## Info

FIGURE 2-16 Conjugate acid-base pairs consist of a proton donor and a proton acceptor. Some compounds, such as acetic acid and ammonium ion, are monoprotic; they can give up only one proton. Others are diprotic (H2CO3 (carbonic acid) and glycine) or triprotic

(H3PO4 (phosphoric acid)). The dissociation reactions for each pair are shown where they occur along a pH gradient. The equilibrium or dissociation constant (Ka) and its negative logarithm, the pKa, are shown for each reaction.

Also included in Figure 2-16 are values of pKa, which is analogous to pH and is defined by the equation pKa = log

-log Ka

The stronger the tendency to dissociate a proton, the stronger is the acid and the lower its pKa. As we shall now see, the pKa of any weak acid can be determined quite easily.

### 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 concentration 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 constant (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 ex pH

pH 5.76

Buffering region pH 3.76

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### Responses

• edward
How does an indicator work ph equal pka?
8 years ago