A. Aqueous Solutions
There are many interesting regularities in the dissociation constants of weak acids and bases. The following are a few examples which draw on the data of Table 12-9. Carboxylic acids tend to have ΚΆ values of around I O- 5, except that as the carbon atom adjacent to the carboxyl group is subsituted with electro
negative groups, such as halogens, the acidity increases. For CCl3COOH, K& = 0.13, for example. This appears to be an inductive effect by which the carboxyl carbon atom is made more positive and the Ο—Η bond is electrostatically weakened. A large number of acids of this type have been studied, and L. P. Hammett has used the data to characterize substituents. Thus in the case of substituted benzoic acids a substituent is assigned a parameter σ, defined as σ = pK0 — pKs, where pK0 = —log K0 , with K0 the dissociation constant of benzoic acid, and pKs = —log Ks, with K8 the dissociation constant of the sub-On the other hand, an ion such as N a+ does not have much ability to form coordi
nate bonds, and the attraction between N a+ and Cl~ is, as noted in the preceding section, mainly of Coulombic origin. We speak of ion association (or ion pairing), then, when we wish to think of the unit as consisting of the intact ions. The distinction between ion pairing and coordinative association is not always easy to make. The association which occurs with, say, Z n2+ and S 04~ may be partly Coulombic and partly coordinative—Zn2+ does, after all, form well-known complex ions. In the case of Co(NH3)e+, however, the coordination sphere is saturated, and the association constant of 1000 observed between this ion and SO2;" is therefore spoken of confidently as due to ion pairing.
To return to the matter of activity coefficients, we find that there is no question that ion pairing does occur in more concentrated solutions, and even in dilute ones if the ions are highly charged. R. M. Fuoss and C. A. Kraus have estimated ion pair dissociation constants for a number of electrolytes from conductivity mea
surements. For uni-univalent electrolytes values are of the order of unity and for di-divalent ones they are around 0.01 or less. Thus the estimated dissociation constants are about 1.4 for K N 03, 0.15 for K S 04" , and 5.3 X I O "3 for Z n S 04 (aqueous solutions at 25°C). The conclusion is that the Debye-Huckel theory must be used with great caution for other than dilute solutions of uni-univalent electro
lytes. Semiempirical equations such as Eq. (12-113) are very helpful, but it must be remembered that the constants Β and C of the equation depend on the total ionic makeup of a solution and not just on the particular electrolyte in question.
Ion pairing, important in aqueous solutions, becomes a dominant feature in nonaqueous systems. As the dielectric constant of a medium is reduced, the Coulomb forces between ions increase, and the degree of dissociation of an electro
lyte drops dramatically. As an example, the dissociation constant of K I is only about 2 χ 1 0-4 in pyridine as solvent. There are a few nonaqueous solvents, of fairly high dielectric constant, in which electrolytes having large ions may be moderately dissociated. The salt K+[ C r ( N H3)2( N C S )4] ~ is fully dissociated in nitromethane, and similar complex ions are moderately dissociated in dipolar aprotic solvents such as dimethylsulfoxide, dimethylformamide, and the like.
COMMENTARY AND NOTES, SECTION 3 479 stituted acid. The σ values are then found to correlate with the behavior of the compounds in other equilibria or in their reaction kinetics.
The electrostatic eifect appears to be very important in determining the pK values of oxyacids. The approximately 105-fold reduction in successive Κ values for H3P 04 is one example. The three protons should be essentially equivalent, except for the increased electrostatic work of dissociation in the series H3P 04, H2P 04-, H P 04~ . A useful empirical rule is that for an oxyacid of the general formula M Om( O H )n , pK± is approximately 7 — 5m, pK2 is 12 — 5m, and so on.
Thus for H3P 04, pKx should be 7 — 5 = 2, pK2 should be about 12 — 5 = 7, and so on; for H2S 04, ρΚλ is predicted to be — 3 , in agreement with the observa
tion that the first dissociation is that of a strong acid, while pK2 should be 2, again about as observed.
Another type of situation is that in which two acid functions are sufficiently separated in a molecule that they should be essentially free of the preceding electrostatic effects. An example is H O O C — ( C H2)W— C O O H , where η is two or more. It might be supposed that Kx and K2 should be the same since the two groups are independent. A statistical factor remains, however. If the acid is represented by HiHgjA, there are two ways for the first-stage dissociation to occur, namely to give Η χ Α- or H2A_. There is only one choice of hydrogen to dissociate in the second stage, but the association reaction H+ + A2- can occur on either position.
Thus Κλ is enhanced and K2 is diminished by this effect. In the case of succinic acid, H O O C — ( C H2)2— C O O H , Κλ = 6.4 χ 10~5, or somewhat more than twice K& for acetic acid, and K2 is 2.7 χ 1 0- 6, or about half Ka for acetic acid.
A related behavior is that of amino acids, typifying electrolytes having separated weakly acidic and weakly basic groups. An amino acid is sometimes shown in the form H2N — R — C O O H , but it appears certain that internal proton transfer is largely complete, so that +H3N — R — C O O ~ is the actual species in aqueous solution. This last is known as a zwitterion. The behavior of an amino acid is then represented in terms of the two stages of dissociation of a dibasic acid:
(H+)(A±)
The isoelectric point is a state of special importance for an amino acid. This is the /?H value such that (A+) = ( A-) . Acid-base equilibria are rapid, which means that an individual amino acid molecule rapidly samples all its possible states of dissociation and at the isoelectric point it therefore spends equal times as A+ and as A-. The effect is that the amino acid behaves as though it were electrically neutral, even though it is still a conducting electrolyte; it displays essentially no net motion in an electrophoresis experiment, for example. Analysis of the preceding equilibrium relationships shows that at the isoelectric point ( H+) = ( X i/ Q1/2. It can also be shown that at this pH the total degree of ionization of the amino acid is at a minimum. For this reason many of the physical properties of an amino acid solution exhibit maxima or minima at the isoelectric point.
β . Brpnsted Treatment of Acids and Bases
The phenomenology of electrolyte behavior in aqueous solutions made it natural for Arrhenius and Ostwald to define an acid as a substance furnishing H+
ions and a base as one furnishing OH~ ions. Neutralization then consisted of the reaction of these ions to give water. This formalism is an adequate and functioning one for the treatment of acid-base equilibria in water solution, although it is some
what misleading chemically. The H+ ion exists in water at least as H30+, if not in more complex forms, and the dissociation of a weak acid is more correctly written as
HA + H20 = A - + H30+ (12-115)
than as H A = H+ + A-. Similarly, a weak base may produce OH~ ions by the reaction
H2o + Β - OH- + HB+ (12-116)
(as, for example, with Β = N H3) .
Bronsted and Lowry illuminated the chemistry of weak acids and bases by re
cognizing (in 1923) that the degree of a reaction such as those given by Eqs. (12-115) and (12-116) must depend on the natures of both reactants and that the reactions are really symmetric. They introduced the more general definitions that an acid is a proton donor and a base is a proton acceptor. Equations (12-115) and (12-116) now fall into the common form
acid + base = conjugate base + conjugate acid
HA + H20 A" + H30 +
H20 + Β = OH" + HB
An acid, on yielding a proton, becomes its conjugate base, and a base, on accepting a proton, becomes its conjugate acid.
The Bronsted picture has been useful in two major ways. First, it emphasizes that the anion of a weak acid is a proton acceptor, or a base, as well as O H- ion and may be capable of reacting directly with a proton donor without going through the route of accepting an H+ ion released by it. There are a number of cases of acid- or base-catalyzed reactions in which direct reaction evidently occurs. The rate of reaction in such cases is found to depend on the specific acid or base present and not just on the pH of the solution.
The second important feature of the Bronsted picture is that it relates aqueous to nonaqueous systems. Other solvents can now be seen in striking analogy to water. Liquid ammonia, for example, autoionizes to give N H4+ and N H2" ions, in analogy to the H30+ and O H- ions of water. Acetic acid in liquid ammonia solution then dissociates according to the reaction
HAc + N H3 = Ac- + NH4+. (12-117)
This dissociation is virtually complete. That is, acetic acid is a strong acid in liquid ammonia solvent, and the reason is clearly that N H3 is a much better