[schnorch]

Hello!

There is this formula for dissociation of an acid:

K_a = H⁺ x A^- / HA

And if it is the three-proton-acid citric acid:

K_a1 = H⁺ x H₂Cit^- / H₃Cit
K_a2 = H⁺ x HCit^-2 / H₂Cit^-
K_a3 = H⁺ x Cit^-3 / HCit^-2

Now my question:
Is the H⁺ the total amount of H⁺ or only the amount of the dissociation step. I mean like this:

K_a1 = H⁺₁ x H₂Cit^- / H₃Cit
K_a2 = H⁺₂ x HCit^-2 / H₂Cit^-
K_a3 = H⁺₃ x Cit^-3 / HCit^-2

And H⁺_a + H⁺_b + H⁺_c = total H⁺
And H⁺_a > H⁺_b > H⁺_c

For me it sounds logical, if the formula doesn't mean the total amount of H⁺.
But I calculated a bit and the results look better, if it does mean the total amount.

Thanks in advance,
I am no native English speaker.

[Borek]

Total. No way to say where did this particular H⁺ came from, they are all identical.

[chenbeier]

Additional 1 mol citric acid contain 3 mol H+, which dissociate in steps.
There are  no partical H+.

[schnorch]

So if I have a pH of 4 (H = 0.0001), this is correct:

log10(3.13) = 0.0001 x H₂Cit^- / H₃Cit
log10(4.76) = 0.0001 x HCit^-2 / H₂Cit^-
log10(6.40) = 0.0001 x Cit^-3 / HCit^-2

And so I have the correct ratios of the citric acid and the anions.
Right?

[chenbeier]

Check this

https://de.m.wikipedia.org/wiki/Citronens%C3%A4ure#/media/Datei%3ACitric_acid_speciation.svg
ph 4 means almost di hydrogen citrate.

[Borek]

So if I have a pH of 4 (H = 0.0001), this is correct:

log10(3.13) = 0.0001 x H₂Cit^- / H₃Cit
log10(4.76) = 0.0001 x HCit^-2 / H₂Cit^-
log10(6.40) = 0.0001 x Cit^-3 / HCit^-2

And so I have the correct ratios of the citric acid and the anions.
Right?

Yes.

[schnorch]

Thanks.

I calculated with 0.0001 in every line further and yes, the most often anion is the di hydrogen citrate: I calculate 20% tri hydrogen citrate, 74% di hydrogen citrate, 6% mono hydrogen citrate and almost nothing of the zero hydrogen citrate.

This means the ratios of the anions depend on the pH and only indirectly on the citric acid concentration. So I could change the ratios of the anions both by adding more or less citric acid but also by adding a strong acid or a strong base. So, if I have a pH 4 citric acid solution (with mainly di hydrogen citrate) and add HCl to it until the pH is 3, I will have new ratios of anions (I calculate ca. 73% three hydrogen citrate, 27% di hydrogen citrate and almost nothing of the others).
Is this right generally? (You don't need to check the exact numbers of course)

[Borek]

This means the ratios of the anions depend on the pH and only indirectly on the citric acid concentration.

Actually as long as we ignore the ionic strength of the solution ratios depend only on pH (and Ka values). Note that there is nothing else in the Ka definition. pH _can_ depend on the citric acid concentration, but can be controlled by other means as well.

So I could change the ratios of the anions both by adding more or less citric acid but also by adding a strong acid or a strong base

in other words: by changing the pH, by any means.

So, if I have a pH 4 citric acid solution (with mainly di hydrogen citrate) and add HCl to it until the pH is 3, I will have new ratios of anions (I calculate ca. 73% three hydrogen citrate, 27% di hydrogen citrate and almost nothing of the others).
Is this right generally? (You don't need to check the exact numbers of course)

General; idea sounds OK, but taking into account that pKa1≈3.1 at pH=3 I would expect the ratio of H₃Citrate to H₂Ctitrate^- to be closer to one.

[schnorch]

Actually as long as we ignore the ionic strength of the solution ratios depend only on pH (and Ka values). Note that there is nothing else in the Ka definition. pH _can_ depend on the citric acid concentration, but can be controlled by other means as wel.

Thanks. I needed a few words more than only "Yes".

General; idea sounds OK, but taking into account that pKa1≈3.1 at pH=3 I would expect the ratio of H₃Citrate to H₂Ctitrate^- to be closer to one.

This is right unfortunately. I calculated from the pKa1=3.13 the ratio at pH=3 must be 1.35 but I calculated 2.7. Strange. Pretty exact twice the number. I think I will find the mistake soon.

[schnorch]

And I found the mistake.

At pH=3 I have 57% tri, 42% di 1% mono and 0% zero hydrogen citrate.
At pH=4 I have 10% tri, 76% di, 13% mono and 1% zero hydrogen citrate.

Thanks a lot!