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Acid-Base Theory Formalism

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DGauss:
When studying the formal theory of acids and bases I came across equations for pH of general acid-base titrations in the work of Robert de Levie.

All articles present the same formalism basically, a good succinct example which shows coverage of acids, bases, ampholytics, and salts, can be found in


* de Levie, Robert. "A general simulator for acid-base titrations." Journal of chemical education 76.7 (1999): 987.
I'm a newbie here so not sure if the better practice would be for me to provide pictures of the equations for example...

My question is, how general is this formalism. In particular, how to define 'total analytical concentration' C for components which are present from multiple different sources.  Say for example I mix $C_a$ (NH4)2HPO4 with $C_b$ NH4H2PO4.

The analytical concentration starting for NH4 is $2C_a+C_b$ right? But how do we handle the computation for HPO4 and H2PO4, is it

[tex]
C_a* F(HPO4) + C_b* F(H2PO4)
[/tex]

or is it

[tex]
(C_a+C_b) *(F(HPO4) + F(H2PO4))
[/tex]

Borek:
No idea what you mean by F.

Can't check the original de Levie paper at the moment, but total analytical concentration of 'phosphoric acid' is just Ca+Cb in this case.

DGauss:
Since someone's biting maybe I am allowed to post pictures from the original paper.

Bit that got cut off saying 'here $p$ denotes the maximum number of dissociable protons an acid or base can accommodate...'.

From the examples de Levie gives I understand that p,q differ between salts and say acids. Phosphoric acid would have p=3, q=3 but if you are putting H2PO4- in solution you start with p=3, q=2 in the F equation.

My question is just, whether is valid to treat contributions from different sources of chemically identical species this way. If so that would be C_a* F(HPO4) + C_b* F(H2PO4) as I put in first post.

Borek:

--- Quote from: DGauss on September 12, 2020, 05:32:23 PM ---My question is just, whether is valid to treat contributions from different sources of chemically identical species this way.
--- End quote ---

Valid - I see no reason to doubt it. This paper lists function F as "defined", but most likely it was defined after someone (either deLevie, or one of authors of the cited papers) solved the problem starting from the first principles and found that this expression appears quite often, so defining it this way makes calculations easier. It wasn't taken from nowhere.

But it is not a total analytical concentration, more like an auxiliary function helping in calculations. Plus, as far as I am aware, it is not something universally used/taught as a part of the acid-base theory formalism.

DGauss:
The total analytical concentration is (what de Levie defined as) C_s and C_t. I don't doubt the equation holds for simple cases like pure acids and bases, I've seen the derivation. It also makes sense for salts or mixtures of salts e.g. CaHPO4 + NaHSO4. In this case you just sum up contributions from Ca2+, Na+, HPO4-, HSO4- (plugging them into the F equation).

What I'm not sure about is specifically case where the same species is contributed by different salts. Can we sum up contributions from different salts independently given the same ions are introduced e.g. NH4+?

I know you already said "Valid" but it felt like most of your post was justifying the equation should hold generally. I'm asking about whether having different sources of same ions is a special case.

Regarding comment about usability: the reason I am looking at de Levie is because it provides a single equation for all acid-base-salt systems. It's useful for work I'm doing regarding propagation of uncertainties to have only one equation describe the titration. I am not aware of any other such approaches, all the rest just use the whole set of equations.

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