Buffers Are Mixtures of Weak Acids and Their Conjugate Bases

Buffers are aqueous systems that tend to resist changes in pH when small amounts of acid (H+) or base (OH-) are added. A buffer system consists of a weak acid (the proton donor) and its conjugate base (the proton acceptor). As an example, a mixture of equal concentrations of acetic acid and acetate ion, found at the midpoint of the titration curve in Figure 2-17, is a buffer system. The titration curve of acetic acid has a relatively flat zone extending about 1 pH unit on either side of its midpoint pH of 4.76. In this zone, an amount of H+ or OH- added to the system has much less effect on pH than the same amount added outside the buffer range. This relatively flat zone is the buffering region of the acetic acid-acetate buffer pair. At the midpoint of the buffering region, where the concentration of the proton donor (acetic acid) exactly equals that of the proton acceptor (acetate), the buffering power of the system is maximal; that is, its pH changes least on addition of H + or OH-. The pH at this point in the titration curve of acetic acid is equal to its pK^. The pH of the acetate buffer system does change slightly when a small amount of H+ or OH- is added, but this change is very small compared with the pH change that would result if the same amount of H+ or OH- were added to pure water or to a solution of the salt of a strong acid and strong base, such as NaCl, which has no buffering power.

Buffering results from two reversible reaction equilibria occurring in a solution of nearly equal concentrations of a proton donor and its conjugate proton acceptor. Figure 2-19 explains how a buffer system works. Whenever H+ or OH- is added to a buffer, the result is a small change in the ratio of the relative concentrations of the weak acid and its anion and thus a small change in pH. The decrease in concentration of one component of the system is balanced exactly by an increase in the other. The sum of the buffer components does not change, only their ratio.

Each conjugate acid-base pair has a characteristic pH zone in which it is an effective buffer (Fig. 2-18). The H2PO-/HPO|- pair has a pKa of 6.86 and thus can serve as an effective buffer system between approximately pH 5.9 and pH 7.9; the NH+/NH3 pair, with a pKa of 9.25, can act as a buffer between approximately pH 8.3 and pH 10.3.

A Simple Expression Relates pH, pKa, and Buffer Concentration

The titration curves of acetic acid, H2PO-, and NH+ (Fig. 2-18) have nearly identical shapes, suggesting that these curves reflect a fundamental law or relationship. This is indeed the case. The shape of the titration curve of any weak acid is described by the Henderson-

Acetic acid HAc (CH3COOH)

Acetic acid HAc (CH3COOH)

Acetate (chjjcoo-)

FIGURE 2-19 The acetic acid-acetate pair as a buffer system. The system is capable of absorbing either H+ or OH- through the reversibility of the dissociation of acetic acid. The proton donor, acetic acid (HAc), contains a reserve of bound H+, which can be released to neutralize an addition of OH- to the system, forming H2O. This happens because the product [H+][OH-] transiently exceeds Kw (1 X 10-14 m2). The equilibrium quickly adjusts so that this product equals 1 X 10-14 m2 (at 25 °C), thus transiently reducing the concentration of H + . But now the quotient [H+][Ac-] / [HAc] is less than Ka, so HAc dissociates further to restore equilibrium. Similarly, the conjugate base, Ac-, can react with H+ ions added to the system; again, the two ionization reactions simultaneously come to equilibrium. Thus a conjugate acid-base pair, such as acetic acid and acetate ion, tends to resist a change in pH when small amounts of acid or base are added. Buffering action is simply the consequence of two reversible reactions taking place simultaneously and reaching their points of equilibrium as governed by their equilibrium constants, KW and Ka.

Hasselbalch equation, which is important for understanding buffer action and acid-base balance in the blood and tissues of vertebrates. This equation is simply a useful way of restating the expression for the dissociation constant of an acid. For the dissociation of a weak acid HA into H+ and A-, the Henderson-Hasselbalch equation can be derived as follows:

Then take the negative logarithm of both sides:

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