pOH from Hydroxide Ion Concentration

pOH is the same logarithmic compression as pH, read from the other end. Take the hydroxide ion concentration in mol/L, take the base-ten logarithm, flip the sign. A 0.0250 M sodium hydroxide solution dissociates completely, so [OH⁻] = 2.50 × 10⁻², and pOH = 2 − log 2.5 = 1.60. Its pH is then 14 − 1.60 = 12.40, and both numbers describe the same bottle.

The reason the base scale exists at all is that base chemistry is naturally written in hydroxide. A caustic titration measures hydroxide; a strong base's concentration is its hydroxide concentration; the Henderson–Hasselbalch equation for a base buffer comes out in pOH and pK_b. Working the whole problem in pOH and converting once at the end is fewer steps than converting to hydrogen ion at the start, and fewer steps is fewer sign errors.

Two things worth being precise about. The 14 that bridges pOH and pH belongs to 25 °C and to water. It is pK_w, water's own ionisation constant in logarithmic dress, and self-ionisation is endothermic, so heating water raises K_w and lowers the bridge: about 13.0 at 60 °C, 12.0 at 100 °C. Neutral water at 100 °C has pH 6.0 and pOH 6.0 and is still exactly neutral, because neutral means pH equals pOH, not pH equals 7.

And the scale is not fenced between 0 and 14. Those bounds are simply where 1 M solutions land. Concentrated sodium hydroxide at 12 M has a negative pOH; concentrated hydrochloric acid has a negative pH. The arithmetic is fine, though activity coefficients depart badly from unity long before you get there, so a measured value in that region needs more than this equation behind it.

The p-notation is Søren Sørensen's, devised at the Carlsberg brewery laboratory in 1909 for hydrogen ion, and it now attaches to anything worth compressing that way — pOH, pK_a, pK_b, pK_w, pCa.