Interrelationship Among Acids, Bases, pH, and Buffers (With Diagram)

According to the Bronsted-Lowry definitions, an acid is a proton (or H ⁺) donor and a base is a proton acceptor. For example, when acetic acid is dissolved in water, a certain number of the acetic acid molecules dissociate as follows:

In the reaction, a proton of acetic acid has been donated to water, producing an anion (acetate) and a cation (the hydronium ion).

Acetic acid donated the proton (H⁺) and is therefore the acid. Water accepted the proton and is a base in the reaction. If the reaction is reversed, the acetate anion acts as a proton accep­tor and therefore fits the criterion of a base.

Acetic acid and acetate ions are referred to as a conjugate acid-base pair. Protons are attracted both to the con­jugate base and to water. An acid that readily donates protons to water is called a strong acid, while an acid that does not readily donate protons to water is termed a weak acid. Each acid is characterized by its tendency to dissociate; the extent of dissociation may be determined from the acid’s dissociation constant, K, defined by

where for a given solution [HA] is the concentration of un-dissociated acid, [A ^–] is the concentration of conju­gate base, and [H ⁺ ] is the hydrogen ion concentra­tion. The dissociation constant varies somewhat ac­cording to the temperature of the solution customarily in physiology and biochemistry, one re­fers to the apparent dissociation constant, K’, of an acid. This value is based on the concentrations of reactants and products that can actually be measured fol­lowing dissociation of the acid in water. Table 3-6 lists the apparent dissociation constants of some common acids.

The concentration of H⁺ in cells varies widely. The range may exceed 0.1 to 10^-10 M. Although these con­centrations may not seem high, small changes in H ⁺ concentration have noticeable effects on cell function. It is inconvenient to express the H⁺ concentration in molar terms (such as 1 x 10^-7 M), and the pH scale pro­posed by S0rensen is used instead.

Accordingly,

pH= -log₁₀ [H⁺] (3-2)

At 25°C, the H⁺ (and OH”) concen­tration of pure water is 1 x 10^-7 M and the solution is at neutrality. At this concentration,

pH= -logi₀ [1.0 x 10^-7] = 7.0 (3-3)

Table 3-7 shows the range of the pH scale and lists the pH values of a number of familiar liquids. In the labor­atory, the pH of a solution is determined potentiometrically using an instrument called a pH meter. The in­strument contains two electrodes that are immersed in the liquid sample; one of these is a reference elec­trode (whose electrical potential is constant) and the other is a glass electrode (whose electrical potential de­pends on the pH of the sample).

An electrometer mea­sures the difference in electrical potential between the two electrodes and this value is then converted to pH units and is displayed. Most pH meters are accu­rate to within 0.01 pH units.A buffer solution is formed by mixing together a weak acid and its conjugate base. These solutions ef­fectively slow the rate of pH change over a limited portion of the pH scale when a quantity of strong acid or base is added to the buffer.

As shown in Figure 3-6, titration of H₃PO₄ (phosphoric acid) with up to about 8 ml of NaOH causes a gradual increase in pH to about 2.5. In contrast, the next few milliliters of NaOH that, are added bring about a rapid rise in pH to about 6.0. The gradual pH change observed on addition of the first 8 ml of base is the result of the conjugate acid- base buffering capacity of the H₃P0₄ and NaH₂P0₄ (i.e., the NaOH reacted with H₃PO₄, forming the NaH₂PO₄ and H₂O), that is,

A second buffering “plateau” is produced by the con­jugate acid-base buffer system of NaH₂PO₄ and Na₂HPO₄. The third plateau is achieved through the actions of Na₂HPO₄, and Na₃PO₄. Just as the hydrogen ion concentration can be ex­pressed in terms of pH (or negative logarithms), the dissociation constant for a weak acid, K_a, can be simi­larly defined:

pK_a= -log K_a (3-4)

The pK for each conjugate acid-base pair occurs at the mid-point of its buffering plateau. The most effec­tive buffering range of an acid-base pair usually ex­tends 0.5 pH units to each side of the pK value. The relationship between pH and pK_a is expressed in the Henderson-Hasselbach equation:

where the weak acid is represented by [HA^–] and its conjugate base by [A^–]. When the concentrations of the two are equal, as at the midpoint of a plateau, the last term of equation 3-5 becomes zero (i.e., log₁₀ 1 = 0), and therefore pH = pK_a. The Henderson- Hasselbach equation can be used to calculate the pH if the concentrations of the acid and base are known.

The equation is also useful for calculating the neces­sary quantities of acid and conjugate base that must be mixed together to prepare a buffer that has a particular pH. However, it should be pointed out that the equation is an approximation and is most accurate when almost equal amounts of the acid and base are mixed. The pH values of several buffers that are routinely used in cellular studies are listed in Table 3-8.