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We have a fluid with $\pu{0.01 M}~\ce{HCl}$ and $\pu{0.02 M}~\ce{K2HPO4}$, so if we assume activity coefficients are $1$ throughout we can find pH as $6.800012$ and confirm that at that pH there is approximately zero balance ($6.104839\!\times\!10^{-13}$) between positive and negative charges calculated as

$$\mathrm{ K^+ +H^+ – OH^- - Cl^- -}\ce{H2PO4-}\mathrm{ - 2\times} \ce{HPO4^2-} \mathrm{\ -\ 3\ \times}\ce{PO4^3-}$$

Now we can find the ionic strength and via Debye-Hückel/Davies find activity coefficients for absolute charge 1-3. This allows correction of the thermodynamic dissociation coefficients for phosphoric acid (and water dissociation) so we can correct the concentrations and find a new pH to minimize charge balance. After $4$ iterations we have pH 6.436864 at a charge balance of $1.429412\!\times\!10^{-15}$. This procedure allows reproduction of the results in a recent paper (Schell et al J Chem Eng Data 2018; 63: 2151-2161) with correlation $>0.9999$.

Now the question: these results requires the charge balance being formulated strictly in concentrations multi-plied by the relevant charges. I simply wonder why we should not for the charge balance equation multiply the found activity coefficients on the charged species so making the balance to minimize a function of $f_3\times 3\times [\ce{PO4}]$ and so forth with $f_3$ being the trivalent activity coefficient from Davies?

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  • $\begingroup$ It doesn't seem strange at all to me. You are doing a balance of charges, and the charges don't know what activity is. $\endgroup$ – Chet Miller Sep 9 '18 at 11:56
  • $\begingroup$ Sticking with concentrations certainly gives a perfect fit compared to other methods, but all the literature on single ion activity coefficients for strong ions made me wonder if the charge should not be discounted. I am happy if that is not the case. $\endgroup$ – user37217 Sep 9 '18 at 17:37
  • $\begingroup$ Would there be any online literature Chester Miller could cite to make it obvious that charges are oblivious to activities? $\endgroup$ – user37217 Sep 10 '18 at 6:09
  • $\begingroup$ I don't know. But check out Handbook of Aqueous Electrolyte Thermodynamics $\endgroup$ – Chet Miller Sep 10 '18 at 12:48
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    $\begingroup$ I would have corrected the typesetting, but I do not understand the formula at all. 2*K+H – OH- Cl -H2PO4 - 2*HPO4 - 3*PO4 What exactly are you adding or subtracting there? It is certainly not the elements/ions, but some kind of property of them. Please try to be more precise about this. I still don't understand the question and believe it should remain closed until it can be clarified. $\endgroup$ – Martin - マーチン Sep 12 '18 at 15:44
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No, charge is not really a activity based property. It is a number. Just as the activity coefficients don't change the number (or moles) of potassium atoms or phosphate anions, they don't change the charge either.

If you told me that one liter of a 1.0 molar potassium chloride solution had activity coefficients of 21 for potassium and 186 for chloride, then the amount of charge in the solution is still one mole of potassium cations and one mole chloride anions.

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