Textbook Errors, 702 G. V. Calder and T. J. Barton Iowa State University Ames, SO10
Actual Effects Controlling the Acidity of Carboxylic Acids
A
discussion of the relationship between the strengths of carboxylic acids and their structure is an integral part of every elementary course in organic chemistry. Virtually every current organic chemistry text1 describes in detail the correlation of acidity and structure by examination of the inductive, resonance, and stereochemical effects of various substituents. The explanation proceeds, more or less, along these lines. The strength of an acid, ionizing according to the reaction HA(aq) = H + ( 4
+ A-(aq)
(1)
is characterized by the equilibrium constant, K.,, which is defined in terms of the standard free energy The standard free energy, in turn, is related to the standard enthalpy change, A H o , and the standard entropy change, AS0, for the reaction a t some constant temperature, T AG"
=
AH' - TAS"
(3)
Up to this point the explanation is correct. Most current texts then suggest that so long as related reactions, such as the ionization of a series of carboxylic acids, are compared, the entropy term remains approximately constant; and for such cases, the acidity correlates with the relative energetic st* bility of the reactants and products in the ionization reaction. In quantitative terms, this means that the acidity correlates with the standard enthalpy change for the ionization reaction. It is further stated that trends in the relative energies of the reactants and products, quantitatively expressed by AHo, can be predicted by examining the inductive, resonance, and Work performed by both authors in the Ames Laboratory of the U S . Atomic Enerev Commission. Contribution No. 2851. Editors Note: ~ n ~ g e s ~ of o nmaterial s suitable for this column and guest wlumns suitable far publication directly should be sent with as mmy details ss possible, and particularly with references to modern textbooks, to W. H. Eberhardt, School of Chemistry, Georgia Institute of Technology, Atlanta, Ga. 30332.
' Since the purpose of this wlumn is to prevent the spread and the wntinustion of errors and not the evaluation of individual texts, the sources of errors discussed will not be cited. In order to be presented an error must occur in a t least two independent recent standard texts. E. "Rate8 See for example: LEFFLER,J. E., AND GRUNWALD, and Equilibria of Organic Reactions," John Wiley & Sons, Inc., New York 1963, pp. 372-3; and CHRISTENSEN, J . J., SLADE, M. D., SMITH,D. E. IZATT, R. M., AND TSANG,J., J. Amer. Chm. Soc. 92,4164 (1970). 338
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Table 1. Thermodynamic Functions for the Ionization of Some W e a k Acids a t Infinite Dilution in W a t e r in 29S°K
Acid Formic Acetic Trimethylacetic Succinic acid K, Suceinic acid KS Iodoacetic Bromoacetio Chloroacetic Fluoroacetic Dibromoacetic Dichloroacetic Difluoroacetic Tribromoscetic Trichloroscetic Trifluoroacetic m-nltrophenol o-nitrophenol n-nit,mnhenol ~ ~~ ~~
TAS" (call/ mole)
AH" (call/ mole)
0 f4710 +4660 C4710 ~ ~
~
-298 -6700 -5190 -5040 r
KeQX
lo6
59000. 0.000445 0.00602 0.00707
Reference
* * "
E V E R E T TD. , H., LANDSMAN. D. A,, AND PINSENT,B. R. W. Proc. Rou. Soc. (London), 215A, 1952, p. 403 and references therein. E., J . Enthalpy from: LEUNG,C. S., AND GRUNWALD, Phys. Chem., 74 687 (1970). M., BATES,R. G., AND ROBINSON, Other data from: PAABO, R. A,, J . Phys. Chem., 70, (1966). CHRISTENS SEN, J. J. SLADE,M. D., SMITH,D. E., IZATT, R. M., AND TSANG,J., $. Aner. Chm. Soc. 92, 4164 (1970) and citations therein. a See LEFFLERJ E., A N D GRUNWALD E., "RatesandEquilibria. of Organic ~eabtions," John Wi1ey.k Sons, Inc., New York, 1963, pp. 372-3, and references therem.
structural effects of substituents on the acid. Unfortunately, this latter apologia simply is not in accord with experimental data. The dataZshow that the enthalpy of ionization of all carboxylic acids in water is very small compared to the magnitude of the TAS" term. In fact, a good rule of thumb is that AHo g 0 + 2 kcal for the ionization reactions of most weak acids in water. Moreover, the small trends that do occur in the AH" of these reactions are, often as not, in a direction opposite that predicted by the structural arguments. The data show that it is the large, negative entropy contribution to K., that is dominant; and although the entropy term is sometimes fairly constant for a series of acids a t a given temperature, its magnitude is such that even relatively small changes in ASo produce substantial changes in the ionization constant. Consider the data in Table 1 as an illustration First, note that in every case the enthalpy terms make the smaller contribution to the free energy and hence the equilibrium constant. Secondly, observe that the electron donating character of the substituents in the series formic, acetic, and trimethylacetic
acid should produce a "strengthening" of the 0-H bond in the acid with a concomitant positive trend in the enthdpy of ionize tion. ExsctJy the reverse trend ia observed.
The two ionizations of succinic acid offer a more dramatic illustration. The standard explanation for the large diierence between the first and second ionization constants is the instability of the doubly charged anion produced in the second step. The data show, however, that the first ionization is endothermic while the second ionization is exothermic. The haloacetic acids are the most commonly used examples of the operation of the inductive effect. It is postulated that the eleetronegative halogen induces a positive charge in the carbon atom to which it is attached. The charge is transferred to the carboxyl group, and this action results in a stabilization of the anion. The data show that irrespective of whether or not the postulate is true, the effect is not reflected in the relative energetic stabilities of the haloacetie acids and their conjugate anions. As a final example, the generally accepted rational for the lower acidity of m-nitrophenol compared to the oand p-nitrophenols is the resonance stabilization of the o- and p-nitrophenolate anions. The enthalpies of ionization cannot be used to substantiate this rational. Another misconception perpetuated in many elementary discussions of acid strengths is the notion that "acidity" is an inherent, immutable property of an acid irrespective of its environment. For example, the usual manner of expressing the relative strengths of weak acids is by comparison of the ionization constants a t some temperature. The choice of 25°C is usually made because most ionization constants have been determined near room temperature. Unfortunately, virtually every textbook ignores the fact that the ionization constants as well as the relative acidity of carboxylie acids are extremely temperature sensitive. The order of strengths of a series of acids at one temperature may be completely scrambled a t another temperature only 20 or 30 'C different. Figure 1 illustrates the point dramatically. Acetic acid is stronger than diethylacetic acid above 30°C but is weaker below 30°C, and isopropylacetie acid is
0.50
-
o
10
20
M
40
so
60
m
1.w
Figure 1. The ionization constant of some alkyl acetic acids as a function of temperoture. Note the changer in he relative acidity a t various temperatures. 0, acetic acid; A, (3-methylbutyrir acid; and @, aethylbutyric acid.
Figure 2. The ionization mnrtanh of sono substituted acetic odds or o function of temperature.
Table 2. Thermodvnamic Functions for the Ionization of Acetic and ~ e n z o i c ~ c i das s a Function of Temperature tfDCI
Aeet~e
( ~ a l / r n o l e ) ~ -AC9,! (caI/'K mole)Benaom Acet~c Beneoic
weaker than acetic acid above 16°C but is stronger below that temperature. Such reversals of relative acidity with changing temperature are a rather general phenomenon (Fig. 2). The temperature sensitivity of the thermodynamic variables related to the ionization of weak acids is dramatically shown (Table 2) by recent measurements of Leung and G r u n ~ a l d . ~Note that for both acetic acid and benzoic acid, even the sign of the enthalpy of ionization changes in the vicinity of room temperature. This means acidity increases, then decreases as the temperature rises, because
Furthermore, if one examines the approximate equation AHo== AH>, AC",(T - 298) (5)
+
it is evident from Table 2 that the heat capacity term is of the same order of magnitude or larger than AH0zw. The large negative ACO, of ionization is a general property2 of weak acids. In addition, the relative sizes of AHoZosand AC", are such that an extremum in the ionization constant of weak acids often occum near 8 L (1970).
~C. ~ S., AND ~ ~GRUNWALD, , E., J. Phya Chem. 74, 687 Volume 48, Number 5, M a y 1971
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339
room temperature. Specifically, if ACo, is assumed to be constant over the temperature range T,t
=
298
- AH"m/ACo,
(6)
Thus, if the temperature for a comparison of relative acidity is changed, the strength of a given acid may rapidly increase or decrease or remain nearly constant depending on the sign and size of AHolssfor the ionization. The essential fallacy of the standard explanation of acid strengths is the neglect of solvent interactions, i.e., presuming water to be a noninteracting medium. The energy cost of removing the proton from the acid is compensated by a gain in energy caused by the increased solvation of the ionic products, with the net result that enthalpies of ionization are very small, and not easily identifiable with simple structural arguments. On the other hand, the extensive ordering of the solvent that occurs about the charged ionization products produces a substantial decrease in the entropy of the
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whole system-HA, A-, HC, and solvent-which retards the ionization process. Any truly meaningful comparison of acid strengths requires that all the relevant variables affecting ionization be taken into account-solvent, temperature, ionic strength, as well as molecular structure. Nevertheless, the various structure-acidity correlations criticized here have withstood the test of time and are not to be frivolously discarded. They have the tremendous advantage of simplicity, intuitive appeal, and more importantly, by and large, they work. They provide chemists with a powerful mnemonic device for recalling an enormous amount of information and making reasonable chemical predictions. But, in our opinion, texts should clearly point out that the structure-acidity correlations, while attractively simple and useful, do not necessarily correspond to the actual processes and mechanisms controlling the ionization reaction.
