We are trying to predict the pH-value of a multicomponent buffer. It consists of:

\begin{array}{lcrr} \# &\text{Component} &C,\,\pu{mol L-1} &\mathrm{p}K_\mathrm{a1} &\mathrm{p}K_\mathrm{a2} &\mathrm{p}K_\mathrm{a3}\\ \hline 1 &\text{Citric acid} &\pu{2.60e-5} &3.13 &4.76 &6.40 \\ 2 &\ce{NaH2PO4} &\pu{5.65e-3} &7.21 & &\\ 3 &\ce{(NH4)2SO4} &\pu{2.27e-3} &9.20 & &\\ 4 &\ce{NaHCO3} &\pu{1.19e-3} &10.33 & & \end{array}

Our problem is that we don't know how to combine several equilibria which exist in the solution. Since $\ce{NaHCO3}$, for example, is an ampholyte, it is difficult to tell if it reacts as an acid or a base.

Although this should be a somewhat common problem, we didn't find any formula or method to calculate the pH of such systems. We would be thankful for any idea!

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    $\begingroup$ Where did you get all this values? If it's real problem then just mix it and check pH. Still it may be homework and it seems it breaks our homework policy. $\endgroup$ – Mithoron Aug 27 '17 at 23:53
  • $\begingroup$ It is a real problem indeed. I already checked the pH, but I am curious though if there's a way to calculate it. We also had the idea to write an excel-sheet or a program which tells us the pH of multicomponent systems, which would be useful in the lab. $\endgroup$ – Simon Pflug Aug 28 '17 at 6:55
  • $\begingroup$ First suggestion, you are missing some pKa's, although I think the only important ones are those of H2CO3 (3.6) and H3PO4 (2.12). Then, clearly undissociated citric acid is not compatible with HCO3- or even H2PO4-. Just make then react and star from there. $\endgroup$ – Zamu Aug 28 '17 at 19:44
  • $\begingroup$ Sorry, in my previous comment I made a mistake, the pKa of H2CO3 seems to be 6.35. $\endgroup$ – Zamu Aug 28 '17 at 21:29
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    $\begingroup$ Let me guess: is the pH you measured about 6.3? $\endgroup$ – Zamu Aug 28 '17 at 22:46