Ionization of Water, Weak Acids, and Weak Bases: -Titration Curves Reveal the pKa of Weak Acids
Titration is used to determine the amount of an acid in a given solution. A measured volume of the acid is titrated with a solution of a strong base, usually sodium hydroxide (NaOH), of known concentration. The NaOH is added in small increments until the acid is consumed (neutralized), as determined with an indicator dye or a pH meter. The concentration of the acid in the original solution can be calculated from the volume and con centration of NaOH added. A plot of pH against the amount of NaOH added (a titration curve) reveals the pKa of the weak acid. Consider the titration of a 0.1 M solution of acetic acid (for simplicity denoted as HAc) with 0.1 M NaOH at 25 C (Fig. 2–17). Two reversible equilibria are involved in the process:
The equilibria must simultaneously conform to their characteristic equilibrium constants, which are, respectively,
At the beginning of the titration, before any NaOH is added, the acetic acid is already slightly ionized, to an extent that can be calculated from its dissociation con stant (Eqn 2–8). As NaOH is gradually introduced, the added OH combines with the free H+ in the solution to form H2O, to an extent that satisfies the equilibrium relationship in Equation 2–7. As free H+ is removed, HAc dissociates further to satisfy its own equilibrium constant (Eqn 2–8). The net result as the titration proceeds is that more and more HAc ionizes, forming Ac-, as the NaOH is added. At the midpoint of the titration, at which exactly 0.5 equivalent of NaOH has been added, one-half of the original acetic acid has undergone dissociation, so that the concentration of the proton donor, [HAc], now equals that of the proton acceptor, [Ac-]. At this midpoint a very important relationship holds: the pH of the equimolar solution of acetic acid and acetate is exactly equal to the pKa of acetic acid (pKa 4.76; Figs 2–16, 2–17). The basis for this relationship, which holds for all weak acids, will soon become clear. As the titration is continued by adding further in crements of NaOH, the remaining nondissociated acetic acid is gradually converted into acetate. The end point of the titration occurs at about pH 7.0: all the acetic acid has lost its protons to OH-, to form H2O and acetate. Throughout the titration the two equilibria (Eqns 2–5, 2–6) coexist, each always conforming to its equilibrium constant. Figure 2–18 compares the titration curves of three weak acids with very different dissociation constants: acetic acid (pKa 4.76); dihydrogen phosphate, H2PO4 (pKa 6.86); and ammonium ion, NH4 (pKa 9.25). Although the titration curves of these acids have the same shape, they are displaced along the pH axis because the three acids have different strengths. Acetic acid, with the highest Ka (lowest pKa) of the three, is the strongest (loses its proton most readily); it is already half dissociated at pH=4.76. Dihydrogen phosphate loses a proton less readily, being half dissociated at pH 6.86. Ammonium ion is the weakest acid of the three and does not become half dissociated until pH 9.25. The most important point about the titration curve of a weak acid is that it shows graphically that a weak acid and its anion—a conjugate acid-base pair—can act as a buffer.
FIGURE 2–17 The titration curve of acetic acid. After addition of each increment of NaOH to the acetic acid solution, the pH of the mixture is measured. This value is plotted against the amount of NaOH expressed as a fraction of the total NaOH required to convert all the acetic acid to its deprotonated form, acetate. The points so obtained yield the titration curve. Shown in the boxes are the predominant ionic forms at the points designated. At the midpoint of the titration, the concentrations of the proton donor and proton acceptor are equal, and the pH is numerically equal to the pKa. The shaded zone is the useful region of buffering power, generally between 10% and 90% titration of the weak acid.
FIGURE 2–18 Comparison of the titration curves of three weak acids. Shown here are the titration curves for CH3COOH, H2PO4-, and NH4. The predominant ionic forms at designated points in the titration are given in boxes. The regions of buffering capacity are indicated at the right. Conjugate acid-base pairs are effective buffers between ap proximately 10% and 90% neutralization of the proton-donor species.
