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I'm trying to work through the calculations of a specific paper (linked here / below) but, my numbers are way off and I can't get them to match for the life of me. I need to make the same buffer but at a lower concentration. I'm not understanding how the paper was able to get the ratios (found in supplementary information) they used to make the buffer.

For example: 0.9M phosphate/citrate buffer, pH 3 Ratios used: disodium hydrogen phosphate (0.87g/100mL); trisodium citrate dihydrate buffer (3.51g/100mL)

How were they able to calculate those ratios? I've tried using Henderson-Hasselback equation but maybe I'm utilizing it incorrectly?

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    $\begingroup$ Those components are not able to reach pH 3. pH would be > 7. // BTW, questions should be self-contained, answerable without following any link, that should serve just as a reference to content origin, or for further reading for better context. $\endgroup$
    – Poutnik
    Commented Jul 31, 2023 at 19:53

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Those components are not able to reach $\text{pH 3}$ without addition of an acid, as both salts gives solutions with alkalic pH values.

At such high concentrations near $\pu{1 M}$, pH calculations are off, unless going a long, long way of experimental determining activity coefficients (as these cannot be reliably predicted for such concentrations either).

pH of such buffers cannot be calculated from basic principles like via the Henderson-Hasselbalch equation. At the best it can be obtained from published empirical functions or tables of mixing ratios for desired pH.

If no such empirical help is available, the $\pu{pH}$ of such buffers must be adjusted experimentally, using pH meter calibrated on standard pH buffers.

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