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From what I see, the buffer capacity of tartrate buffer is generally decreasing as buffer pH increases. Why is this? Also, does this mean that tartrate buffer doesn't have a maximum buffer capacity at pH=pKa?

Or is there a more reliable source where I can get the buffer capacity vs. buffer pH graph for buffers of tartaric acid? This image is from a blog, and I can't find the real source of this image, even with Google image search.

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  • $\begingroup$ See: researchgate.net/publication/… $\endgroup$ – MaxW Mar 30 at 17:01
  • $\begingroup$ @MaxW I have seen that source, but for some reason the equation they give for their monoprotic buffer capacity is very different from what is given here (chembuddy.com/?left=pH-calculation&right=pH-buffer-capacity) and the equation for their diprotic buffer capacity gives extremely high values as [H+]/Kw, which is a part of the equation, gives, for example, 10^10, when pH = 4.0. I'm not sure why there's such a big difference from other sources, seeing that the unit are both mol/L/pH. Or am I mistaken about the units being the same? $\endgroup$ – YeRyeon Seo Mar 30 at 17:20
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Generally, the maximum buffer capacity is at $\ce{pK_a}$ . The tartaric acid is somewhat special for 2 reasons:

  1. It is a diprotic acid with both $\ce{pK_a}$ very close, with the $\ce{pK_{a1}}$ rather low, being affected by the reason 2. :

    $$\ce{pK_{a1}}=2.89,\ce{pK_{a2}}= 4.40 (L+)$$

  2. The solution buffer capacity (not limited to presence of specific buffer substances) generally increases toward $\ce{pH}=0$. It means, the buffer capacity is not given by concentration of of conjugated acid and base, but also by concentration of $\ce{H+}$ itself. That in large extent masks the $\ce{pK_a}$ maximum. It means, at a slope, a local peak must be big enough to be a peak.
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  • $\begingroup$ So can the maximum buffer capacity of tartaric acid only be determined experimentally? I've seen a lot of sources that state that tartaric acid is special because of the first reason you've mentioned, but no source actually states what the buffer capacity would look like graphed against buffer pH. Also, the second reason is slightly confusing. Why does buffer capacity generally increase toward pH=0? Could you expand a bit? $\endgroup$ – YeRyeon Seo Mar 30 at 17:15
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    $\begingroup$ Sorry, I'm not very good with buffers -- could you explain why there's a maximum "given by the solubility of the tartaric acid?" $\endgroup$ – YeRyeon Seo Mar 30 at 17:23
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    $\begingroup$ It can be created by computation. See also updated answer. $\endgroup$ – Poutnik Mar 30 at 17:51
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    $\begingroup$ pH dependency of buffer capacity - Let's make it simple. Buffer capacity is defined as the moles necessary to change pH +/- 1 pH unit. So if we have a two solutions of HCl in water, one with a pH of 2 and another with a pH of 5. It is going to take a lot more acid to raise the pH 2 solution to 1, than it will take to raise the pH 5 solution to 4. $\endgroup$ – MaxW Mar 30 at 18:16
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    $\begingroup$ For a diprotic acid see aqion.de/site/184 You'll need to plug $a_1$ and $a_2$ from formulas (2.3b) and (2.3c) into formula (5.1a) $\endgroup$ – MaxW Mar 30 at 19:04

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