C. R. Allen and P. 0. Wright1
Queen's College Dundee, Scotland
I
Entropy and Equilibrium
1
Interpretations of ionization d a t a for organic acids
1
Attempts are sometimes made to interpret chemical equilibria in terms of effects on the energy of a molecular system, without reference to entropy. Consider, however, the relation of an equilibrium constant K a t temperature T to standard changes in relevant thermodynamic functions (energy U; enthalpy H = U pV, where p is pressure and V is volume; and entropy S)
+
In general terms an adequate account of chemical equilibria must refer to the second law of thermodynamics, and for quantitative success must consider explicitly the final factor e4se/Z. Wheland ( I ) , writing in 1944, pointed out that some groups of reactions were known among which differences in entropy were more important than diierences in energy, but argued that in many cases the AUe must be treated as the dominating factor if an interpretation were to be made a t all. Hammett (2) had given a very clear forewarning of the dangers of such an approach, but a t that time there were relatively few experimental results complete enough to allow a full analysis of equilibria in terms of the various thermodynamic functions separately. Wheland stressed that interpretations ignoring entropy might be expected to be most successful for large differences in equilibrium constants. (He further argued that, if a primarily electrostatic interpretation were put forward, the entropy would be allowed for implicitly, electrical potentials corresponding directly to a free energy G = H - TS.) It is clearly useful to scrutinize the relative importance of enthalpies and entropies in analogous reactions for which reliable data are available. Such an analysis shows that there are many reactions for which differences of entropy are decisive, and emphasizes the longestablished and important point that any suggested explanation of chemical observations is inadequate if it conforms to the data a t one temperature hut not at other temperatures. Ionization of Organic Acids
There have been several valuable discussions of the strengths of organic acids: Waters (5) stressed the close resemblance of all the simple fatty acids, and Hammett ( 9 analysed the data in thermodynamic terms. Since these discussions appeared, further deEdward A. Deeds Fellow of Queen's College, Dundee
tailed investigations of the ionization of organic acids have provided extensive and reliable thermodynamic data (4, 6). The newer measurements strongly reinforce the arguments and conclusions of Waters (5) and Hammett (9). Some typical results are reproduced in Table 1, which gives data for equilibria of the type HX(aq)
+ CHzCOO-(aq) * X-(ap) + CH.COOH(aq)
i.e., for competition for a proton between the anionic bases X- (up) and CH,COO-(aqj. Thus the thermodynamic functions refer to the strength of various acids HX relative to acetic acid (pK. 4.756 a t 25'C): the notation AH..?, etc. (as distinct from AH,: etc., for the ionization of an acid) has been adopted accordingly. In this form, the data are particularly suitable for the discussion of differences in the strengths of acids and are, moreover, in many cases the results of accurate direct determinations (4). Compilations of data in the more conventional form referring explicitly to ionization HX(aq)
+ HBOW= X-(ad + HsO+(aq)
(AH:, etc.) are given by, for example, Harned and Owen (6). Toble 1. Thermodynamic Functions for the Process (25'C) HX(ag)
-
) + CH,COO-(aq)14, 5X-(aq) + CHGOOH(aq)
One strikmg point arising from the data (Table 1) is that in a large proportion of cases the term (- TAS,,?) is greater than the term AHJ, so that strengths of these organic acids differ, more often than not, mainly because of differencesin the entropies of ionization. In particular, formic acid, benzoic acid, and p-nitrobenzoic acid are stronger than acetic acid solely because ionization is favored by the changes of entropy involved. (The heats of ionization, if different from Volume 41, Number 5, Moy 1964 / 251
zero by more than the experimental error, would actually tend to make these acids weaker than acetic acid.) Thus, any interpretation of the relative strengths of these acids must deal explicitly with entropies of ionization. In particular, it is impossible to consider adequate the nai've view that acetic acid is weaker than formic acid because an inductive effect of the methyl group CHa-CO-0--H
results in an enhanced probability of finding electrons between the final 0 and H, and so makes it harder to remove a proton. An extension of the more naive electronic theories has been proposed for treating entropies of ionization explicitly (7), but before considering this further, some other relevant experimental evidence will be examined. From the data (4, 5) for 25'C cited in Table 1, it is seen that in the straight-chain acids up to hexanoic the strengths of all the higher members lie within the small gap between those of acetic and propanoic acids, and that there is an irregular variation in the strengths of the three methyl-substituted acetic acids. This lack of close correlation with details of molecular structure is not to be expected on the basis of "inductive effects" of various alkyl groups. I t is interesting t o note that, for all these acids, differences from acetic acid are the result of terms AH..? and (-TAS.,?) which are of opposite signs and nearly cancel each other out: the term (-TAS,,?) is in each case the larger of the taro. A more serious difficulty for electronic views, but an effect not surprising if examined in thermodynamical terms, lies in the fact that there are pairs of acids (of roughly comparable strength ) whose order of strength can be reversed by change of temperature or by change of solvent. The latter point is exemplified (8) by the observation that in aqueous solution o-nitrohenzoic acid (pK. 2.21) is stronger than 3,5-dinitrobenzoic acid (pK. 2.80), whereas in ethanolic solution the opposite is the case (respective vK.'s 8.62 and 8.09). The former point (4, 5) is illustrated by the following data: Temperatures a t which the Order of Acid Strength is Inverted (The first member of each pair is the stronger at temperatures below t,hat stated.)
We note, for example, that 2-ethyl butanoic acid is stronger than acetic acid below 2Q°Cand weaker above that temperature. It would thus appear that, if the differences of strength were really a consequence of inductive effects, the inductive effect of two ethyl groups substituted in the methyl group of acetic acid acts in one sense below 2Q°C and in the opposite sense above 29% KO inversion of relative strength, by rl~nngvoi trrnprruture or oi sol\wit, KIII he r~rcountrd fw hy an interprrration busrd sole-ly on consi(1t~rntiol1 of a molecular formula. Consider in quantitative terms the relation between ionization constants K A , Ke for acids A and B. Let AHA8, AHBa, etc., be the relevant thermodynamic 252
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lournol o f Chemical Education
functions for the ionization of these acids. Then
If K Aand Ka are approximately equal, Usaand AHA8 may still differ significantly if there is a compensating difference between ASB8 and AS*'. In such a case the equilibrium constant associated with the (numerically) larger AH8 varies more rapidly with temperature. Consequently, a t a certain temperature2 the two equilibrium constants are exactly equal, with one of them the greater at higher temperatures and the smaller at lower temperatures. The inversion takes place where Inversions by change of solvent may be analyzed thermodynamically in an analogous way: the condition for such an inversion is AHB! - AHA,@>T(ASB,~ - ASA,~) AH& - AHA+< T(ASBZB- Ash%@) where the subscripts 1,2 refer to the two solvents. On the basis of this thermodynamical formulation, the extended electronic account (7) of the ionization of acids may now he examined. Let acids A,B be substituted formic acids, A with a substituent of the kind regarded as "electron-attracting," and B with a snbstituent of the kind regarded as "electron-repelling." 0
Y-C
/
0
z-C
//
Any process of ionization, if expressible as a binary fission MX-M++X-
would be expected, on statistical grounds, to have a positive ASa. There will, however, be a negative contribution due to solvation of the charged products. For the ionization of acids, the cation produced is always the solvated proton: consequently the difference (ASea - A&') could be attributed to differences in the solvation of the two anions. Acid A with an "electronattracting" substituent would be regarded as forming an anion (YCOO-) with the negative charge more distributed than that on the anion (ZCOO-) of acid B. The (negative) contribution of solvation to ASa would then be of lesser absolute magnitude for A than for B. Thus AS: would be smaller (7) than ASna,or AS^' ASAa)
