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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

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Email:
Tel:1-201-478-8534
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Fax: 1-516-927-0118
Address: 2200 Smithtown Avenue, Room 1 Ronkonkoma, NY 11779-7329 USA