PH Paradoxes: Demonstrating That It Is Not True That pH ≡ -log[H+

Abstract

Six demonstrations highlighting paradoxes that arise if pH is incorrectly defined as -log[H+] are presented as justification for the recommendation that pH should be correctly defined as pH = -log aH+ in textbooks. For example, when acid with pH ~1 is diluted with an equal volume of 5 M MgCl2, one would expect the pH calculated as -log[H+] to increase as the concentration of acid is halved; surprisingly, it decreases to values below zero, as demonstrated with a pH meter or methyl green indicator. If a sample of the acid at pH ~2, and a second sample, diluted with salt solution so that it has pH ~0.5 are titrated with NaOH solution, equal volumes of base solution are required; but [H+] = antilog(-pH) is 0.01 in the first case and 0.32 in the second, leading to predictions of much different volumes of titrant. We could tolerate an approach to pH calculations that sacrificed reasonable practical answers for a sound theoretical foundation, but our current pedagogy seems to provide neither!