e.g. Citric Acid and Trisodium Citrate

$\ce{H3C6H5O7 <=>[ka_1] H2C6H5O7- + H+ <=>[ka_2] HC6H5O7^2- + H+ <=>[ka_3] C6H5O7^3- + H+}$

Using the definition of Ka and substituting for intermediates, I can get the relation:

$$\ce{[C6H5O7^3-] = (ka1\times ka2\times ka3\times [H3C6H5O7])/[H+]^3}$$

Taking the negative log of both sides gives:

$$\mathrm{-\log[}\ce{C6H5O7^3-}\mathrm{] = pka1+pka2+pka3-\log[\ce{H3C6H5O7}]-3\times pH}$$

$$\mathrm{\log(\frac{[\ce{H3C6H5O7}]}{[\ce{C6H5O7^3-}]}) = pka1+pka2+pka3-3\times pH}$$

$$\mathrm{\frac{[\ce{H3C6H5O7}]}{[\ce{C6H5O7^3-}]} = 10^{(pka1 + pka2 + pka3 - 3\times pH)}}$$

$$\mathrm{[\ce{H3C6H5O7}] = 10^{(pka1+pka2+pka3-3\times pH)} \times [\ce{C6H5O7^3-}]}$$

For Citric Acid's pkas of $3.13,~4.76,~6.4$, this equation implies that you need Trisodium Citrate at 5000x the concentration of Citric Acid to get a pH of 6, which makes no sense as that's essentially pure Sodium Citrate, which has a pH in the $8-9$ range. What am I doing wrong here?

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    $\begingroup$ HINT - Look at the stoichiometry. At pH 3.13 citric acid equals sodium citrate. At pH 4.76 sodium citrate equals disodium citrate. At pH 6.4 disodium citrate equals trisodium citrate. $\endgroup$ – MaxW Aug 23 '18 at 3:16

Nothing is wrong with your equations; you are simply misinterpreting your calculated result. At a pH of 6, sodium citrate is present at 5000-fold the concentration of citric acid, but these are not the only species in solution, and sodium citrate is not the dominant species in solution.

The hydrogen citrate dianion is, and is thus the main contributor to the pH of the solution.

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