Entropy and Equilibria A Reassessment of Ionization Data for Substituted Acetic Acids John T. Edward McGill University. Montreal. Quebec. Canada H3A 2K6 Ostwald showed that substitution of hydrogen by chlorine in carboxylic acids enhanced their acidity ( I ). In 1916, G. N. Lewis ( 2 ) suggested that this enhancement was caused by electron-pair shifts toward chlorine: by what came later to he called the "inductive effect." This and other electron shifts formed the basis of an electronic theory of organic chemistry, elaborated by Lapworth, Robinson, Ingold and their colleagues, which proved remarkably successful, and which is still adequate, 50 years later, for most purposes of the practicing organic chemist. This success has been achieved in spite of theoretical difficulties which have long been recognized, and 18 years ago by Allen which were reviewed in THIS JOURNAL and Wright (3), under the same title as that given above. They pointed out
Thermodynamic Parameters (in kcallmol) for reactions 1 and 2 In gas phase (300PK)' X H CH3 CH3CH2 F CI Br
I
I
0 -1.2 -2.0 -10.5 -12.7 -14.1
0 -1.2 -2.0 -10.9 -13.1 -14.5
4
0 0 0 +0.4 +0.4 +0.4
I
In water (298°K)b A%I -TA~O,,I
0 +0.15 +0.07 -2.97 -2.59 -2.55
0 -0.12 -0.62 -1.37 -1.10 -1.22
0 +0.27 CO.69 -1.5 -1.5 -1.4
F r o m ref (6). dFrom ref (6).
in the gas phase. Proton-transfers of this type have been studied by Kebarle and his co-workers using a high pressure mass spectrometer. Measurement of AG$,, =, -RT In Kg,) that Eethylbutanoic acid [Et&HCOzH] is a stronger acid than acetic acid below 29T, and weaker above that temperature. It would appear for a large number of reactions has led to contmuous acidity that if differencesof strength were really a consequence of inductive ladders; from the variation of AGF,,) with temperature the effects, the inductive effect of two ethyl groups substituted in the AH:,,) and AS:,,)for a certain number of proton-transfers have methyl group of acetic acid acts in one sense below 29°C and in the been established. Thermodynamic parameters for a few of opposite sense above 29°C. these gas-phase reactions are given in the table. I t is immediatelv" aooarent that. as exuected. in the aas A second (and related) difficulty appears when we consider .. phase entropy effects arc smnll, and thnt the relatfve strennl~s the equilibrium constant Kt(,) for the proton-transfer reacof carhoxylir acids are inriefnl dctrrmined by enthalpv diition ferences, as rnluiwd hy simple theorv. However, the strt.nyths of the aliphatic acids decrease in the ordrr: butyr~c> propionic > acetic, the reverse ot'the onl(,r in nquegrus soiutim. Similar reversalsare nuticed in thearidities~,I'alcohul;i( 8 , in which acetate and substituted acetate ion compete for a 9),ammonium ions (lo), and other compounds in the gas I K aCmeasure H ~ C O ~ H ~phase, ~ ~ ~and ) indicate that in the ahsence of solvent alkyl groups proton; Kt(as) ( ~ K X C H ~ C O ~ ~ . ~ ~gives of the relative strengths of the two acids. Because eqn. (1) is stabilize all ions, positive and negative, by a polarizahility symmetrical, it has usually been assumed ( 4 ) that the entropy effect E which drops off rapidly with distance r change will he negligible, and that the effect of differing substituents X on the internal energies of the various moleE = -ae2/2Dr' (3) cules and ions will show up in the different enthalpy changes where a is the polarizahility of the group, e the electronic AH:,, for the reactions. Indeed, we can see from the data in charge, and D the effective dielectric constant (9). ConseTable 1that change in X does lead to change in AH&.,), hut quently, the addition of a methylene group to acetate ion to that these changes are often less important than the changes give propionate has a greater effect in stabilizing the ion in TAS:(.,). Furthermore, the AH:(,) value often has the (&AH$ = -1.2 Kcal.mo1-') than the addition of a second, wrong sign if we accept the simple theory of inductive effects. more distant methylene group to propiouate ion to give Thus, it is usual to explain the fact that in water propionic acid hutyrate (&AH: = -0.8 Kcalmol-I). Any classical inductive (X = CH3 in eqn. (1)) is a weaker acid than acetic (AGF,,, effect (which would stabilize positive ions hut destabilize positive) by the electron-releasing effect of the X = methyl negative ions) must hevery much weaker (9,12) and may not group. This should lead to a positive AH&ap)in eqn. (1); hut, exist (13). in fact, AH!(,) is negative, and propionic acld is a weaker acid Substitution of a hydrogen atom by fluorine, chlorine, or term overpowers the AH:,,,, than acetic because the TASFlaq) bromine has a very much bigger effect than substitution by term. alkyl in strengthening the acid in the gas phase. This is shown These theoretical difficulties arise from the fact that the by the large negative AH:(,, values in the table. The dipole original electronic theory paid little attention to the effect of moments of the three C-X groups are about the same (I ), solvent, which is mentioned on only 19 of the 828 pages of and so the stabilization E by charge-dipole interaction (9). Ingold's classic text of 1953 ( 1 ) . The importance of this effect was pointed out by Hepler (inter alia) in a long series of paE = fep cos BIDr2 (4) pers (7),' and has since been emphasized by the more recent work of Brauman (8),Taft (91,Aue (lo), Arnett (111, and (where 0 is the angle between the dipole vector and the line others on proton-transfers in the gas phase. These reveal joining the mid-point of the dipole to the charge center) should completely unexpected effects. I t is the thesis of this paper be about the same for the three acids. Consequently, the order of acid strength (hromoacetic > chloroacetic > fluoroacetic) that study of the effects of a suhstituent X should start with study of the equilibrium Mv indebtedness to the ceneral ideas of HeDler is obvious: however. XCH2C02H(g) CH3CO,(g) F. XCH2C0,(g) my apbroach in mas paper ~~"sl~ghlly d fterent horn he in tak ng, as pod of departure, recent work in the gas phase + CH3COzH(g) (2)
+
354
Journal of Chemical Education
'
A B C Figwe 1. Scale drawings (based on refs. 18and 19)of (A) Na+.HP:(6)CI-.H20: (C) CI-(H20)2.Kebarle el ai. ( 15)give reasons for believing that the first few molecules of water complexingCI- md other anions are symmehically oriented. as in Band C. but that when lamer numbers of molecules are accommodated
abo4 me an on. n oecomes energetlcal y advantageous10 wvc unsymmelrlca orlentallan soth a Colllnesr arrangement of CiH - On1
0
E
Figlre 2. Scale drawings (based on refs. (16).( 18-20))of (D)nitrite ion, hydrogen bonded to two water molecules, and (Q propionate ion. is probably due to an additional polarizahility effect (Br > CI
> F ) (14).
We now consider the effect of carrying out the proton transfers, not in the gas phase (eqn. (2)), hut in water (eqn. (1)). I t has long been known that the permanent and induced dinoles of the solvent molecules clusterine about an ion in solurion stahilile it, the rxtmt of stabilizatioti hein:: roughlv dtwcndent on the dielectric cunstant of the sol\.cnt [the h r n equation). However, a satisfactory theory of solvation must consider interactions a t the molecular level, for which a macroscopic solvent parameter such as dielectric constant is inadequate. The beginnings of such a theory have come with the studies of Keharle and his colleagues (15-17) on the stepwise complexation of cations and anions in the gas phase by water, methanol, formic acid, and other neutral molecules. The concentrations of the complexed ions as a function of the pressure of the neutral compo"nd can be determined by mass spectrometry, and thence equilibrium constants and theriodvnamic ~ a r a m e t e rfor s the comnlexation nrocess. These show that the enthalpy of hydration iepends on the size of the ion (which determines r, eqn. (4)), so that the euthalpy of hydration of Na+ to form Na+.H20 (A in Figure 1)is much greater than the enthalpy of hydration of C1- to form CI-.H*O (B in Figure 1). Secondly, the enthalpy of solvation of a given anion by a series of hydrogen-bonding molecules RH is proportional to the acidity of RH. Thirdly, in the stepwise solvation of an ion, the enthalpy change drops as each successive solvent molecule is complexed. Thus, -AH is greater for reaction ( 5 ) , forming B of Figure 1, than for reaction (61,forming
~~.~ ~
C.
The reason for this is annarent from examination of B and C: addition of the second water molecule to form C is exothermic because of charee-diuole - . interaction. but with an endothermic contribution because of dipole-dipole interaction. This effect can be expected to be very general: as the number of dipoles (from substituent and/or solvent) in the neighborhood of a charged center increases, the stabilizing effect that can he attributed to any one of them decreases (the
rule of "diminishing stabilizing effect" or DSE, which we shall invoke on several occasions later). Kebarle and his co-workers studied ion-molecule clusters containing up to six or seven molecules. These entities are probably good models for the ion and the solvent molecules immediatelv surroundine it in a solution. However, uarticularly in the Ease of water and other hydrogen honded Ho~vents (sulfuric acid, plycerol, ethylene glycol (21)) more distant interactions must he considered. water, in particular, seems to he unique among liquids in the extent to which it retains on meltine and warmine- uu. to room temnerature a threedimensional, hydrogen-bonded structure. The actual nature of the structure is still hotlv debated (22). hut consensus is perhaps shifting toward the-view that '"li&d water consists of a macrosconicallv connected, random network of hvdroaen bonds, with irequint strained and broken bonds; that is continuallv undereoing touolo~ical reformation" (23) rather . . than a fluciuating&xt&e of local "icihergs" and monomeric water molecules (24). Non-polar solute molecules such as the noble gases and hydrocarbons strengthen the hydrogen-bonded water structure about themselves with a small exothermicity but a large decrease in entropy: the so-called "hydrophobic effect" (23). Ions such as Na+ and C1- also structure the water about them. the intense electric field a t their surfaces (several million voltslcentimeter) (25a) causing the firm adhesion of one and perhaps two layers of water molecules. However, these molecules will he oriented in such a way that on one side of the ion they cannot fit into a continuous, hydrogen-bonded structure, so that in that region the hydrated ion is in contact with a zone of disorganized or superfluid water. The total effect of the ion depends on the balance between "structure-making" in the inner zone and "structure-breaking" in the outer zone. Small ions such as Li+ are heavily hydrated and are predominantly "structure-making;" largi ions of dispersed charge, such i s NO;, are lightly hydrated and are predominantly "structure-hreakine." These structural effects lead to differences in the entrod; of solvation (26) and in transport (256) and (ex.. viscositv . .( 2 5 .~ )~ronerties . . . - . the B-coefficient in the Jones-Dole equation ( 2 5 ~ ) ) . The -COT erouu. has almost the same shane. dimensions. and charge disr ributiun as t he iso(41!ctronicit111 NO, ~cotnpare IJ and 1.: in Firurc, ?I. A rood model i t x the un)uinoate ion E is NO; with an ethyl group glued on the &&en, and its properties should result from the dual effects of a charged half and an alkyl half. The charged COT group should he surrounded by an inner layer of firmly-bound water and an outer zone of disorganized and superfluid water: with the formate ion HCOT the structure-breaking effect is predominant (27); with the acetate ion the volume of the superfluid zone has been sufficiently diminished by the alkyl group so that i t is on balance structure-forming and has a positive B-coefficient ( 2 5 ~ )the ; same is true, a fortiori, with carhoxylate ions having larger alkyl groups, such as propionate. We nuw attempt 111 (.xl~lninthe (hnnyvi in A(;!. AH:, ;ind AS, 011 goilly trwn the gas phase r l r aqueous sduriun. These changrl nrr ~leprnrlrnron thrrm(rlynamic hydration parameters A;,,, w,,,and AS, for tran
