pH and pOH Relation

Water is never merely water. A small fraction of it is always pulled apart into H⁺ and OH⁻, and the equilibrium between them fixes the product of their concentrations at a constant: $K_w = [\text{H}^+][\text{OH}^-] = 1.0\times10^{-14}$ at 25 °C. Because it is a product that is constant, the two concentrations are locked in a see-saw — push one up and the other must come down by the same factor. Take negative logarithms of both sides and the product becomes a sum: $\mathrm{pH} + \mathrm{pOH} = 14$. So pH and pOH are not two independent measurements. They are one number written two ways, and knowing either gives the other for free.

A worked case. Dissolve enough sodium hydroxide to make a 0.010 M solution: it dissociates completely, so $[\text{OH}^-] = 1.0\times10^{-2}$ and pOH = 2.00. Then pH = 14 − 2.00 = 12.00. Check it the long way, $[\text{H}^+] = K_w/[\text{OH}^-] = 10^{-14}/10^{-2} = 10^{-12}$, giving pH 12.00 — and the two routes agree, as they must.

The "14" is not a magic number, it is $\mathrm{p}K_w$, and the exact value at 25 °C is 13.995. The whole logarithmic apparatus came from Søren Sørensen at the Carlsberg laboratory in 1909, who needed a compact way to talk about hydrogen ion concentrations spanning more than ten orders of magnitude in brewing. The p-prefix now attaches to anything worth compressing that way: pOH, pKa, pKw, pCa.

The trap is that 14 belongs to 25 °C and nothing else. Self-ionisation is endothermic, so heating water drives it forward and $K_w$ rises: pKw is about 14.9 at 0 °C, 13.0 at 60 °C, and 12.0 at 100 °C. Which means neutral water at 100 °C has a pH of 6.0 — and it is still perfectly neutral, not acidic, because pH still equals pOH. This matters wherever hot water is measured: boiler water sampled at temperature and boiler water sampled after cooling do not read the same, and the difference is the equation moving, not the chemistry changing. Anyone reading pH on a hot sample needs to know whether the meter is compensating and what reference temperature it is compensating to.

Which leads to the deeper misconception. Neutral does not mean pH 7; neutral means pH equals pOH. The two coincide at 25 °C by arithmetic accident, and part company at every other temperature. Two smaller notes: the relation is aqueous only — it says nothing about a non-aqueous solvent, which has its own autoionisation constant if it has one at all — and the pH scale is not fenced between 0 and 14. Those bounds are just where 1 M solutions land. Concentrated hydrochloric acid at 12 M has a negative pH, and concentrated sodium hydroxide runs above 14, with the sum still holding.