Sometimes it is inconvenient to use the concentration units. For example, a reactant’s concentration may change by many orders of magnitude. If we are interested in viewing the progress of the reaction graphically, we might wish to plot the reactant’s concentration as a function of time or as a function of the volume of a reagent being added to the reaction. Such is the case in Figure 1, where the molar concentration of H+ is plotted (y-axis on left side of figure) as a function of the volume of NaOH added to a solution of HCl. The initial [H+] is 0.10 mol/L, and its concentration after adding 75 mL of NaOH is 5.0 × 10-13 mol/L. We can easily follow changes in the [H+] over the first 14 additions of NaOH. For the last ten additions of NaOH, however, changes in the [H+] are too small to be seen.
Figure 1. Graph of [H+] versus volume of NaOH and pH versus volume of NaOH for the reaction of 0.10 mol/L HCl with 0.10 mol/L NaOH.
When working with concentrations that span many orders of magnitude, it is often more convenient to express the concentration as a p-function. The p-function of a number X is written as pX and is defined as
pX = –lg(X)
Thus, the pH of a solution that is 0.10 mol/L H+ is
pH = –lg[H+] = –lg(0.10) = 1.00
and the pH of 5.0 × 10-13 mol/L H+ is
pH = –lg[H+] = –lg(5.0 × 10-13) = 12.30