Definition of the pH Value

The pH value is the negative base-10 logarithm of the hydronium concentration: $pH = -lg([H_{3}O^{+}])$, with the concentration in $\frac{mol}{L}$. Example: $\frac{0.01 mol}{L}$ hydrochloric acid is completely dissociated, so $[H_{3}O^{+}] =\frac{ 0.01 mol}{L} =\frac{ 10^{-2} mol}{L}$. Then $pH = -lg(10^{-2}) = 2$. The higher the hydronium concentration, the smaller the pH and the more acidic the solution. Neutral water has a pH of 7 at 25 °C. Conversely you compute the concentration with $[H_{3}O^{+}] = 10^{(-pH)}$. Cola is around pH 2.5, blood very constant at 7.4. Make sure to insert the concentration in $\frac{mol}{L}$.

The hydronium concentrations in aqueous solutions span an enormous range, from about $\frac{1 mol}{L}$ in strong acids to $\frac{10^{-14} mol}{L}$ in strong bases. A linear scale would be completely impractical for this. The negative base-10 logarithm compresses these many powers of ten onto a manageable scale of about 0 to 14. Therefore each pH unit corresponds to a factor of 10 in concentration: a solution with pH 3 is ten times more acidic than one with pH 4 and a hundred times more acidic than one with pH 5. A common mistake is to treat pH values linearly and think pH 6 is only slightly more acidic than pH 7, although it is the tenfold value.

Because the pH is the negative base-10 logarithm of the concentration, each pH unit corresponds to a factor of 10. If the pH rises by two units, the hydronium concentration falls by a factor of 100, that is by two powers of ten. Example: from pH 3 with $[H_{3}O^{+}] =\frac{ 10^{-3} mol}{L}$ to pH 5 with $[H_{3}O^{+}] =\frac{ 10^{-5} mol}{L}$ the concentration becomes a hundred times smaller. A rising pH means a decreasing acid concentration, so the solution becomes more basic. Conversely a pH falling by two units means a hundredfold higher hydronium concentration. You do this calculation fastest via the powers of ten, without reaching for the calculator.

The pH describes the hydronium concentration via $pH = -lg([H_{3}O^{+}])$, the pOH analogously the hydroxide concentration via $pOH = -lg([OH^{-}])$. In aqueous solutions both are linked through the ion product of water: at 25 °$C pH + pOH = 14$ holds. If you know one value, you get the other by subtracting from 14. An acidic solution has a low pH and a high pOH, a basic one the other way round. At pH 7 both equal 7 and the solution is neutral. The pOH is especially handy when a base is given and you first know the hydroxide concentration; via $pH = 14 - pOH$ you then conveniently reach the pH value.

Pure water dissociates slightly by itself into hydronium and hydroxide ions; this is called autoprotolysis. At 25 °C exactly equal numbers of H₃O⁺ and OH⁻ ions are present, each $\frac{10^{-7} mol}{L}$. Inserting this concentration into $pH = -lg([H_{3}O^{+}])$ gives $pH = -lg(10^{-7}) = 7$. Because hydronium and hydroxide have equal concentration, the solution is neither acidic nor basic, that is neutral. Importantly, the neutral point is temperature-dependent: at higher temperature the autoprotolysis increases, the ion product rises, and the neutral pH then lies somewhat below 7. So the value 7 strictly holds only at 25 °C.