The pH Scale

Acid/base solutions are usually dealt with in the concentration range $10^{-1}$ to $10^{-7}$ M -- an inconveniently wide span to express directly. Sorensen introduced a logarithmic scale, the pH scale (from the French puissance de hydrogene, 'power of hydrogen'), defined as $pH = -\log_{10}[H_3O^+]$, so that $[H_3O^+]$ can be recovered from a known pH via $[H_3O^+]=10^{-pH}$ (the antilog of $-pH$). The analogous quantity for hydroxide is $pOH = -\log_{10}[OH^-]$. In a neutral solution at $25^\circ C$, $[H_3O^+]=[OH^-]=1\times10^{-7}$ M, so both pH and pOH equal 7. Because of the negative sign, a rising $[H_3O^+]$ means a falling pH -- e.g. as $[H_3O^+]$ rises from $10^{-7}$ to $10^{-5}$ M, the pH falls from 7 to 5. Since acidic solutions have $[H_3O^+]>10^{-7}$ and basic solutions have $[H_3O^+]<10^{-7}$, it follows that acidic solutions have pH less than 7 and basic solutions have pH greater than 7. …