Hydrolysis of esters of oxy acids: pKa values for

Hydrolysis of esters of oxy acids: pKa values for strong acids; Brflnsted relationship for attack of water at methyl; free energies of hydrolysis of esters of oxy acids; and a linear relationship between free energy of hydrolysis and pKaholding over a range of 20 pK units J . PETERGUTHRIE'

Can. J. Chem. Downloaded from www.nrcresearchpress.com by 211.142.236.132 on 06/03/13 For personal use only.

Depnrt~nentof Chemistry, Ur~ir'ersityof Western Ontario, London, Ont., Canada N6A 5B7 Received October 26, 19772

J. PETERGUTHRIE. Can. J. Chem. 56.2342 (1978). By combining various kinds of evidence from the literature it is possible to derive a n internally consistent set of pKa values for the strong mineral acids and the arenesulfonic acids; the values are referred to dilute aqueous solution a s standard state and a r e expected to be correct within 0.5 log unit. Using these pKa values and literature data for hydrolysis of methyl esters of acids of the type Y-X03Me,,, where Y is 0 , O H , OMe, alkyl, or aryl and X is C1, S, o r P, a Brwnsted plot can be constructed with slope equal to 1.02 0.04. From the free energies of hydrolysis for dimethyl sulfate and the methyl phosphates it is possible t o calculate rate constants for the microscopic reverse reaction. These define a Brwnsted line of slope 0.27 ? 0.3, from which rate constants for the formation of the esters of perchloric and various sulfonic acids may be estimated. This permits calculation of free energies of hydrolysis for these esters. Thermochemical data in the literature permit calculation of the free energies of hydrolysis of dimethyl sulfate, trimethyl arsenite, and tetraethyl orthosilicate. In the case of dimethyl sulfate the calculation (using the previously reported eq. [I]) leads to a pK, value in close agreement with theoretical expectation, confirming that eq. [I] is valid for acids of pK, 2 -3. For tetraethyl orthosilicate the thermochemical data are less precise but are in satisfactory agreement with the predictions of eq. [I]. The free energies of hydrolysis derived f r o m the Bransted correlations are also in good agreement with expectation based on eq. [I]. For acids where resonance phenomena are important either in the acid itself (boric acid) or in the anion (nitric acid, nitrous acid, carboxylic acids) the experimental free energies of formation fall far from the line defined by eq. [I]. It is concluded that eq. [I] is limited to species where there is no n delocalization involving the reacting oxygen, but where this condition is satisfied, the equation holds over the entire accessible range of oxy acid pK, values, i.e., from -6.4 to 16.

+

J. PETERGUTHRIE. Can. J. Chem. 56,2342 (1978). En combinant divers types d e donnees provenant de la littbature, il est possible d'obtenir une sCrie autocoherente de valeurs de pK, pour les acides inorganiques forts et les acides arenesulfoniques; les valeurs se referent aux solutions aqueuses dilutes comme Ctat de reference et on les croit correctes a k0.5 unites log. Faisant appel a ces valeurs d e pK, et aux donnCes de la litttrature pour l'hydrolyse des esters methyliques des acides d u type Y-X03Me,, oh Y = 0 , O H , Me, alkyle ou aryle, et X = CI, S ou P, on peut Ctablir une droite de Bronsted avec une pente tgale a 1.02 0.04. Utilisant les energies libres d'hydrolyse du sulfate du mtthyle et des phosphates de methyle, il est possible de calculer les constantes de vitesses pour la reaction microscopique inverse. Ces valeurs definissent une droite de Bransted d e pente 0.27 k 0.3, a partir de laquelle on peut evaluer des constantes de vitesse pour la formation des esters des acides perchloriques et de divers acides sulfoniques. Ces valeurs permettent de calculer les energies libres d'hydrolyse d e ces esters. Les donnees thermochimiques retrouvees dans la litttrature permettent de calculer les energies libres d'hydrolyse du sulfate de dimethyle, de l'arsenite d e trimtthyle et de I'orthosilicate de tetraethyle. Dans le cas du sulfate d e dimethyle, les calculs (utilisant I'Cq. [ I ] rapportte anterieurement) conduisent a une valeur de pK, qui est raisonnablement pres de la valeur attendue d'une facon thkorique; ceci confirme que I'eq. [ l ] est valide p o u r les acides de pK, 2 - 3. Dans le cas de I'orthosilicate de tetraethyle, les donntes thermochimiques sont moins precises mais elles presentent une concordance satisfaisante avec les predictions de 1'Cq. [I]. Les Cnergies libres d'hydrolyse obtenues a partir des correlations de Bransted sont aussi en bon accord avec les valeurs attendues en se basant sur 1'Cq. [I]. Dans le cas des acides oh le phenomene d e la resonance est important, soit dans I'acide lui-mCme (acide borique) ou dans I'anion (acide nitrique, acide nitreux, acides carboxyliques), les energies libres obtenues exptrimentalement pour la formation sont tres loin de la ligne definie par I'eq. [I]. On en conclut que I'eq. [I] est limitte a des especes oh il n'y a pas d e delocalisation pi impliquant I'oxygene qui reagit; toutefois dans le cas oh cette condition est satisfaite, I'Cquation est valable pour la gamme complete des valeurs d e pK, des acides oxygtnes soit de - 6.4 a 16. [Traduit par le journal] 'Alfred P. Sloan Fellow, 1975-1979. ZRevision received May 17, 1978.


Introduction Recently (1) we reported a linear correlation between the free energy change for replacing a hydroxyl group in a molecule by an alkoxyl group and the electronic properties of the rest of the molecules. Initially (1) this was done for ethers using the cr* values for the substituents on the carbon atom bearing OH or OR, but this has since been extended to other classes of compound by using the pK, of the OH compound as a measure of the electron withdrawing properties of the rest of the molecule (2). Equation [ l ] gives the relationship between the free

Ij

Ii I' 1 1

the entire accessible range of acids which can exist in aqueous solution and within its range of applicability can be used with confidence to estimate unknown equilibrium constants.

Results and Discussion Thermodynamic properties for all compounds discussed in this paper (including quantities calculated in this work) are found in Table 1. Literature data were supplemented where necessary by estimated quantities calculated using accepted procedures. Details are found in the Appendix.

pK, Values for Strong Acids AG" = -4.78(f 0.28) + 0.336(&0.024)pKa [l] For acids with pK, values lower than -2 there is energy change, corrected for any steric or symmetry no generally satisfactory way to measure the pK,, effects and the pK, of the hydroxyl compound for referred to aqueous solution. Table 2 summarizes process [2]. Since this correlation worked well for various values which have been suggested. Attempts have been made using nmr data (3-5) but these X-OR + HZO = XOH + HOR [2] methods involve severe assumptions and long extraphosphate esters it seemed worthwhile to see how far polations, and generally lead to values for the pK, it could be extended and what limitations exist for it. which seem unduly high. Although Raman (6, 7) and Accordingly we wish to report the results of an infrared (8, 9) measurements can lead to concentraexamination of the hydrolysis equilibria for several tions of undissociated acid even for perchloric (6) and esters of inorganic acids. The correlation appears to sulfuric acids (7-9), these measurements are only be useful for any acids where resonance is unim- possible in very concentrated acid solutions, so that a portant in stabilizing the anion but does not work at long and uncertain extrapolation would be needed to all for acids for which resonance plays a role. refer them to dilute aqueous solution. Direct meaTo extend the method to acids stronger than surements on dilute aqueous solutions of very strong phosphoric, it was necessary to have pK, values for acids seem unlikely to lead to pK, values unless some strong mineral acids such as sulfuric and perchloric new technical breakthrough occurs. Attempts have been made to calculate pK, values acid, since from these pK, values and previously reported kinetic studies of the hydrolysis of the for the strong mineral acids using a number of methyl esters of these acids it would be possible to approaches. Pauling's rules (ref. 10, cited in ref. 25) make indirect estimates of the free energies of and some elaborations of them (11) are empirical hydrolysis of the esters which could be compared correlations which work well for acids with pK, values with the predictions of eq. [I]. A review of the data in the measurable range. Pauling's rules are: (a) in the literature permits the calculation of a mutually pK, = 7 - 5n, where rz is taken from the structural consistent set of pK, values for acids as strong as formula XO,,(OH),; (b) K,, K,, K,, etc., are in the fluorosulfonic acid, referred to dilute aqueous solu- ratio 1: 10-lo. Use of the first rule suggests tion as standard state. These pK, values permit that for H,SO,, pKl = - 3, and for HCIO,, pK, = construction of a Brernsted plot for rates of hydrolysis - 8. Slightly more elaborate was the attempt to calcuof methyl esters of tetracoordinate oxy acids, which serves as an additional test of the correctness of the late pK, values for inorganic acids reported by pK, values deduced for the strong acids. A much less Kossiakoff and Harker (12), who employed a simple satisfactory Brernsted plot can be constructed for the electrostatic model based on the distribution of (unobservable) reverse reaction, but the number of formal charges deduced from the octet rule. Their points is inadequate to specify the line very well. calculations were remarkably successful and led to Nevertheless, this line permits the calculation of the predicted pK, values of -3.0 for H 2 S 0 4 and -7.3 rate constants for the reverse reactions, and so the for HC10,. Schwartzenbach (13) employed a similar calculation of the equilibrium constants for hy- model to calculate pK, values for these acids and drolysis of the esters. These equilibrium constants supported his results by consideration of the series are in agreement with the values anticipated from the HP0,'-, pK = 12.3; HS04-, pK = 1.9; HCIO,, linear free energy relationship between the free pK = -8.6; similarly, H2P04-, pK = 7.2; H2S04, energy of hydrolysis and the pK, of the acid. Thus pK = - 3.1. Thus for each increase of the formal the results in this paper demonstrate that the free charge on the central atom by 1 unit, the pK deenergy relationship which we have reported covers creases by about 10 units.

CAN. J . CHEM. VOL. 56, 1978

TABLE 1. T h e r l n o d y n a r n i c

d a t a for c o m p o u n d s discussed i n this paper"

( u ) Compounds for which free energies o f formation have not been reported

AH,O(g)

Compound

S0(g)'

AGr"(g)

AH, b .

AHr"(I)"

AGln(aq)b . '


( 6 ) Compounds for which free energies o f formation in aqileous solution have been reported AGr"(aq)

Compound

Compound

AGlo(aq)

Compound

AGf"(aq)

( c ) Compounds for which the free energies of formation in aqueous solution have been calculated in this work Conlpound

AGlo(aq)

Compound

AGro(aq)

Compound

AGr"(aq)

aAt 25'C, standard states are ideal gas at I otm, pure liquid, and 1 M aqueous solution with a n infinitely dilute reference state, unless otherwise n o t e d . keal mol-1. =In cal deg-' mol-I. W e a t o f vaporization. 'Unless otherwise noted, caleulated from AGrn(g) a n d the AG, value in Table 6.

JRefcrencc . ........- - 55 ...

9Reference 56. "Calculated from otlier values in this table. 'Calculated usins a value for AG, estimated as described in the Auuendix. .. jReference 57. kCalculated using the entropy o f liquid methyl nitrate (58) and the solubility o f the liquid in water (59) 'Reference 60. ~ -.~ ~ mCalculaled using the atomic eontribulions method o f Benson and Buss (51). "Calculated using the bond contributions given in ref. 52. 'Calculated from the vapour pressure data given in ref. 61, using data for pressures between 1 and 4 0 T o r r ; Bradley el a/. (62) report AH, = 11.25 k c a l mol-' but did not specify the pressure range employed. nRecalculated from the data o f Flitcroft and Skinner (42) using the modern value for AHro of amorphous SiOl (63). qFree energy of formation o f H + and the monoanion. 'Reference 53. ~

~

wRcference 37. xCaleulated from the free energy o f formation of the anion and the ph', (Table 2). calculated a s descritied in the text. 'Standard state is the pure liquid.

All of these calculations are based upon considerations of formal charge; although this approach has been very successful at least for acids of measurable pK,, including bisulfate, extension to perchlorate involves a particular kind of extrapolation unique to this system and therefore not generally recognized, namely the assumption that a formal charge of plus three can be interpreted in the same sense as one of plus two, i.e., that the electronic effects of the central atom continue to be linear in the formal charge even when this is three. The possibility that nonlinearity might set in seems not to have been considered. The electroneeativitv of the central chlorine would be so drastically increased by the formal charge of plus three (14) that charge redistribution by inductive withdrawal from the neighboring oxygens could well lead to a smaller than

-

anticipated increment in effective charge on the central atom upon changing from SV1to CIV". This effect need not be dependent upon n bonding involving d orbitals, although the orbital contracting effect of a large formal charge could well make such TG bonding more important in C10,- than in other oxy acids of the nonmetals. Of these various predictions, that which seems t o be on the firmest ground is the prediction of the pK, of H2S04by Kossiakoff and Harker (12), although in fact the other methods lead to very similar values. The reason for preferring Kossiakoff and Harker's value is that from their table of ~redictedDK values one can see that they can predict the difference between successive pK, values within one log unit for those cases which are well behaved acids (without resonance or tautomerization effects to confuse the

TABLE2. pK, values which have been reported for strong acids Acid

PK,

Reference

Method

HC104

-9 . 9 -8.6 -7.3 -7.7 -2.7 -1.6 -5.4 -4.1 -6.2 -1.3 -4.0 -3.1 -3.0 -6.0 -9.4 -8.3

34 13 12 32 4 3 32 66 67 68 34 13 12 32 69 70

Based on pK in sulfi~ricacid Theoretical Theoretical Based on pK in organic solvents Nuclear magnetic resonance Nuclear magnetic resonance Based on pK in organic solvents Solubility Spectrophotometric; based on Hot' Nuclear magnetic resonance Based on pK in formic acid Theoretical Theoretical Based on pK in organic solvents Based on acidity function Curve fitting to nmr data


p-TsOH

HzSO,

issue), and that they successfully predicted the second pK, of sulfuric acid. Thus it seems reasonable to expect that the first pK, of sulfuric acid will be -3 f 1. It was also desirable to have pK, values for a number of sulfonic acids, referred to dilute aqueous solution. Organic folklore suggests that FSO,H, CF3S03H, and the various arenesulfonic acids have very negative pK, values. However, consideration of both theoretical expectations and experimental results shows that even FS03H is unlikely to have a pK, less than -7.5. The starting point for the theoretical argument is the experimental value for the pK, of methanesulfonic acid in water, which has been measured as - 1.92 f 0.01 (15). In the same investigation the pK, value for ethanesulfonic acid was found to be - 1.68 f 0.02. As a model for the effect of substituents upon the pK,, we consider the behavior of phosphonic acids; Kresge and Tang (16a) have reported that for the thermodynamic second pK, values of alkyl phosphonates, there is a good correlation with o*: pK,

=

(8.10 f 0.10) - (1.26 f 0.07)0*

Martin and Griffin (16b) have reported a similar correlation with o* = 1.12 for the first ionization but they used appa;ent pK, values measured at unspecified ionic strength, and it is not clear whether the techniques used to determine these rather low pK, values were adequate. Although it is quite possible to measure pK, values less than 2.5 in water by titration, it is imperative to correct for titration of H + either by calculation (17) or by differential titration (18). pK2 values for some arenephosphonic acids are available but only for benzene phosphonic acid is there a thermodynamic value. Makitio and Konttinen (19) report that pK2 is 6.99 at an ionic strength

of 0.1 M and 7.43 at zero ionic strength. Jaffk et al. (20) have reported apparent pK, values for a number of arenephosphonic acids, including benzenephosphonic acid for which they give pK2 = 7.07. Their values were corrected making the assumption that pK, - pK,' will be the same for all arenephosphonates. o* values for substituted aryl groups can be calculated from the pK, values of the appropriate arylacetic acids (21) using the equation reported by Charton (22); (o, was converted to o* using the standard factor of 6.23 (22)). The pK, values of Jaff6 et al. (20) fall very close to the line defined by Kresge's data when these o* values are used (see Fig. 1). We conclude that the second pK, values of both alkyl and arylphosphonic acids can be correlated and presumably predicted by the same equation and that it is very probable that the thermodynamic first pK, will show a very similar p*. Thus the preferred method for predicting the pK, values of sulfonic acids should be to use a p* value of 1.26, and extrapolate from the known value for methanesulfonic acid. The value of p* for sulfonic acids should not be expected to be exactly equal to that for phosphonic acids but consideration of the range of p* values encountered for various classes of acids Y-X-OH suggests that it is extremely unlikely to vary by more than f0.5. Although this uncertainty could give rise to a range of f 1.5 in pK, for o* = 3, it still places stringent limits on the reasonable values for the pK, of, for example, FSO,H, for which o,* = 3.24 (23) and excludes any value for pK, more negative than -7.5. If the apparent pK2 values for phosphate monoesters (2, 19) (including phosphoric acid with a suitable symmetry correction) are similarly plotted against o* values for the alkoxy or aryloxy (calculated from pK, values for the aryloxyacetic acids (24)) substituents, a good linear correlation is obtained,


2346

CAN. J . CHEM. VOL. 56, 1978

FIG.1. Dependence of pK, upon o* for phosphonic and sulfonic acids: (-) least-squares line for alkyl phosphonic acid pK2 (16a), ( 0 ) alkyl phosphonic acids, (W) aryl phosphonic acids (ref. 20; see text); (---) least-squares line for phosphate monoesters pK2, (A) monoesters (ref. 2; see text), (r)monofluorophosphoric acid (ref. 82); (----) predicted line for sulfonic acids; (0) alkylsulfonic acids, (0) arylsulfonic acids, ( 0 )halosulfonic acids, ( A ) sulfuric acid and monomethyl sulfate; see text for sources of pK, values.

with pK, = 9.27 - 1.360*. It should be noted that carbon and oxygen substituents give different though rather similar lines; thus we must not expect to find sulfate esters or sulfuric acid itself falling on the line for sulfonic acids. The pK, for fluorophosphate falls between the lines for phosphate esters and phosphonic acids. The considerations discussed above lead to predicted values for the pK, values of sulfonic acids as follows (error limits are imposed by the assumed uncertainty of 0.5 in p* or are set at 0.5 log unit, whichever is larger): .Ph-S03H, -2.7 f 0.5; pBrC6H4-S03H, - 3.0 f 0.5; pN02-C6H4-S03H, -3.6 f 0.7; C1-S03H, -5.2 1.3; CF3S03H, - 5.2 f 1.3; FS03H, -6.0 f 1.6. Measurements in 100% sulfuric acid as solvent have led to dissociation constants of 1.0 x m for HClO, (25), 8.0 x m for CF3S03H (26), m for 2.3 x m for FS03H (27), and 9.0 x ClS03H (27). These results lead to pK, values relative to HClO, (the weakest acid in the series) of - 1.4 for FS03H, - 1.0 for C1S03H, and -0.9 for CF3S0,H. For a series of structurally similar acids it seems reasonable to expect that relative ionization constants in highly ionizing solvents such as water or sulfuric acid will be closely similar; this is equivalent to assuming that the only significant difference in the two solvents is the dramatic difference in solvent basicity. Bessikre (28,29) has determined the ionization constants for sulfuric and perchloric acids in trifluoro-

+

acetic acid as solvent; his values for pKi are 2.4 and 0.8, respectively. It must be borne in mind that trifluoroacetic acid is a solvent of low dielectricconstant ( E = 8.4) (28), and that the processes of ionization, i.e., heterolytic cleavage of the H-X bond must be considered separately from dissociation to give free ions, the latter being quite unfavorable. Bessikre has also reported 'global dissociation constants' for formation of free ions from ion pairs plus unionized acid; the corresponding pK values are 4.5 for perchloric acid, 6.3 for sulfuric acid, and 7.1 for methanesulfonic acid (28). Kolthoff and Bruckenstein (30) have reported the ionization constant for perchloric acid in acetic acid as p K i = 1.0 and have reported pK values for global ionization of 4.87 for perchloric acid, 7.24 for sulfuric acid, and 8.46 for toluenesulfonic acid (3 1). The global ionization constants seem to be more widely dispersed in acetic acid; unfortunately, there seems to have been n o determination of a value of pKi for sulfuric acid in acetic acid. The values of pKi, since they refer to a single process, are to be preferred as a measure of acidity; these values lead to a pK, difference of 1.6 between perchloric and sulfuric acids. From a study of the reaction I + HA = IHA, where I is an indicator, Bessikre (20) has constructed a scale of relative acidities in trifluoroacetic acid; this scale places sulfuric acid 1.7 log units less acidic than perchloric acid and both methanesulfonic acid and p-toluenesulfonic acid 2.3 log units less acidic than perchloric acid. (Chlorosulfonic acid is placed slightly less acidic than sulfuric acid but in the absence of control experiments t o demonstrate that chlorosulfonic acid is the actual acid species in mixtures of chlorosulfonic and trifluoroacetic acids, this can not be considered definitely established. I n sulfuric acid as solvent, chlorosulfonicacid is stronger than sulfuric acid (27).) Since these acidities are based on experiments which d o not distinguish between unionized acid, HA, and the ion pair, H f A-, the interpretation is less clear than would be desirable. Furthermore, it is not entirely clear how the relative acidities reported were actually calculated; if the data for indicators only are employed (Tables I11 and IV of ref. 29) somewhat different values are obtained, namely pK, differences relative to perchloric acid of 1.9 for sulfuric acid and 3.1 for methanesulfonic acid and p-toluenesulfonic acid. The agreement between different approaches t o these pK, differences is considerably less perfect than might be desired but all available data can be summarized by stating that sulfuric acid is 2.0 f 0.4 p K units less acidic than perchloric acid and that methanesulfonic acid and toluenesulfonic acids (which appear indistinguishable in these experiments) are 3.1 f 0.5 pK units less acidic than perchloric acid.

GUTHRIE

TABLE3. pK, values for acids discussed in this paper"


Acid

P Kc,

Acid

PK~

HNO3 HNOz H2CO3 CH3OCOzH HCOOH CH,COOH

~ ~ e f e r e n li ie: *Estimated as described in the text.