Why is pH not averaged directly (6 and 8 to 7)?

pH is logarithmic; [H+] must be averaged

pH of mixture: 400 ml pH 6 and 700 ml pH 8

Short answer

Combine hydrogen-ion amounts: final H+ = (400e-6 + 700e-8)/1100 = 3.70e-7 mol/l. Taking the negative log gives pH = 6.43.

If 400 ml of water with a pH of 6 is mixed with 700 ml of water with a pH of 8, what will be the resultant pH of the mixture?

pH $=-\log_{10}[H^+]$ . On mixing, the moles of H $^+$ add, so the mixture's $[H^+]$ is the volume-weighted average (buffering is ignored).

\begin{aligned} [H^+]_{mix} &= \frac{400\times10^{-6} + 700\times10^{-8}}{400+700} \\ &= \frac{4.0\times10^{-4} + 7.0\times10^{-6}}{1100} = 3.70\times10^{-7}\ \text{mol/l} \end{aligned}

pH = -\log_{10}(3.70\times10^{-7}) = 6.43

Answer: pH of the mixture = 6.43.

✓ Answer checked by Claude Opus 5.5 (high effort)

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