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Being a physicist by training, having worked in software development for the last 10 years. Having heard my last chemistry lecture 15 years a go I am a bit lost in regards to how one can calculate the pH of a mixture of an acid with a buffer.

I have acetic acid solution at pH 1.8, to be mixed with phosphate buffer (ph 7) at ratio 1:10. What is the pH of the mixture?

First attempt

I tried to work out the mixture based on concentrations I calculated from the pH.

$$10\cdot 10^{-pH(Mixture)} = 10^{-1.8} + 9\cdot 10^{-7}$$

But I don't think this accounts for the buffer trying to neutralize some acidity of the mixture. So after some thought I remembered that there was this equation with $pK_S$.

Attempt with Henderson Hasselbalch

Remembering the Henderson Hasselbalch equation, I am stuck at how to apply it in this situation.

$$\mathrm{pH}=\mathrm pK_S +\log{\frac{[\ce{A-}]}{[\ce{HA}]}}$$

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    $\begingroup$ The system is not sufficiently defined, as there must be known the total phosphate concentration or equivalent data. Otherwise, the final pH is undefined. // Also, pH 1.8 gives by extrapolation mass percentage of acetic acid more then 80%. At such conditions, pH cannot be easily defined, predicted nor measured. Therefore, all the task is rather made up without touch with reality. $\endgroup$
    – Poutnik
    Dec 6, 2023 at 18:23
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    $\begingroup$ Neither of your solutions are well enough defined to be used in calculating the pH of a mixture. You need to define total acetate and total phosphate species. You also need to define how the pH of each solution was adjusted/made. $\endgroup$
    – MaxW
    Dec 6, 2023 at 18:58
  • $\begingroup$ Hmm, then I have to gather more information. A colleague is receiving a shipment and was trying to anticipate at what ratio they would have to mix with the buffer so that the buffer would stay within its pH range $\endgroup$
    – wirrbel
    Dec 6, 2023 at 19:02
  • $\begingroup$ There is the concept of buffer capacity which indicates how much acid or base can be added so that the pH change is 1 unit. So you'll also need to know how much of a pH change your colleague is willing to tolerate. $\endgroup$
    – MaxW
    Dec 7, 2023 at 4:43

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