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The Henderson–Hasselbalch equation can be used to estimate the pH of a buffer solution by approximating the actual concentration ratio as the ratio of the analytical concentrations of the acid and of a salt, MA. The equation can also be applied to bases by specifying the protonated form of the base as the acid.
For example, the pH of a 0.01 in moles per litreM solution of hydrochloric acid (HCl) is equal to 2 (pH = −log 10 (0.01)), while the pOH of a 0.01 M solution of sodium hydroxide (NaOH) is equal to 2 (pOH = −log 10 (0.01)), which corresponds to a pH of about 12.
Unlike a linear scale where each unit of distance corresponds to the same increment, on a logarithmic scale each unit of length is a multiple of some base value raised to a power, and corresponds to the multiplication of the previous value in the scale by the base value. In common use, logarithmic scales are in base 10 (unless otherwise specified).
The pH can be calculated using an ICE table. Note that in this example, we are assuming that the acid is not very weak, and that the concentration is not very dilute, so that the concentration of [OH −] ions can be neglected. This is equivalent to the assumption that the final pH will be below about 6 or so. See pH calculations for more details.
A log–log plot of y = x (blue), y = x 2 (green), and y = x 3 (red). Note the logarithmic scale markings on each of the axes, and that the log x and log y axes (where the logarithms are 0) are where x and y themselves are 1. Comparison of linear, concave, and convex functions when plotted using a linear scale (left) or a log scale (right).
The multiple valued version of log(z) is a set, but it is easier to write it without braces and using it in formulas follows obvious rules. log(z) is the set of complex numbers v which satisfy e v = z; arg(z) is the set of possible values of the arg function applied to z. When k is any integer:
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