The H+ and OH– log concentration lines are the same ones that we saw in Fig. 1. The other two lines show how the concentrations of CH3COOH and of the the acetate ion vary with the pH of the solution.

How do we construct the plots for [HAc] and [Ac–]? If you look carefully at Fig 2, you will observe that each line is horizontal at the top, and then bends to become diagonal. There are thus three parameters that define these two lines: the location of their top, horizontal parts, their crossing points with the other lines, and the slopes of their diagonal parts.

The horizonal sections of these lines are placed at 3 on the ordinate scale, corresponding to the nominal acid concentration of 10–3 M. This value corresponds to

Ca = [HAc] + [Ac–]

which you will recognize as the mass balance condition saying that "acetate" is conserved; Ca is the nominal "acid concentration" of the solution, and is to be distinguished from the concentration of the actual acidic species HAc.

At low pH values (strongly acidic solution) the acetate species is completely protonated, so [HAc] = 10–3 M and [Ac–]=0. Similarly, at high pH, –log [Ac–]=3$ and [HAc]=0. If the solution had some other nominal concentration, such as 0.1 M or 10–5, we would simply move the pair of lines up or down.

The diagonal parts of the lines have slopes of equal magnitude but opposite sign. It can easily be shown that these slopes d(–log [HAc]}/d{pH} etc.are +-1, corresponding to the slopes of the [OH–] and [H+] lines. Using the latter as a guide, the diagonal portions of lines 3 and 4 Can easily be drawn.

The crossing point of the plots for the acid and base forms corresponds to the condition [HAc]=[Ac–]. You already know that this condition holds when the pH is the same as the pKa of the acid, so the the pH coordinate of the crossing point must be 4.75 for acetic acid. The vertical location of the crossing point is found as follows: When [HAc] = [Ac], the concentration of each species must be Ca/2 or in this case 0.0005 M. The logarithm of 1/2 is 0.3, so a 50% reduction in the concentration of a species will shift its location down on the log concentration scale by 0.3 unit. The crossing point therefore falls at a log-C value of (–3) – 0.3 = –3.3. Knowing the value of log100.5 is one of the few new "facts" that must be learned in order to construct these graphs.