# How to calculate the pH of a mixture of an acid with a buffered solution?

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.

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

• 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. Dec 6, 2023 at 18:23
• 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.
– MaxW
Dec 6, 2023 at 18:58
• 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 Dec 6, 2023 at 19:02
• 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.
– MaxW
Dec 7, 2023 at 4:43