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There are a lot of textbook examples showing what happens to the pH of a buffered solution when you add strong acids and strong bases. Searching for an example calculation where you add weak acids or bases instead, I did not find any information.

The purpose of this question is to establish a model answer for this type of problem. To give a specific example, we start with a phosphate buffer (total phosphate concentration of 100 mmol/L) with a pH adjusted to 8. What will happen when you add weak acid to a concentration of 10 mmol/L? Because the strength of the weak acid might matter, give the answer for a p$K_\mathrm{a}$ of 6.0, 8.0 and 10.0. Does it matter if the weak acid is one of the substances already present in the buffer?

This question is related, but not a duplicate of questions about titrating weak acids.

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    $\begingroup$ Such cases are well solved as 2 pH buffer systems, linked by mutual neutralization, with conjugate pair ratios fitting the same pH. $\endgroup$
    – Poutnik
    Oct 17, 2022 at 19:57
  • $\begingroup$ I would just say pretty much nothing happens, and call it a deal. Calculation would be difficult and resulting pH very close to original. Questions are about strong acids, because they have a serious effect. Also, now I'm tempted to find a duplicate :) $\endgroup$
    – Mithoron
    Oct 17, 2022 at 22:32
  • $\begingroup$ The buffer pH depends on the ratio of weak acid to its conjugate base. Adding any weak acid will increase the acid content lowering the pH of the buffer solution and possibly changing the buffer capacity $\endgroup$
    – jimchmst
    Oct 17, 2022 at 23:16
  • $\begingroup$ @Poutnik Do you know of a good reference that explains broad range buffer mixtures? I do see a connection between them and this question. $\endgroup$
    – Karsten
    Oct 18, 2022 at 1:07

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Weak acids at a concentration of 10 mmol/L and the given range of p$K_\mathrm{a}$ values dissociate very little in pure water. How much it dissociates in a buffered solution depends on the pH of the solution and the p$K_\mathrm{a}$ of the weak acid. Here, the pH is close to 8. With the information given, it is impossible to calculate the exact pH change. It is possible, however, to quantify how much strong acid you would have to add to get the same effect.

  • p$K_\mathrm{a} = 6$: The weak acid is fully (or to 99%) dissociated. It's effect on the buffer is similar to that of adding strong acid as long as you don't exceed the buffer capacity.

  • p$K_\mathrm{a} = 10$: The weak acid hardly dissociates (99% protonated). It's effect on the buffer is negligible.

  • p$K_\mathrm{a} = 8$: If the weak acid you are adding is identical to the conjugate acid of the buffer system, you are increasing its concentration by 10 mmol/L. If it is a different acid, about 50% of it will dissociate. This is the same as adding half the amount of strong acid. However, the weak acid will also increase the buffer strength.

So it really depends on the p$K_\mathrm{a}$ of the weak acid added. It can either have an effect comparable to that of a strong acid, or hardly any effect at all, or something in between.

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