and also almost to the Henderson-Hasselbalch equation. The reason for this interest is that this apparent SID in urine subtracted from the appropriate match of plasma SID (without the ammonium term) is identical to the classical assessment of net acid excretion: titrable acidity plus ammonium excretion. You will probably recognize immediately this as a mathematical tautology but I needed a bit or work to make sure about that. But acutally handling urine to perform classical measurement of net acid excretion is quite complicated - hence if there were a simple effective short cut from the measured SID it might be a really good thing for those of us who wants to do experiments with renal acid base regulation. Finally, I strongly believe the classical acid-base accounting is essentially wrong and the renal excretion exactly of SID components is what matters - hence I need these but in raw form where I agree and understand that corrections are unneeded. But I guess they are needed for my primary aim which is to deconstruct the classical acid-base model in renal physiology. So I need these corrections to deconstruct a theory I find ugly and difficult to use - so it is indeed a pity that the corrections come out so weak and unsure.
Anyway I learn, thanks again
Troels

6. Mar 19, 2009

### tring

Dear friends - I now have 9 complicated urine like fluids of phosphate, creatinine, Na, K , Cl, oxalate, urate, magnesium, citrate of computed ionic stregnths from 0.16 to 0.46 and measured pH from 3 to 9. I fit a monotone relationship without any corrections for nonideal behaviour from 2.5 to 8 so it is not very good. Applying dbh and Davis give large overshots in computed pH. It wasn earlier mentioned that if I had known concentrations and fitted H from charge balance I wouldn't need any corrections for ionic strenght. Does that mean that all I then have to do is applaying the Davis correction to find activity of protons? That does help quie a bit but seems not logical - so probably some other meaning was intended in the earlier reply?

Best wishes
Troels

7. Mar 19, 2009

### Staff: Mentor

I am not sure what you mean - you fit what to what?

8. Mar 19, 2009

### tring

Thanks, - I have 9 solutions of citrate, Na, K , Cl, phosphate, oxalate, urate, magnesium, creatinine, ammonium all together, with ionic strenghts as mentioned. I know the compositions - and fit the pH knowing all the standard pks for citrate and phosphate etc. The pH was measured by the lab -. and I was then told the results. According to theory as the thread started that should be feasible provided behaviour was if not ideal then decent at least. Using Davis or Debye-HÃ¼ckel leads to pH being more overfitted than underfitted without correction. Of course I can not be sure pH was measured without error. I couldn't have Ca since oxalate was there. But otherwise it was meant to be concentrations typical of urine and also containg urea which was ignored in the computation. I'll make more diluted solutions but would like to have better possibilities to fit pH in the original solutions too if possible.

Best wishes
Troels