Chapter 2

Water, pH, and Ionic Equilibria

Some of the magic: Students and teacher view a coral crab in Graham's Harbour, San Salvador Island, the Bahamas. (Lara Call)

"If ther is magic on this planet, it is contained in water." LOREN EISLEY Inscribed on the wall of the National Aquarium in Baltimore,MD

Water is a major chemical component of the earth’s surface. It is indispensable to life. Indeed, it is the only liquid that most organisms ever encounter. We alternately take it for granted because of its ubiquity and bland nature or marvel at its many unusual and fascinating properties. At the center of this fascination is the role of water as the medium of life. Life originated, evolved, and thrives in the seas. Organisms invaded and occupied terrestrial and aerial niches, but none gained true independence from water. Typically, organisms are constituted of 70 to 90% water. Indeed, normal metabolic activity can occur only when cells are at least 65% H₂O. This dependency of life on water is not a simple matter, but it can be grasped through a consideration of the unusual chemical and physical properties of H₂O. Subsequent chapters establish that water and its ionization products, hydrogen ions and hydroxide ions, are critical determinants of the structure and function of proteins, nucleic acids, and membranes. In yet another essential role, water is an indirect participant—a difference in the concentration of hydrogen ions on opposite sides of a membrane represents an energized condition essential to biological mechanisms of energy transformation. First, let’s review the remarkable properties of water.

2.1 · Properties of Water

Unusual Properties
In comparison with chemical compounds of similar atomic organization and molecular size, water displays unexpected properties. For example, compare water, the hydride of oxygen, with hydrides of oxygen’s nearest neighbors in the periodic table, namely, ammonia (NH₃) and hydrogen fluoride (HF), or with the hydride of its nearest congener, sulfur (H₂S). Water has a substantially higher boiling point, melting point, heat of vaporization, and surface tension. Indeed, all of these physical properties are anomalously high for a substance of this molecular weight that is neither metallic nor ionic. These properties suggest that intermolecular forces of attraction between H₂O molecules are high. Thus, the internal cohesion of this substance is high. Furthermore, water has an unusually high dielectric constant, its maximum density is found in the liquid (not the solid) state, and it has a negative volume of melting (that is, the solid form, ice, occupies more space than does the liquid form, water). It is truly remarkable that so many eccentric properties should occur together in a single substance. As chemists, we expect to find an explanation for these apparent anomalies in the structure of water. The key to its intermolecular attractions must lie in its atomic constitution. Indeed, the unrivaled ability to form hydrogen bonds is the crucial fact to understanding its properties.

Figure 2.1 • The structure of water. Two lobes of negative charge formed by the lone-pair electrons of the oxygen atom lie above and below the plane of the diagram. This electron density contributes substantially to the large dipole moment and polarizability of the water molecule. The dipole moment of water corresponds to the O—H bonds having 33% ionic character. Note that the H—O—H angle is 104.3^o, not 109^o, the angular value found in molecules with tetrahedral symmetry, such as CH₄. Many of the important properties of water derive from this angular value, such as the decreased density of its crystalline state, ice. (The dipole moment in this figure points in the direction from negative to positive, the convention used by physicists and physical chemists; organic chemists draw it pointing in the opposite direction.)

Structure of Water
The two hydrogen atoms of water are linked covalently to oxygen, each sharing an electron pair, to give a nonlinear arrangement (Figure 2.1). This “bent” structure of the H₂O molecule is of enormous significance to its properties. If H₂O were linear, it would be a nonpolar substance. In the bent configuration, however, the electronegative O atom and the two H atoms form a dipole that rendersthemolecule distinctly polar. Furthermore, this structure is ideally suited to H-bond formation. Water can serve asboth an H donor and an H acceptor in H-bond formation. The potential to form four H bonds per water molecule is the source of the strong intermolecular attractions that endow this substance with its anomalously high boiling point, melting point, heat of vaporization, and surface tension. In ordinary ice, the common crystalline form of water, each H₂O molecule has four nearest neighbors to which it is hydrogen bonded: each H atom donates an H bond to the O of a neighbor, while the O atom serves as an H-bond acceptor from H atoms bound to two different water molecules (Figure 2.2). A local tetrahedral symmetry results.

Figure 2.2 • The structure of normal ice. The hydrogen bonds in ice form a three-dimensional network. The smallest number of H₂O molecules in any closed circuit of H-bonded molecules is six, so that this structure bears the name hexagonal ice. Covalent bonds are represented as solid lines, whereas hydrogen bonds are shown as dashed lines. The directional preference of H bonds leads to a rather open lattice structure for crystalline water and, consequently, a low density for the solid state. The distance between neighboring oxygen atoms linked by a hydrogen bond is 0.274 nm. Because the covalent H-O bond is 0.995 nm, the H-O hydrogen bond length in ice is 0.18 nm.

     Hydrogen bonding in water is cooperative. That is, an H-bonded water molecule serving as an acceptor is a better H-bond donor than an unbonded molecule (and an H₂O molecule serving as an H-bond donor becomes a better H-bond acceptor). Thus, participation in H bonding by H₂O molecules is a phenomenon of mutual reinforcement. The H bonds between neighboring molecules are weak (23 kJ/mol each) relative to the H-O covalent bonds (420 kJ/mol). As a consequence, the hydrogen atoms are situated asymmetrically between the two oxygen atoms along the O-O axis. There is never any ambiguity about which O atom the H atom is chemically bound to, nor to which O it is H-bonded.

Structure of Ice
In ice, the hydrogen bonds form a space-filling, three-dimensional network. These bonds are directional and straight; that is, the H atom lies on a direct line between the two O atoms. This linearity and directionality mean that the resultant H bonds are strong. In addition, the directional preference of the H bonds leads to an open lattice structure. For example, if the water molecules are approximated as rigid spheres centered at the positions of the O atoms in the lattice, then the observed density of ice is actually only 57% of that expected for a tightly packed arrangement of such spheres. The H bonds in ice hold the water molecules apart. Melting involves breaking some of the H bonds that maintain the crystal structure of ice so that the molecules of water (now liquid) can actually pack closer together. Thus, the density of ice is slightly less than the density of water. Ice floats, a property of great importance to aquatic organisms in cold climates.
     In liquid water, the rigidity of ice is replaced by fluidity, and the crystalline periodicity of ice gives way to spatial homogeneity. The H₂O molecules in liquid water form a random, H-bonded network with each molecule having an average of 4.4 close neighbors situated within a center-to-center distance of 0.284 nm (). At least half of the hydrogen bonds have nonideal orientations (that is, they are not perfectly straight); consequently, liquid H₂O lacks the regular latticelike structure of ice. The space about an O atom is not defined by the presence of four hydrogens, but can be occupied by other water molecules randomly oriented so that the local environment, over time, is essentially uniform. Nevertheless, the heat of melting for ice is but a small fraction (13%) of the heat of sublimation for ice (the energy needed to go from the solid to the vapor state). This fact indicates that the majority of H bonds between H₂O molecules survive the transition from solid to liquid. At 10°C, 2.3 H bonds per H₂O molecule remain, and the tetrahedral bond order persists even though substantial disorder is now present.

Molecular Interactions in Liquid Water
The present interpretation of water structure is that water molecules are connected by uninterrupted H bond paths running in every direction, spanning the whole sample. The participation of each water molecule in an average state of H bonding to its neighbors means that each molecule is connected to every other in a fluid network of H bonds. The average lifetime of an H-bonded connection between two H₂O molecules in water is 9.5 psec (picoseconds, where 1 psec = 10^-12sec). Thus, about every 10 psec, the average H₂O molecule moves, reorients, and interacts with new neighbors, as illustrated in Figure 2.3.

Figure 2.3 • The fluid network of H bonds linking
water molecules in the liquid state. It is
revealing to note that, in 10 psec, a photon of
light (which travels at 3 x 10⁸ m/sec) would
move a distance of only 0.003 m.

In summary, pure liquid water consists of H₂O molecules held in a random, three-dimensional network that has a local preference for tetrahedral geometry but contains a large number of strained or broken hydrogen bonds. The presence of strain creates a kinetic situation in which H₂O molecules can switch H-bond allegiances; fluidity ensues.

Solvent Properties
Because of its highly polar nature, water is an excellent solvent for ionic substances such as salts; nonionic but polar substances such as sugars, simple alcohols, and amines; and carbonyl-containing molecules such as aldehydes and ketones. Although the electrostatic attractions between the positive and negative ions in the crystal lattice of a salt are very strong, water readily dissolves salts. For example, sodium chloride is dissolved because dipolar water molecules participate in strong electrostatic interactions with the Na⁺ and Cl^- ions, leading to the formation of hydration shells surrounding these ions (Figure 2.4).

Figure 2.4 • Hydration shells surrounding ions in solution. Water molecules orient so that the electrical charge on the ion is sequestered by the water dipole. For positive ions (cations), the partially negative oxygen atom of H₂O is toward the ion in solution. Negatively charged ions (anions) attract the partially positive hydrogen atoms of water in creating their hydration shells.

Although hydration shells are stable structures, they are also dynamic. Each water molecule in the inner hydration shell around a Na⁺ ion is replaced on average every 2 to 4 nsec (nanoseconds, where 1 nsec = 10^-9sec) by another H₂O. Consequently, a water molecule is trapped only several hundred times longer by the electrostatic force field of an ion than it is by the H-bonded network of water. (Recall that the average lifetime of H bonds between water molecules is about 10 psec.)

Water Has a High Dielectric Constant
The attractions between the water molecules interacting with, or hydrating, ions are much greater than the tendency of oppositely charged ions to attract one another. The ability of water to surround ions in dipole interactions and diminish their attraction for one another is a measure of its dielectric constant,D. Indeed, ionization in solution depends on the dielectric constant of the solvent; otherwise the strongly attracted positive and negative ions would unite to form neutral molecules. The strength of the dielectric constant is related to the force, F, experienced between two ions of opposite charge separated by a distance, r, as given in the relationship

F = e₁e₂ / Dr²

where e₁ and e₂ are the charges on the two ions. Table 2.1 lists the dielectric constants of some common liquids. Note that the dielectric constant for water is more than twice that of methanol and more than 40 times that of hexane.

*The dielectric constant is also referred to as relative permittivity by physical chemists.

Water Forms H Bonds with Polar Solutes
In the case of nonionic but polar compounds such as sugars, the excellent solvent properties of water stem from its ability to readily form hydrogen bonds with the polar functional groups on these compounds, such as hydroxyls, amines, and carbonyls. These polar interactions between solvent and solute are stronger than the intermolecular attractions between solute molecules caused by van der Waals forces and weaker hydrogen bonding. Thus, the solute molecules readily dissolve in water.

Hydrophobic Interactions
The behavior of water toward nonpolar solutes is different from the interactions just discussed. Nonpolar solutes (or nonpolar functional groups on biological macromolecules) do not readily H bond to H₂O, and, as a result, such compounds tend to be only sparingly soluble in water. The process of dissolving such substances is accompanied by significant reorganization of the water surrounding the solute so that the response of the solvent water to such solutes can be equated to “structure making.” Because nonpolar solutes must occupy space, the random H-bond network of water must reorganize to accommodate them. At the same time, the water molecules participate in as many H-bonded interactions with one another as the temperature permits. Consequently, the H-bonded water network rearranges toward formation of a local cagelike (clathrate) structure surrounding each solute molecule (Figure 2.5).

Figure 2.5 • Formation of a clathrate structure by water molecules surrounding a hydrophobic solute.

This fixed orientation of water molecules around a hydrophobic “solute” molecule results in a hydration shell. A major consequence of this rearrangement is that the molecules of H₂O participating in the cage layer have markedly reduced orientational options. Water molecules tend to straddle the nonpolar solute such that two or three tetrahedral directions (H-bonding vectors) are tangential to the space occupied by the inert solute. This “straddling” means that no water H-bonding capacity is lost because no H-bond donor or acceptor of the H₂O is directed toward the caged solute. The water molecules forming these clathrates are involved in highly ordered structures. That is, clathrate formation is accompanied by significant ordering of structure or negative entropy.
     Under these conditions, nonpolar solute molecules experience a net attraction for one another that is called hydrophobic interaction. The basis of this interaction is that when two nonpolar molecules meet, their joint solvation cage involves less surface area and less overall ordering of the water molecules than in their separate cages. The “attraction” between nonpolar solutes is an entropy-driven process due to a net decrease in order among the H₂O molecules. To be specific, hydrophobic interactions between nonpolar molecules are maintained not so much by direct interactions between the inert solutes themselves as by the increase in entropy when the water cages coalesce and reorganize. Because interactions between nonpolar solute molecules and the water surrounding them are of uncertain stoichiometry and do not share the equality of atom-to-atom participation implicit in chemical bonding, the term hydrophobic interaction is more correct than the misleading expression hydrophobic bond.

Amphiphilic Molecules
Compounds containing both strongly polar and strongly nonpolar groups are called amphiphilic molecules (from the Greek amphi meaning “both,” and philos meaning “loving”), also referred to as amphipathic molecules (from the Greek pathos meaning “passion”). Salts of fatty acids are a typical example that has biological relevance. They have a long nonpolar hydrocarbon tail and a strongly polar carboxyl head group, as in the sodium salt of palmitic acid (Figure 2.6).

Figure 2.6 • An amphiphilic molecule: sodium palmitate. Amphiphilic molecules are frequently symbolized by a ball and zig-zag line structure,, where the ball represents the hydrophilic polar head and the zig-zag represents the nonpolar hydrophobic hydrocarbon tail.

Their behavior in aqueous solution reflects the combination of the contrasting polar and nonpolar nature of these substances. The ionic carboxylate function hydrates readily, whereas the long hydrophobic tail is intrinsically insoluble. Nevertheless, sodium palmitate and other amphiphilic molecules readily disperse in water because the hydrocarbon tails of these substances are joined together in hydrophobic interactions as their polar carboxylate functions are hydrated in typical hydrophilic fashion. Such clusters of amphipathic molecules are termed micelles; Figure 2.7 depicts their structure.

Figure 2.7· Micelle formation by amphiphilic molecules in aqueous solution. Negatively charged carboxylate head groups orient to the micelle surface and interact with the polar H₂O molecules via H bonding. The nonpolar hydrocarbon tails cluster in the interior of the spherical micelle, driven by hydrophobic exclusion from the solvent and the formation of favorable van der Waals interactions. Because of their negatively charged surfaces, neighboring micelles repel one another and thereby maintain a relative stability in solution.

Of enormous biological significance is the contrasting solute behavior of the two ends of amphipathic molecules upon introduction into aqueous solutions. The polar ends express their hydrophilicity in ionic interactions with the solvent, whereas their nonpolar counterparts are excluded from the water into a hydrophobic domain constituted from the hydrocarbon tails of many like molecules. It is this behavior that accounts for the formation of membranes, the structures that define the limits and compartments of cells (see Chapter 9).

Influence of Solutes on Water Properties
The presence of dissolved substances disturbs the structure of liquid water so that its properties change. The dynamic hydrogen-bonding pattern of water must now accommodate the intruding substance. The net effect is that solutes, regardless of whether they are polar or nonpolar, fix nearby water molecules in a more ordered array. Ions, by the establishment of hydration shells through interactions with the water dipoles, create local order. Hydrophobic effects, for different reasons, make structures within water. To put it another way, by limiting the orientations that neighboring water molecules can assume, solutes give order to the solvent and diminish the dynamic interplay among H₂O molecules that occurs in pure water.

Colligative Properties
This influence of the solute on water is reflected in a set of characteristic changes in behavior that are termed colligative properties, or properties related by a common principle. These alterations in solvent properties are related in that they all depend only on the number of solute particles per unit volume of solvent and not on the chemical nature of the solute. These effects include freezing point depression, boiling point elevation, vapor pressure lowering, and osmotic pressure effects. For example, 1 mol of an ideal solute dissolved in 1000 g of water (a 1 m, or molal, solution) at 1 atm pressure depresses the freezing point by 1.86°C, raises the boiling point by 0.543°C, lowers the vapor pressure in a temperature-dependent manner, and yields a solution whose osmotic pressure relative to pure water is 22.4 atm. In effect, by imposing local order on the water molecules, solutes make it more difficult for water to assume its crystalline lattice (freeze) or escape into the atmosphere (boil or vaporize). Furthermore, when a solution (such as the 1 m solution discussed here) is separated from a volume of pure water by a semipermeable membrane, the solution draws water molecules across this barrier. The water molecules are moving from a region of higher effective concentration (pure H₂O) to a region of lower effective concentration (the solution). This movement of water into the solution dilutes the effects of the solute that is present. The osmotic force exerted by each mole of solute is so strong that it requires the imposition of 22.4 atm of pressure to be negated (Figure 2.8).

Figure 2.8 • The osmotic pressure of a 1 molal (m) solution is equal to 22.4 atmospheres of pressure. (a) If a nonpermeant solute is separated from pure water by a semipermeable membrane through which H₂O passes freely, (b) water molecules enter the solution (osmosis) and the height of the solution column in the tube rises. The pressure necessary to push water back through the membrane at a rate exactly equaled by the water influx is the osmotic pressure of the solution. (c) For a 1 m solution, this force is equal to 22.4 atm of pressure. Osmotic pressure is directly proportional to the concentration of the nonpermeant solute.

     Osmotic pressure from high concentrations of dissolved solutes is a serious problem for cells. Bacterial and plant cells have strong, rigid cell walls to contain these pressures. In contrast, animal cells are bathed in extracellular fluids of comparable osmolarity, so no net osmotic gradient exists. Also, to minimize the osmotic pressure created by the contents of their cytosol, cells tend to store substances such as amino acids and sugars in polymeric form. For example, a molecule of glycogen or starch containing 1000 glucose units exerts only 1/1000 the osmotic pressure that 1000 free glucose molecules would.

Ionization of Water
Water shows a small but finite tendency to form ions. This tendency is demonstrated by the electrical conductivity of pure water, a property that clearly establishes the presence of charged species (ions). Water ionizes because the larger, strongly electronegative oxygen atom strips the electron from one of its hydrogen atoms, leaving the proton to dissociate (Figure 2.9):

Figure 2.9 • The ionization of water.

Two ions are thus formed: protons or hydrogen ions, H⁺, and hydroxyl ions, OH^-. Free protons are immediately hydrated to form hydronium ions, H₃O⁺:

Indeed, because most hydrogen atoms in liquid water are hydrogen-bonded to a neighboring water molecule, this protonic hydration is an instantaneous process and the ion products of water are H₃O⁺ and OH^-:

The amount of H₃O⁺ or OH^- in 1 L (liter) of pure water at 25°C is 1 x 10^-7mol; the concentrations are equal because the dissociation is stoichiometric.
     Although it is important to keep in mind that the hydronium ion, or hydrated hydrogen ion, represents the true state in solution, the convention is to speak of hydrogen ion concentrations in aqueous solution, even though “naked” protons are virtually nonexistent. Indeed, H₃O⁺ itself attracts a hydration shell by H bonding to adjacent water molecules to form an H₉O₄⁺ species (Figure 2.10)

Figure 2.10 • The hydration of H₃O⁺. Solid lines denote covalent bonds; dashed lines represent the H bonds formed between the hydronium ion and its waters of hydration.

and even more highly hydrated forms. Similarly, the hydroxyl ion, like all other highly charged species, is also hydrated.

Proton Jumping
Because of the high degree of hydrogen bonding in water, H⁺ ions show an apparent rate of migration in an electrical field that is vastly greater than other univalent cations in aqueous solution, such as Na⁺ and K⁺. In effect, the net transfer of a proton from molecule to molecule throughout the H-bonded network accounts for this apparent rapidity of migration (Figure 2.11).

Figure 2.11· Proton jumping via the hydrogen-bonded network of water molecules.

That is, the H-bonded network provides a natural route for rapid H⁺ transport. This phenomenon of proton jumping thus occurs with little actual movement of the water molecules themselves. Ice has an electrical conductivity close to that of water because such proton jumps also readily occur even when the water molecules are fixed in a crystal lattice. Such conduction of protons via H-bonded networks has been offered as an explanation for a number of rapid proton transfers of biological significance.

K_w, the Ion Product of Water
The dissociation of water into hydrogen ions and hydroxyl ions occurs to the extent that 10^-7mol of H⁺ and 10^-7mol of OH^- are present at equilibrium in 1 L of water at 25^oC.

H₂O ® H⁺ + OH^-

The equilibrium constant for this process is

where brackets denote concentrations in moles per liter. Because the concentration of H₂O in 1 L of pure water is equal to the number of grams in a liter divided by the gram molecular weight of H₂O, or 1000/18, the molar concentration of H₂O in pure water is 55.5 M (molar). The decrease in H₂O concentration as a result of ion formation ([H⁺], [OH^-] = 10^-7M) is negligible in comparison, and thus its influence on the overall concentration of H₂O can be ignored. Thus,

Because the concentration of H₂O in pure water is essentially constant, a new constant, K_w, the ion product of water, can be written as

K_w = 55.5 K_eq = 10^-14 = [H⁺][OH^-]

The equation has the virtue of revealing the reciprocal relationship between H⁺ and OH^- concentrations of aqueous solutions. If a solution is acidic, that is, of significant [H⁺], then the ion product of water dictates that the OH- concentration is correspondingly less. For example, if [H⁺] is 10^-2 M, [OH^-] must be 10^-12 M (K_w = 10^-14 = [10^-2][OH^-]; [OH^-] = 10^-12 M). Similarly, in an alkaline, or basic, solution in which [OH^-] is great, [H⁺] is low.

2.2 · pH
To avoid the cumbersome use of negative exponents to express concentrations that range over 14 orders of magnitude, Sørensen, a Danish biochemist, devised the pH scale by defining pH as the negative logarithm of the hydrogen ion concentration¹:

pH = -log₁₀[H⁺]

Table 2.2 gives the pH scale. Note again the reciprocal relationship between [H⁺] and [OH^-]. Also, because the pH scale is based on negative logarithms, low pH values represent the highest H⁺ concentrations (and the lowest OH^- concentrations, as K_w specifies). Note also that

pK_w = pH + pOH = 14

The pH scale is widely used in biological applications because hydrogen ion concentrations in biological fluids are very low, about 10^-M or 0.0000001 M, a value more easily represented as pH 7. The pH of blood plasma, for example, is 7.4 or 0.00000004 M H⁺. Certain disease conditions may lower the plasma pH level to 6.8 or less, a situation that may result in death. At pH 6.8, the H⁺ concentration is 0.00000016 M, four times greater than at pH 7.4.
     At pH 7, [H⁺] = [OH^-]; that is, there is no excess acidity or basicity. The point of neutrality is at pH 7, and solutions having a pH of 7 are said to be at neutral pH. The pH values of various fluids of biological origin or relevance are given in Table 2.3.

Because the pH scale is a logarithmic scale, two solutions whose pH values differ by one pH unit have a 10-fold difference in [H⁺]. For example, grapefruit juice at pH 3.2 contains more than 12 times as much H⁺ as orange juice at pH 4.3.

Dissociation of Strong Electrolytes
Substances that are almost completely dissociated to form ions in solution are called strong electrolytes. The term electrolyte describes substances capable of generating ions in solution and thereby causing an increase in the electrical conductivity of the solution. Many salts (such as NaCl and K₂SO₄) fit this category, as do strong acids (such as HCl) and strong bases (such as NaOH). Recall from general chemistry that acids are proton donors and bases are proton acceptors. In effect, the dissociation of a strong acid such as HCl in water can be treated as a proton transfer reaction between the acid HCl and the base H₂O to give the conjugate acid H₃O⁺ and the conjugate base Cl^-:

HCl + H₂O ® H₃O⁺ + Cl^-

The equilibrium constant for this reaction is

Customarily, because the term [H₂O] is essentially constant in dilute aqueous solutions, it is incorporated into the equilibrium constant K to give a new term, K_a, the acid dissociation constant (where K_a = K [H₂O]). Also, the term [H₃O⁺] is often replaced by H⁺, such that

For HCl, the value of K_a is exceedingly large because the concentration of HCl in aqueous solution is vanishingly small. Because this is so, the pH of HCl solutions is readily calculated from the amount of HCl used to make the solution:

[H⁺] in solution = [HCl] added to solution

Thus, a 1 M solution of HCl has a pH of 0; a 1 mM HCl solution has a pH of 3. Similarly, a 0.1 M NaOH solution has a pH of 13. (Because [OH^-] = 0.1 M, [H⁺] must be 10^-13 M.)
     Viewing the dissociation of strong electrolytes another way, we see that the ions formed show little affinity for one another. For example, in HCl in water, Cl^- has very little affinity for H⁺:

HCl $#174; H⁺ + Cl^-

and in NaOH solutions, Na⁺ has little affinity for OH^-. The dissociation of these substances in water is effectively complete.

Dissociation of Weak Electrolytes
Substances with only a slight tendency to dissociate to form ions in solution are called weak electrolytes. Acetic acid, CH₃COOH, is a good example:

The acid dissociation constant K_a for acetic acid is 1.74 x 10^-5:

The term K_ais also called an ionization constant because it states the extent to which a substance forms ions in water. The relatively low value of K_a for acetic acid reveals that the un-ionized form, CH₃COOH, predominates over H⁺ and CH₃COO^- in aqueous solutions of acetic acid. Viewed another way, CH₃COO^-, the acetate ion, has a high affinity for H⁺.

EXAMPLE

where Ac^- represents the acetate ion, CH₃COO^-. In solution, some amount x of HAc dissociates, generating x amount of Ac^- and an equal amount x of H⁺. Ionic equilibria characteristically are established very rapidly. At equilibrium, the concentration of HAc + Ac^- must equal 0.1 M. So, [HAc] can be represented as (0.1 - x) M, and [Ac^-] and [H⁺] then both equal x molar. From 1.74 x 10^-5 = ([H⁺][Ac^-])/[HAc], we get 1.74 x 10^-5 = x²/[0.1 - x]. The solution to quadratic equations of this form (ax² + bx + c = 0) is x = (<f”MathematicalPi-One”>2b <f”MathematicalPi-One”>6 However, the calculation of x can be simplified by noting that, because K_a is quite small, x ´ 0.1 M. Therefore, K_a is essentially equal to x2/0.1. This simplification yields x² = 1.74 x 10^-6, or x = 1.32 x 10^-3 M and pH = 2.88.

Henderson-Hasselbalch Equation
Consider the ionization of some weak acid, HA, occurring with an acid dissociation constant, K_a. Then,

And

Rearranging this expression in terms of the parameter of interest, [H⁺], we have

Taking the logarithm of both sides gives

If we change the signs and define pK_a = -log K_a, we have

Table 2.4
Acid Dissociation Constants and pKa Values for Some Weak Electrolytes (at 25°C)
Acid	Ka (M)	pKa
HCOOH (formic acid)	1.78 x 10-4	3.75
CH3COOH (acetic acid)	1.74 x 10-5	4.76
CH3CH2COOH (propionic acid)	1.35 x 10-5	4.87
CH3CHOHCOOH (lactic acid)	1.38 x 10-4	3.86
HOOCCH2CH2COOH (succinic acid) pK1*	6.16 x 10-5	4.21
HOOCCH2CH2COO- (succinic acid) pK2	2.34 x 10-6	5.63
H3PO4 (phosphoric acid) pK1	7.08 x 10-3	2.15
H2PO4- (phosphoric acid) pK2	6.31 x 10-8	7.20
HPO42- (phosphoric acid) pK3	3.98 x 10-13	12.40
C3N2H5+ (imidazole)	1.02 x 10-7	6.99
C6O2N3H11+ (histidine - imidazole group) pKR†	9.12 x 10-7	6.04
H2CO3 (carbonic acid) pK1	1.70 x 10-4	3.77
HCO3- (bicarbonate) pK2	5.75 x 10-11	10.24
(HOCH2)3CNH3+ (tris-hydroxymethyl aminomethane)	8.32 x 10-9	8.07
NH4+ (ammonium)	5.62 x 10-10	9.25
CH3NH3+ (methylammonium)	2.46 x 10-11	10.62

*These pK values listed as pK₁, pK₂, or pK₃ are in actuality pK_a values for the respective dissociations. This simplification in notation is used throughout this book.
†pK_R refers to the imidazole ionization of histidine.
Data from CRC Handbook of Biochemistry, The Chemical Rubber Co., 1968.

or

This relationship is known as the Henderson-Hasselbalch equation. Thus, the pH of a solution can be calculated, provided K_a and the concentrations of the weak acid HA and its conjugate base A^- are known. Note particularly that when [HA] = [A^-], pH = pK_a. For example, if equal volumes of 0.1 M HAc and 0.1 M sodium acetate are mixed, then

pH = pK_a = 4.76

pK_a = -log K_a = -log₁₀(1.74 x 10^-5) = 4.76

(Sodium acetate, the sodium salt of acetic acid, is a strong electrolyte and dissociates completely in water to yield Na⁺ and Ac^-.)
     The Henderson-Hasselbalch equation provides a general solution to the quantitative treatment of acid-base equilibria in biological systems. Table 2.4 gives the acid dissociation constants and pK_a values for some weak electrolytes of biochemical interest.

EXAMPLE

OH^- + HAc $#174; Ac^- + H₂O

0.02 mol of the original 0.03 mol of HAc remains essentially undissociated. The final volume is 250 mL.

pH = 4.76 - log₁₀ 2 = 4.46

If 150 mL of 0.2 M HAc had merely been diluted with 100 mL of water, this would leave 250 mL of a 0.12 M HAc solution. The pH would be given by:

x = 1.44 x 10^-3 = [H⁺]

pH = 2.84

Clearly, the presence of sodium hydroxide has mostly neutralized the acidity of the acetic acid through formation of acetate ion.

Titration Curves
Titration is the analytical method used to determine the amount of acid in a solution. A measured volume of the acid solution is titrated by slowly adding a solution of base, typically NaOH, of known concentration. As incremental amounts of NaOH are added, the pH of the solution is determined and a plot of the pH of the solution versus the amount of OH^- added yields a titration curve. The titration curve for acetic acid is shown in Figure 2.12.

Figure 2.12 • The titration curve for acetic acid. Note that the titration curve is relatively flat at pH values near the pK_a; in other words, the pH changes relatively little as OH^- is added in this region of the titration curve.

In considering the progress of this titration, keep in mind two important equilibria:

1.

2.

As the titration begins, mostly HAc is present, plus some H⁺ and Ac^- in amounts that can be calculated (see the Example on page 45). Addition of a solution of NaOH allows hydroxide ions to neutralize any H⁺ present. Note that reaction (2) as written is strongly favored; its apparent equilibrium constant is greater than 10¹⁵! As H⁺ is neutralized, more HAc dissociates to H⁺ and Ac^-. As further NaOH is added, the pH gradually increases as Ac^- accumulates at the expense of diminishing HAc and the neutralization of H⁺. At the point where half of the HAc has been neutralized, that is, where 0.5 equivalent of OH^- has been added, the concentrations of HAc and Ac^- are equal and pH = pK_a for HAc. Thus, we have an experimental method for determining the pK_a values of weak electrolytes. These pK_a values lie at the midpoint of their respective titration curves. After all of the acid has been neutralized (that is, when one equivalent of base has been added), the pH rises exponentially.
     The shapes of the titration curves of weak electrolytes are identical, as Figure 2.13

Figure 2.13 • The titration curves of several weak electrolytes: acetic acid, imidazole, and ammonium. Note that the shape of these different curves is identical. Only their position along the pH scale is displaced, in accordance with their respective affinities for H⁺ ions, as reflected in their differing pK_a values.

reveals. Note, however, that the midpoints of the different curves vary in a way that characterizes the particular electrolytes. The pK_a for acetic acid is 4.76, the pK_a for imidazole is 6.99, and that for ammonium is 9.25. These pK_a values are directly related to the dissociation constants of these substances, or, viewed the other way, to the relative affinities of the conjugate bases for protons. NH₃ has a high affinity for protons compared to Ac^-; NH₄⁺ is a poor acid compared to HAc.

Phosphoric Acid Has Three Dissociable H⁺
Figure 2.14 shows the titration curve for phosphoric acid, H₃PO₄.

Figure 2.14 • The titration curve for phosphoric acid. The chemical formulas show the prevailing ionic species present at various pH values. Phosphoric acid (H₃PO₄) has three titratable hydrogens and therefore three midpoints are seen: at pH 2.15 (pK₁), pH 7.20 (pK₂), and pH 12.4 (pK₃).

This substance is a polyprotic acid, meaning it has more than one dissociable proton. Indeed, it has three, and thus three equivalents of OH^- are required to neutralize it, as Figure 2.14 shows. Note that the three dissociable H⁺ are lost in discrete steps, each dissociation showing a characteristic pK_a. Note that pK₁ occurs at pH = 2.15, and the concentrations of the acid H₃PO₄ and the conjugate base H₂PO₄^- are equal. As the next dissociation is approached, H₂PO₄^- is treated as the acid and HPO₄^2- is its conjugate base. Their concentrations are equal at pH 7.20, so pK₂ = 7.20. (Note that at this point, 1.5 equivalents of OH^- have been added.) As more OH^- is added, the last dissociable hydrogen is titrated, and pK₃ occurs at pH = 12.4, where [HPO₄^2-] = [PO₄^3-].
A biologically important point is revealed by the basic shape of the titration curves of weak electrolytes: in the region of the pK_a, pH remains relatively unaffected as increments of OH^- (or H⁺) are added. The weak acid and its conjugate base are acting as a buffer.

2.3 · Buffers
Buffers are solutions that tend to resist changes in their pH as acid or base is added. Typically, a buffer system is composed of a weak acid and its conjugate base. A solution of a weak acid that has a pH nearly equal to its pK_a by definition contains an amount of the conjugate base nearly equivalent to the weak acid. Note that in this region, the titration curve is relatively flat (Figure 2.15).

Figure 2.15 • A buffer system consists of a weak acid, HA, and its conjugate base, A^-. The pH varies only slightly in the region of the titration curve where [HA] = [A^-]. The unshaded box denotes this area of greatest buffering capacity. Buffer action: when HA and A^- are both available in sufficient concentration, the solution can absorb input of either H⁺ or OH^-, and pH is maintained essentially constant.

Addition of H⁺ then has little effect because it is absorbed by the following reaction:

H⁺ + A^- ® HA

Similarly, added OH^- is consumed by the process

OH^- + HA ® A^- + H₂O

The pH then remains relatively constant. The components of a buffer system are chosen such that the pKa of the weak acid is close to the pH of interest. It is at the pK_a that the buffer system shows its greatest buffering capacity. At pH values more than one pH unit from the pK_a, buffer systems become ineffective because the concentration of one of the components is too low to absorb the influx of H⁺ or OH^-. The molarity of a buffer is defined as the sum of the concentrations of the acid and conjugate base forms.
     Maintenance of pH is vital to all cells. Cellular processes such as metabolism are dependent on the activities of enzymes, and in turn, enzyme activity is markedly influenced by pH, as the graphs in Figure 2.16 show.

Figure 2.16 • pH versus enzymatic activity. The activity of enzymes is very sensitive to pH. The pH optimum of an enzyme is one of its most important characteristics. Pepsin is a protein-digesting enzyme active in the gastric fluid. Trypsin is also a proteolytic enzyme, but it acts in the more alkaline milieu of the small intestine. Lysozyme digests the cell walls of bacteria; it is found in tears.

Consequently, changes in pH would be very disruptive to metabolism for reasons that become apparent in later chapters. Organisms have a variety of mechanisms to keep the pH of their intra- and extracellular fluids essentially constant, but the primary protection against harmful pH changes is provided by buffer systems. The buffer systems selected reflect both the need for a pK_a value near pH 7 and the compatibility of the buffer components with the metabolic machinery of cells. Two buffer systems act to maintain intracellular pH essentially constant—the phosphate (HPO₄^2-/H₂PO₄^-) system and the histidine system. The pH of the extracellular fluid that bathes the cells and tissues of animals is maintained by the bicarbonate/carbonic acid (HCO₃^-/H₂CO₃) system.

Phosphate System
The phosphate system serves to buffer the intracellular fluid of cells at physiological pH because pK₂ lies near this pH value. The intracellular pH of most cells is maintained in the range between 6.9 and 7.4. Phosphate is an abundant anion in cells, both in inorganic form and as an important functional group on organic molecules that serve as metabolites or macromolecular precursors. In both organic and inorganic forms, its characteristic pK₂ means that the ionic species present at physiological pH are sufficient to donate or accept hydrogen ions to buffer any changes in pH, as the titration curve for H₃PO₄ in Figure 2.14 reveals. For example, if the total cellular concentration of phosphate is 20 mM (millimolar) and the pH is 7.4, the distribution of the major phosphate species is given by

Thus, if [HPO₄^2-] + [H₂PO₄^-] = 20 mM, then

[HPO₄^2-] = 12.25 mMand [H₂PO₄^-] = 7.75 mM

Histidine System
Histidine is one of the 20 naturally occurring amino acids commonly found in proteins (see Chapter 4). It possesses as part of its structure an imidazole group, a five-membered heterocyclic ring possessing two nitrogen atoms. The pKa for dissociation of the imidazole hydrogen of histidine is 6.04.

In cells, histidine occurs as the free amino acid, as a constituent of proteins, and as part of dipeptides in combination with other amino acids. Because the concentration of free histidine is low and its imidazole pK_a is more than 1 pH unit removed from prevailing intracellular pH, its role in intracellular buffering is minor. However, protein-bound and dipeptide histidine may be the dominant buffering system in some cells. In combination with other amino acids, as in proteins or dipeptides, the imidazole pK_a may increase substantially. For example, the imidazole pK_a is 7.04 in anserine, a dipeptide containing b-alanine and histidine (Figure 2.17).

Figure 2.17 • Anserine (N-b-alanyl-3-methyl-L-histidine) is an important dipeptide buffer in the maintenance of intracellular pH in some tissues. The structure shown is the predominant ionic species at pH 7. pK₁ (COOH) = 2.64; pK₂ (imidazole-N⁺H) = 7.04; pK₃ (NH₃⁺) = 9.49.

Thus, this pK_a is near physiological pH, and some histidine peptides are well suited for buffering at physiological pH.

The Bicarbonate Buffer System of Blood Plasma
The important buffer system of blood plasma is the bicarbonate/carbonic acid couple:

The relevant pK_a, pK₁ for carbonic acid, has a value far removed from the normal pH of blood plasma (pH 7.4). (The pK₁ for H₂CO₃ at 25^oC is 3.77 (Table 2.4), but at 37^oC, pK₁ is 3.57.) At pH 7.4, the concentration of H₂CO₃ is a minuscule fraction of the HCO₃^- concentration, and thus the plasma appears to be poorly protected against an influx of OH^- ions.

For example, if [HCO₃^-] = 24 mM, then [H₂CO₃] is only 3.55 mM (3.55 x 10^-6M), and an equivalent amount of OH- (its usual concentration in plasma) would swamp the buffer system, causing a dangerous rise in the plasma pH. How, then, can this bicarbonate system function effectively? The bicarbonate buffer system works well because the critical concentration of H₂CO₃ is maintained relatively constant through equilibrium with dissolved CO₂ produced in the tissues and available as a gaseous CO₂ reservoir in the lungs.²

“Good” Buffers
Not many common substances have pK_a values in the range from 6 to 8. Consequently, biochemists conducting in vitro experiments were limited in their choice of buffers effective at or near physiological pH. In 1966, N.E. Good devised a set of synthetic buffers to remedy this problem, and over the years the list has expanded so that a “good” selection is available (Figure 2.18).

Figure 2.18 • The pK_a values and pH range of some “good” buffers.

2.4 · Water’s Unique Role in the Fitness of the Environment
The remarkable properties of water render it particularly suitable to its unique role in living processes and the environment, and its presence in abundance favors the existence of life. Let’s examine water’s physical and chemical properties to see the extent to which they provide conditions that are advantageous to organisms.
     As a solvent, water is powerful yet innocuous. No other chemically inert solvent compares with water for the substances it can dissolve. Also, it is very important to life that water is a “poor” solvent for nonpolar substances. Thus, through hydrophobic interactions, lipids coalesce, membranes form, boundaries are created delimiting compartments, and the cellular nature of life is established. Because of its very high dielectric constant, water is a medium for ionization. Ions enrich the living environment in that they enhance the variety of chemical species and introduce an important class of chemical reactions. They provide electrical properties to solutions and therefore to organisms. Aqueous solutions are the prime source of ions.
     The thermal properties of water are especially relevant to its environmental fitness. It has great power as a buffer resisting thermal (temperature) change. Its heat capacity, or specific heat (4.1840 J/g°C), is remarkably high; it is ten times greater than iron, five times greater than quartz or salt, and twice as great as hexane. Its heat of fusion is 335 J/g. Thus, at 0°C, it takes a loss of 335 J to change the state of 1 g of H₂O from liquid to solid. Its heat of vaporization, 2.24 kJ/g, is exceptionally high. These thermal properties mean that it takes substantial changes in heat content to alter the temperature and especially the state of water. Water’s thermal properties allow it to buffer the climate through such processes as condensation, evaporation, melting, and freezing. Furthermore, these properties allow effective temperature regulation in living organisms. For example, heat generated within an organism as a result of metabolism can be efficiently eliminated by evaporation or conduction. The thermal conductivity of water is very high in comparison with other liquids. The anomalous expansion of water as it cools to temperatures near its freezing point is a unique attribute of great significance to its natural fitness. As water cools, H bonding increases because the thermal motions of the molecules are lessened. Hydrogen bonding tends to separate the water molecules (Figure 2.2), and thus the density of water decreases. These changes in density mean that, at temperatures below 4°C, cool water rises and, most importantly, ice freezes on the surface of bodies of water, forming an insulating layer protecting the liquid water underneath.
     Water has the highest surface tension (75 dyne/cm) of all common liquids (except mercury). Together, surface tension and density determine how high a liquid rises in a capillary system. Capillary movement of water plays a prominent role in the life of plants. Lastly, consider osmosis, the bulk movement of water in the direction from a dilute aqueous solution to a more concentrated one across a semipermeable boundary. Such bulk movements determine the shape and form of living things.
     Water is truly a crucial determinant of the fitness of the environment. In a very real sense, organisms are aqueous systems in a watery world.