If I try to find the concentration of citric acid through back titration or reverse titration, the base I would use, like NaOH, would react with both acids to form sodium citrate and sodium tartrate, which are both white compounds that are colourless in aqueous form. How do I find the concentration of citric acid?

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    $\begingroup$ You cannot do this by ordinary classical titrations until and unless you know a way to separate tartaric acid. You can find total acidity but not individual components. Modern methods rely on chromatography or infrared spectra. $\endgroup$ – M. Farooq Dec 12 '19 at 14:24
  • $\begingroup$ Use 1H NMR spectroscopy and quantify the different components present. $\endgroup$ – Robert Law Dec 15 '19 at 18:53

Citric acid has $\mathrm{p}K_\mathrm{a}$-values of 3.1, 4.7, and 6.4, while those of tartaric acid are 3.0 and 4.3. If you adjust the $\mathrm{pH}$ to 6.4, tartaric acid would be roughly 100% deprotonated, while 50% of citric acid still has one proton to give off.

If you titrate this solution with $\ce{NaOH},$ you could estimate the buffer capacity, giving you an estimate of the concentration. The biggest systematic error is that the apparent $\mathrm{p}K_\mathrm{a}$ is dependent on ionic strength, which you don't know unless you know the concentrations in the first place.

  • $\begingroup$ "Adjusting" pH to 6.4 would be difficult. Titrating with NaOH solution and simultaneously measuring pH so as to plot a curve would allow calculation, using 6.4 pH as the reference even if you didn't actually hit 6.4 on the nose. $\endgroup$ – James Gaidis Dec 12 '19 at 15:15
  • $\begingroup$ @JamesGaidis That's a good idea: Just add NaOH continuously and monitor the pH. Then, get the midpoint of the titration empirically, and proceed to estimate the citric acid concentration. $\endgroup$ – Karsten Theis Dec 12 '19 at 15:17
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    $\begingroup$ @andselisk Thanks for a year of improving the typography (and spelling) of my posts. You would think I have \mathrm{p}K_\mathrm{a} down by now (or figured out the shortcut button). Anyway, hats off to you! $\endgroup$ – Karsten Theis Dec 12 '19 at 15:20
  • $\begingroup$ Buffer capacity is already something that is wonkey to determine even with pure solutions. I doubt this method will give you an accurate enough reading. I would say precipitation and dissolution is a safer analytical choice. $\endgroup$ – Martin - マーチン Dec 15 '19 at 20:08

I am afraid the measurement of the pH at half titration does not give a useful information on the pKa.

There has been a detailed series of measurements of the pH at half titration for different concentrations of phosphoric acid. See Cecile Canlet, BUP 938, 1, p. 1129, November 2011. For the first H atom, the theoretical pKa should be 2.12. But the pH measured at half-titration is 1.99 at 0.2 M, 2.06 at 0.1 M, 2.41 at 0.01 M.

For the second H atom, the pKa is 7.21 in the tables. But the measured pH at half titration is is 6.69 at 0.2 M, 6.71 at 0.1 M, and 6.99 at 0.01 M.

So the pH at half-titration may be different from the pKa by a factor as high as 0.4 pH unit. The reason is to be found in the ionic strength.

  • $\begingroup$ This is probably a homework-type theoretical problem. In theory there is no difference between theory and practice. But, in practice, there is. $\endgroup$ – James Gaidis Dec 13 '19 at 14:06

You could try reacting the mixture with excess calcium hydroxide to precipitate insoluble calcium citrate/tartarate.

You could then filter off this mixture to obtain calcium citrate/tartarate.

Reacting these with just enough sulfuric acid till the original pH is reached would give you citric acid/tartaric acid (and calcium sulfate which can be filtered off).

Then dry the solids and weigh them. Redissolve the citric/tartaric acid mixture and titrate it against NaOH.

You could then calculate the amount of citric acid/tartaric acid in the solution.

  • $\begingroup$ Would this work or would it be very inefficient? $\endgroup$ – sekharm Dec 13 '19 at 15:44

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