Hydrolysis of esters of oxy acids: pKa values for strong acids; Brflnsted relationship forattack 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 UNIV GUELPH on 10/16/14 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. Their points is inadequate to specify the line very well. 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. cited in ref. these measurements are only be useful for any acids where resonance is unim.. the pK deenergy relationship which we have reported covers creases by about 10 units.. Pauling's rules are: (a) in the literature permits the calculation of a mutually pK.3.3. pK = 7. (b) K.nrcresearchpress.78(f 0. 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. similarly. H2P04-. Although Raman (6. linear free energy relationship between the free pK = -8. are in the fluorosulfonic acid.1. Results and Discussion Thermodynamic properties for all compounds discussed in this paper (including quantities calculated in this work) are found in Table 1. and generally lead to values for the pK.2. values for acids as strong as formula XO. corrected for any steric or symmetry no generally satisfactory way to measure the pK. Table 2 summarizes process [2]. etc.'-. Thus pK = . but this has since been extended to other classes of compound by using the pK. H2S04. effects and the pK.336(&0.Can. Attempts have been made to calculate pK. HS04-.model to calculate pK. pK = 1. Chem. referred to dilute aqueous solu. Schwartzenbach (13) employed a similar calculation of the equilibrium constants for hy. calculations were remarkably successful and led to Nevertheless.28) + 0. K. it could be extended and what limitations exist for it. and so the for HC10. who employed a simple satisfactory Brernsted plot can be constructed for the electrostatic model based on the distribution of (unobservable) reverse reaction. of the OH compound as a measure of the electron withdrawing properties of the rest of the molecule (2).. pK. HCIO.ratio 1: 10-lo.6. Downloaded from www. Literature data were supplemented where necessary by estimated quantities calculated using accepted procedures.. values with the predictions of eq.3. Slightly more elaborate was the attempt to calcuof methyl esters of tetracoordinate oxy acids. values acid. Initially (1) this was done for ethers using the cr* values for the substituents on the carbon atom bearing OH or OR. 7) and Accordingly we wish to report the results of an infrared (8. values deduced for the strong acids. J. Details are found in the Appendix. Since this correlation worked well for various values which have been suggested. energy of hydrolysis and the pK.SO. values of -3.5n. refer them to dilute aqueous solution. The correlation appears to sulfuric acids (7-9). pK = 12. A review of the data in the measurable range. since from these pK. values for acids seem unlikely to lead to pK. Thus for each increase of the formal the results in this paper demonstrate that the free charge on the central atom by 1 unit. Use of the first rule suggests tion as standard state. values unless some strong mineral acids such as sulfuric and perchloric new technical breakthrough occurs.. 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. but the number of formal charges deduced from the octet rule.possible in very concentrated acid solutions. = construction of a Brernsted plot for rates of hydrolysis . 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.. pK. = 7 . Pauling's rules (ref. 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. K. A much less Kossiakoff and Harker (12). 10.. values for inorganic acids reported by pK. Values for Strong Acids AG" = -4. and for HCIO. 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. These pK. it was necessary to have pK. . These equilibrium constants supported his results by consideration of the series are in agreement with the values anticipated from the HP0.8.. values lower than -2 there is energy change.. 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.(OH).0 for H 2 S 0 4 and -7. pKl = . values permit that for H. of the acid.. which seem unduly high..3 rate constants for the reverse reactions. values for these acids and drolysis of the esters. Direct meaTo extend the method to acids stronger than surements on dilute aqueous solutions of very strong phosphoric. [I].9.com by UNIV GUELPH on 10/16/14 For personal use only.024)pKa [l] For acids with pK. of the hydroxyl compound for referred to aqueous solution. where rz is taken from the structural consistent set of pK. this line permits the calculation of the predicted pK. which serves as an additional test of the correctness of the late pK. .com by UNIV GUELPH on 10/16/14 For personal use only. that the electronic effects of the central atom continue to be linear in the formal charge even when this is three. J.. W e a t o f vaporization. "Calculated from otlier values in this table. 'Standard state is the pure liquid. JRefcrencc . Bradley el a/. AHr"(I)" AGln(aq)b . ~ -. J .nrcresearchpress. ~ ~ wRcference 37. qFree energy of formation o f H + and the monoanion..~ ~ mCalculaled using the atomic eontribulions method o f Benson and Buss (51). nRecalculated from the data o f Flitcroft and Skinner (42) using the modern value for AHro of amorphous SiOl (63). b . 1978 TABLE 1. This effect need not be dependent upon n bonding involving d orbitals. pure liquid. that which seems t o be on the firmest ground is the prediction of the pK. jReference 57.25 k c a l mol-' but did not specify the pressure range employed. . 'Calculated usins a value for AG. caleulated from AGrn(g) a n d the AG. unless otherwise n o t e d . extension to perchlorate involves a particular kind of extrapolation unique to this system and therefore not generally recognized.. Of these various predictions.. Chem..than in other oxy acids of the nonmetals. calculated a s descritied in the text...CAN. (Table 2). 61.. "Calculated using the bond contributions given in ref. 9Reference 56. ' Can. of H2S04by Kossiakoff and Harker (12). = 11. 52. kCalculated using the entropy o f liquid methyl nitrate (58) and the solubility o f the liquid in water (59) 'Reference 60. estimated as described in the Auuendix. 56. The possibility that nonlinearity might set in seems not to have been considered. =In cal deg-' mol-I. xCaleulated from the free energy o f formation of the anion and the ph'. value in Table 6.. Downloaded from www.55 . i. keal mol-1. ( 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. 'Reference 53. although the orbital contracting effect of a large formal charge could well make such TG bonding more important in C10... and 1 M aqueous solution with a n infinitely dilute reference state. standard states are ideal gas at I otm. 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. (62) report AH. 'Calculated from the vapour pressure data given in ref. using data for pressures between 1 and 4 0 T o r r . 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". 'Unless otherwise noted..e.O(g) Compound S0(g)' AGr"(g) AH.. including bisulfate. VOL. 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. All of these calculations are based upon considerations of formal charge.. values within one log unit for those cases which are well behaved acids (without resonance or tautomerization effects to confuse the . CHEM. . namely the assumption that a formal charge of plus three can be interpreted in the same sense as one of plus two. although this approach has been very successful at least for acids of measurable pK. including benzenephosphonic acid for which they give pK2 = 7. values measured at unspecified ionic strength. values for a number of arenephosphonic acids.* = 3. values of Jaff6 et al. value for ethanesulfonic acid was found to be . If the apparent pK2 values for phosphate monoesters (2.43 at zero ionic strength. of sulfuric acid will be -3 f 1. and extrapolate from the known value for methanesulfonic acid. Although it is quite possible to measure pK. and that they successfully predicted the second pK.10) .1 -3.07)0* Martin and Griffin (16b) have reported a similar correlation with o* = 1.(1.5. 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.TABLE2. The pK. consideration of both theoretical expectations and experimental results shows that even FS03H is unlikely to have a pK. it still places stringent limits on the reasonable values for the pK. values less than 2. values for a number of sulfonic acids.ent pK.5 in pK. we consider the behavior of phosphonic acids.3 -7.0 -6.pK. and it is not clear whether the techniques used to determine these rather low pK. of sulfuric acid. of methanesulfonic acid in water.99 at an ionic strength of 0.H. = (8. there is a good correlation with o*: pK.6 -7.02. Jaffk et al.92 f 0. pK2 values for some arenephosphonic acids are available but only for benzene phosphonic acid is there a thermodynamic value. Kresge and Tang (16a) have reported that for the thermodynamic second pK.3 -4.10 f 0. values.7 -2.3 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. As a model for the effect of substituents upon the pK.68 f 0.4 -8. (o. less than -7.1 -6. Downloaded from www.1. and the various arenesulfonic acids have very negative pK. more negative than -7. Organic folklore suggests that FSO.7 -1. it is imperative to correct for titration of H + either by calculation (17) or by differential titration (18).5 in water by titration. (20) fall very close to the line defined by Kresge's data when these o* values are used (see Fig.12 for the first ionization but they used appa. 9 -8. CF3S03H. FSO.6 -5. The starting point for the theoretical argument is the experimental value for the pK.26 f 0. However.2 -1. It was also desirable to have pK. of. We conclude that the second pK. will show a very similar p*. (20) have reported apparent pK. o* values for substituted aryl groups can be calculated from the pK. values which have been reported for strong acids Acid PK.' will be the same for all arenephosphonates. Chem. Reference Method HC104 -9 .H. . J. Thus the preferred method for predicting the pK.26.23 (22)). for example. In the same investigation the pK.com by UNIV GUELPH on 10/16/14 For personal use only. values were adequate. for o* = 3. Thus it seems reasonable to expect that the first pK. values of the appropriate arylacetic acids (21) using the equation reported by Charton (22).07. pK.0 -9. a good linear correlation is obtained. values of sulfonic acids should be to use a p* value of 1.4 -4. 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 Can. values for the aryloxyacetic acids (24)) substituents. Although this uncertainty could give rise to a range of f 1. 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. was converted to o* using the standard factor of 6. which has been measured as .nrcresearchpress. for which o. .5.01 (15). Makitio and Konttinen (19) report that pK2 is 6..1 M and 7. referred to dilute aqueous solution.0 -3. values of alkyl phosphonates. p-TsOH HzSO.5. 19) (including phosphoric acid with a suitable symmetry correction) are similarly plotted against o* values for the alkoxy or aryloxy (calculated from pK.24 (23) and excludes any value for pK. issue). Their values were corrected making the assumption that pK. 1).1. It should be noted that carbon and oxygen substituents give different though rather similar lines. 2. and the ion pair.0 x m for CF3S03H (26).46 for toluenesulfonic acid (3 1). differences relative to perchloric acid of 1. Measurements in 100% sulfuric acid as solvent have led to dissociation constants of 1.3.com by UNIV GUELPH on 10/16/14 For personal use only. -3. (the weakest acid in the series) of . (0) alkylsulfonic acids. see text for sources of pK. From a study of the reaction I + HA = IHA.7 f 0. . for fluorophosphate falls between the lines for phosphate esters and phosphonic acids. 7. respectively.7 log units less acidic than perchloric acid and both methanesulfonic acid and p-toluenesulfonic acid 2. pBrC6H4-S03H. 2346 CAN. (r)monofluorophosphoric acid (ref. These results lead to pK.5. are to be preferred as a measure of acidity. Bessikre has also reported 'global dissociation constants' for formation of free ions from ion pairs plus unionized acid.27 . Chem. Dependence of pK. Kolthoff and Bruckenstein (30) have reported the ionization constant for perchloric acid in acetic acid as p K i = 1. 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.1 for methanesulfonic acid and p-toluenesulfonic acid. thus we must not expect to find sulfate esters or sulfuric acid itself falling on the line for sulfonic acids. and that the processes of ionization. m for 2. chlorosulfonicacid is stronger than sulfuric acid (27). -2. The pK.1. The global ionization constants seem to be more widely dispersed in acetic acid. 1978 FIG.2 f 1. The agreement between different approaches t o these pK. where I is an indicator.3. Downloaded from www. (---) least-squares line for phosphate monoesters pK2.9 for CF3S0. the latter being quite unfavorable. 82).5 in p* or are set at 0. this can not be considered definitely established. . (A) monoesters (ref. values relative to HClO.H. with pK. (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. 29) somewhat different values are obtained. difference of 1. the corresponding pK values are 4. J . Bessikre (28. i. see text).8. Bessikre (20) has constructed a scale of relative acidities in trifluoroacetic acid.0 f 1.0 x ClS03H (27). ( 0 ) alkyl phosphonic acids. 8.) Since these acidities are based on experiments which d o not distinguish between unionized acid. since they refer to a single process. his values for pKi are 2. and 7. differences is considerably less perfect than might be desired but all available data can be summarized by stating that sulfuric acid is 2. Furthermore. (25).Ph-S03H.6 f 0. CF3S03H.6 between perchloric and sulfuric acids.5 pK units less acidic than perchloric acid.3 log units less acidic than perchloric acid. pN02-C6H4-S03H. C1-S03H.7. It must be borne in mind that trifluoroacetic acid is a solvent of low dielectricconstant ( E = 8. HA. this is equivalent to assuming that the only significant difference in the two solvents is the dramatic difference in solvent basicity. FS03H. I n sulfuric acid as solvent. (W) aryl phosphonic acids (ref. 20.4 and 0. H f A-. heterolytic cleavage of the H-X bond must be considered separately from dissociation to give free ions. 6. ( 0 )halosulfonic acids. .0 and have reported pK values for global ionization of 4.4 for FS03H. there seems to have been n o determination of a value of pKi for sulfuric acid in acetic acid.1.Can.1. whichever is larger): . unfortunately. J.5.3 for sulfuric acid.2 1..nrcresearchpress.3.4 p K units less acidic than perchloric acid and that methanesulfonic acid and toluenesulfonic acids (which appear indistinguishable in these experiments) are 3.1. The values of pKi. ( A ) sulfuric acid and monomethyl sulfate. and 8.360*.0 f 0. VOL.3 x m for FS03H (27). see text).0 f 0. if the data for indicators only are employed (Tables I11 and IV of ref. -5.87 for perchloric acid. namely pK.0 x m for HClO.1 for methanesulfonic acid (28).5. values. upon o* for phosphonic and sulfonic acids: (-) least-squares line for alkyl phosphonic acid pK2 (16a). The considerations discussed above lead to predicted values for the pK. .24 for sulfuric acid.6. and 9. 56. it is not entirely clear how the relative acidities reported were actually calculated.5 for perchloric acid. CHEM. values of sulfonic acids as follows (error limits are imposed by the assumed uncertainty of 0.29) has determined the ionization constants for sulfuric and perchloric acids in trifluoro- + acetic acid as solvent. = 9.1 f 0.9 for sulfuric acid and 3. these values lead to a pK. -6.0 for C1S03H.4) (28). (----) predicted line for sulfonic acids. the interpretation is less clear than would be desirable.5 log unit. this scale places sulfuric acid 1.e. and -0. (0) arylsulfonic acids. ' which in the case of weak acids such a s acetic acid are probably very similar t o ionization constants but which may be very different for strong acids which will ionize t o give ion pairs in a solvent of low polarity such a s ethanol.5. since the apparent ionization constants for HCI a n d for CsCl are very similar in ethanol (35). J.0 pK. that of trifluoromethanesulfonic acid is . gReference 74.9 0. This argument would lead to a much more negative scale based on Bessiere's data if HCI is used a s reference acid. o f HCI in water. there is actually increased uncertainty. Figure 1 shows that these values are in good agreement with the predicted line.GUTHRIE TABLE3.3 (6) C1is quite different in structure and presumably in ions used in this work solvation from the Y-X0.0 0. of the arenesulfonic + + acids seem to be those based on the predicted line. unit.4 0.. and all others used in this paper.5. this scale is determined by the choice of HCI as reference acid. values of methane. and that of fluorosulfonic acid . Thus the relative acidity of toluenesulfonic acid must be considered less reliable.6. measurements of ion pair formation could well be perturbed by noncovalent interactions involving the benzene rings of the indicator bases and the toluenesulfonic acid. Acid PK~ HNO3 HNOz H2CO3 CH3OCOzH HCOOH CH. These pK. values for acids discussed in this paper" Can. the pK.6. of .5 from the data in acetic and trifluoroacetic acids.nrcresearchpress. so that the danger of serious 3Bessiere chose a value o f . It is somewhat surprising that toluenesulfonic acid and methanesulfonic acid appear so similar.7 for the pK. using the more generally accepted value of . values. of -5. are found in Table 3. which increases our confidence in the assignment. it seems probable that the global ionization constant for HC1 is really measuring dissociation of an ion pair.to construct a scale. Chem. this value is derived from a scale of acidity in absolute ethanol (34).3. of chlorosulfonic acid is . to allow for the inconsistent result in acetic and trifluoroacetic acids the error limits are increased to f 1. because of the apparent near identity of the pK. of HCl in aqueous solution is imperfectly defined. However. *Reference 75.5. in water for HC104 becomes -11. Bessiire (32) has proposed a rather different set of pK. in water of HCI (33). This value is rejected for reasons discussed in the text. of -2. Then from the data in sulfuric acid we can calculate that the pK. Acid P Kc. Downloaded from www. T h e scale for absolute ethanol has been based on 'global ionization constants. We now have enough information to construct a scale of acidity values.COOH ~ ~ e f e r e n li ie: *Estimated as described in the text. 'Reference 73. There appear to be three fundamental objections to these choices : (a) the pK.and toluenesulfonic acids. For the arenesulfonic acids.8 rt_ 0.5. pK. Starting with methanesulfonic acid. for the moment the best estimates for the pK. since both on theoretical (o* values) and experimental (leaving group behavior) grounds one expects toluenesulfonic acid to be the stronger. and by the choice of the pK. which has a well-established pK. 'Reference 33. values based upon his data. <Reference 72.92. for aqueous HCI. and that perchloric acid has a pK.7 for the pK.com by UNIV GUELPH on 10/16/14 For personal use only.1. .5. and values very different from that chosen by Bessiere (33) have been proposed. we can calculate that sulfuric acid has a pK.0 f 0. 89 could not have been obtained. This was done by a modifica. 1978 variations in solvation effects is considerable.. J . and trifluoroacetic acid is far more prone to undergo nucleophilic addition than are less electron deficient carboxylic acids (37). (a Brsnsted plot) is expected to show a simple relationship provided that-the pK. This effect is 0. so no such [4] MeO-SO. HCI has a significant tendency to add to carbonyl groups as shown by chloroalkyl ether formation (36). pK. of the Sulfuric Acid and its Methyl Esters nucleophile and leaving group and give linear It is possible to test the pK. with a total of . it is without precedent to have curvature so extreme at such low values When free energies of hydrolysis for the two stages of of the observed rate constant.badly. marked curvature. It is quite generally found that rates of nucleophilic substitutions are related t o the pK. CHEM. value or of eq. perchloric acid had a pK. values for strong acids derived above.Can. in particular. using data collected in ref. then the average slope of the Brsnsted For the overall hydrolysis.employed in substitution at carbonyl (49. in excellent agreement with the thermochemical value.nrcresearchpress. values t o these acids. For example. Unlike the other acids nitric acid derives some dynamic data refer to the ions.82 kcal mol-I. Downloaded from www. [I]. Although it is possible to construct a Bronsted plot [5] .12.74 and -5. A plot of log k vs.2 solvolyses (79). This approach has been more frequently value which can be deduced from the heat of forma..com by UNIV GUELPH on 10/16/14 For personal use only. when the equilibrium is not shifted by dissociation into Hf and Cl-. of ca. respec. [I] depends upon which carbon simply because of the scarcity of data satisis considered the better established but in any case fying the second criterion. The effect was assumed to be the same as the of the assignment of pK.mining step. (c) it has not been demonstrated as far as one can tell that HCI in trifluoroacetic acid is actually HCI and has not to some considerable extent undergone covalent addition to the acid. but that methyl nitrate deviates monoesters are strong acids the available thermo. had in pK. ... value derived for Brsnsted plots. this value was used to estimate the other pK. the balance between ionization and dissociation constants is likely to be quite different and thus the meaning of the global ionization constant will not be the same for different structural types. H a d average (symmetry corrected) change in pK. values are correct but should show no pattern or a physically unreasonable one if they are seriously in error. Since sulfuric acid and its type Y-XO. For/~~atior~ and Soluolysis It is possible to test the entire set of pK. [ l ] with the type (44). stabilization of the anion. provided that the reactions correlated sulfuric acid in aqueous solution by comparing the all have the same rate determining step and provided value of the free energy of hydrolysis of dimethyl that the variable reagents are of similar structural sulfate derived from this pK. Br~nstedCorrelations for Methyl Ester. VOL.O =$ MeOH + HzSO. serious disagreement would cast doubt on one if not as a result of the present work and recent work from both. suggested. the values equilibrium process preceding a fast rate deterobtained are -6. Thus a linear Bransted plot is what would be expected.46 kcal rnol-'. by taking advantage of the large amount of work which has been done studying the kinetics of hydrolysis of the methyl esters of these acids.10 as has been values for inorganic esters reported in Table 3.-OMe + H 2 0=$ MeOH explanation is possible.37 corresponding to a .H.the line determined by methyl mesylate and trition of a method which we have previously e~nployed methyl phosphate constitutes a strong confirmation (2).. 2. tively. Chem. in order to estimate a value for the pK. A pK.72 kcal mol-l. 2a shows that a good Equation [ I ] predicts the free energy of hydrolysis. using eq. (Whether this is best regarded as a phoryl (46). and Fig. the thermodynamic plot from methanesulfonate to perchlorate as leaving data in Table 1 lead to a free energy change of group would have been -0. the strong acids fall within their uncertainty limits of of monomethyl sulfate. phostion of the ester. it now remains to correct for the effect of replacing The observation that the points for the esters of OH by OR. J. observed these acids been as strong as has sometimes been sugfor phosphoric acid and its mono and dimethyl gested (see Table 2) then a straight line Bronsted plot esters.) this laboratory. Brsnsted correlation exists for the rate constants for for the process converting an ester to the unionized uncatalyzed hydrolysis of methyl esters of acids of the acid in aqueous solution. The reactions being considered here are believed to be simple S. 2348 C A N . value for considerable part of its acidity from resonance sulfuric acid in aqueous solution has been derived. 56. or sulfonyl (47) centres than at aliphatic test of the pK. A set of data now exists. Although curved Bransted plots are by no means unknown (44). when there is no prehydrolysis are calculated using eq. MeO-SO2-OH + H.12. the equilibrium lies far on the side of hydrolysis.+ has a rather small slope. The extreme lines are drawn so that they will just pass within the error bars for the data.39(*0. it is not clear how similar the slopes should be expected to be. The best line as well as the extreme lines allowed by the data are shown.e. Chem. For all of the cases where the rate of hydrolysis is measureable. it was assumed that the bounds on the line were the same as the bounds on the data.1. so that it is difficult to assess the reasonableness of the result. the rate constants for ester formation should be calculated for the microscopic reverse of this reaction. and lines parallel to the best line were drawn.23. these lines are used to assess the error bounds for extrapolations of the line beyond the range specified by the data.09) . Figure26 shows this Brsnsted plot and also the extreme lines which are allowed by the error limits on the data points.02(+0. This condition is satisfied for dimethyl sulfate and the methyl phosphates. (0)methyl nitrate. attack of the anion on protonated methanol. A somewhat more analogous system is the reaction of anions with S-(2-chloroethyl)thiironium ion (486). Kevill's p value can be converted to a Bransted slope of +0. Since the rate determining step for the hydrolysis is attack of water on the methyl carbon leading to protonated methanol as the initial product along with the leaving group as anion. (b) Br~nsted plot for the calculated rate constants for formation of methyl esters by attack of oxy anions upon protonated methyl. i. (@) acids without resonance effects. Since the equilibrium constants are calculated from thermochemical data and so are imprecise. these rate constants and free energies of hydrolysis derived from them are found in Table 4. from the data in ref. Since Kevill's data refer to a reaction with a neutral substrate in a dipolar aprotic solvent. the rate constants for ester formation are subject to uncertainties of at least an order of magnitude. for the reverse reaction this is less satisfactory because the available points do not cover a wide enough range. the Brsnsted slope for nucleophilic attack is f0.OH..69. GUTHRIE FIG. Rate constants for the formation of the esters for which hydrolysis rate constants are available were taken from this correlation line. Using the pK. (0)B r ~ n s t e dplot for hydrolysis of methyl esters of oxy acids. 26. witherror limits taken from the extreme lines. this is similar to the upper limit for the slope of Fig.2. subject to large uncertainties. Unfortunately there do not seem to be any other studies of the kinetics of nucleophilic attack of a series of oxygen monoanions on a cationic substrate. 48b it may be calculated that for sulfate and phosphate dianions. The line was determined by weighted least squares: log kll. Although these values are subject to much greater uncertainty than is desirable.nrcresearchpress. Within this range.o = -7. however.04)pKa. J.. Downloaded from www. This is also an imperfect model since the reaction is one of dianions with a highly strained substrate but it is encouraging a . there has been to our knowledge no other method reported to give any information concerning these free energies of hydrolysis.com by UNIV GUELPH on 10/16/14 For personal use only. The Brsnsted line for the attack of oxy anions on CH. rather than a cationic substrate in protic solvent.Can. One related study is by Kevill and Wang (480) of the nucleophilic attack of a series of arenesulfonate anions upon methyl triflate in acetonitrile. values for arenesulfonates derived in this work. the rate constant for ester formation can be calculated if the rate constant and the equilibrium constant for hydrolysis are known. 46. J. VOL. of acida log klr.Reference 76.46. and third stages of hydrolysis: -2. 9Estimated from rate constants for the ethyl ester at 25°C in 100 and 80% aqueous ethanol.312. In the absence of experimental knowledge concerning the thermodynamics of solution of organic arsenic compounds there is unavoidably some additional uncertainty in the numerical value of the free energy of formation of the ester in solution. it is probably unrealistic to expect predictions to be much better than to within a kcal for the extent of structural variation involved in extending a relationship originally derived for carbon compounds to a n arsenic derivative. Arsenious Acid and its Methyl Esters Arsenious oxide (As203) is sparingly soluble in water and it is considered that in aqueous solution ". 2b.ob log krcvc AGhydrold AGOc nFrom Table 3. J.11. The acid species does not have an As-H bond by contrast to H3P03 (38). 'Reference 79. Downloaded from www. "eference 78. bPseudo-first-order rate constant for hydrolysis in water at 25'C (s-I) divided by the number of hydrolyzable methyl groups. 56. Thus in calculating the free energy of formation of the ester in aqueous solution it was necessary to estimate the free energy of transfer as described in the Appendix. .69 kcal mol-'. [l] gives a useful.the standard state for water is the pure liquid.-+ H20CH3+. Furthermore the thermodynamic data upon which the 'experimental' free energy of hydrolysis is based are subject to more than the usual uncertainty because of our imperfect knowledge of the solution chemistry of arsenic. -2. CSecond-order rate constant for attack o f the anion upon protonated methanol. The heat of hydrolysis of tetraethyl . and -2. second. error limits taken from the extreme lines. with free energy of formation equal to .2350 CAN.. The heat of hydrolysis of trimethyl arsenite has been measured and it is reported that the ester hydrolyzed extremely rapidly in water (39). However. )Reference 2.com by UNIV GUELPH on 10/16/14 For personal use only. + + that a reaction with similar charge types and the same solvent shows a similar Brsnsted slope.57 kcal mol-' (41). (40). CHEM. Data for Bransted plots Can. It seems not unreasonable to conclude that eq. estimate of the free energy of hydrolysis even for an arsenic derivative.42 kcal rnol-' or -7. 'Values taken from the best line in Fig. amounting to 3. 'Free energy change for the process: XOCH. and for solutes is 1 M aqueous solution. [l] leads t o (MeO). =Free energy change for the process: XOCH. (77) assuming that log k was linear in Y and that the methyl to ethyl ratio was the same as for ROSOICl (76).As + 3 H z 0 e 3MeOH + H3As03 the following values for the first. H1O = XOH HOCH. the predominant species is probably As(OH). can be derived from thermochemical data in the literature. Chem. The thermodynamic data in Table 1 lead to an overall free energy of hydrolysis of . . Ester pK.nrcresearchpress. [I] some further free energies of hydrolysis for esters of acids of known PK. Silicic Acid and its Ethyl Esters It is now accepted that the species in solutions of S i 0 2 or its hydrates at low pH is Si(OH). 1978 TABLE 4. Application of eq. as described in the text. . 'Calculated from k H l oand equilibrium constant." (38). The discrepancy is disturbingly large.34 kcal rnol-' overall.03 1. Free Energies of Hydrolysis of Some Other Esters To supplement the Set of compounds X-0-R which can be used to test the range of applicability of eq. or somewhat over 1 kcal per step. albeit imprecise.7 kcal overall. + H 2 0 = XO. values for the mono-. (Transesterification in neutral alcohol is reported to be very fast (49). J. Methyl Nitrite Although the free energy of formation of the gaseous ester is well defined. di-.64 kcal mol-'.3 kcal with the experimental value of -6.3. Cqrrelation of Free Energy of Ester Hydrolysis with Acid pK.6.8. though plausible. for silicic acid is reported to be 9.75 $_ 0. the following values for . and for lack of any better approach were estimated on the assumption that they would be the same as for tetraethyl orthocarbonate.71 kcal mol-'. Methyl Nitrate The data in Table 1 lead to free energy of hydrolysis of . and triester's are estimated as already described. Just as eq.nrcresearchpress. reported for nitrous acid) a value of the free energy of transfer of the acid could be obtained. [7] and not to the process shown in eq. and large. of 15. Equally clearly. and triesters were calculated using eq. the deviations for those acids which do have important resonance effects are very substantial. of 11. this is in fair agreement with expectations from Pauling's rule and the discrepancy can be rationalized in terms of the low electronegativity of the central atom.9 for nitric acid. as well as those reported earlier. Free Energies of Transfer for Inorganic Acids From thermodynamic data for the gaseous acids (50) and free energies of formation o f the aqueous acids from the present work. [ l ] leads to anomalously high pK.3 log units. We conclude that eq. values for acids for which the anion shows increased resonance.1. which is markedly different from the observed value of 3. use of eq. free energies of formation of mono and dimethyl borate in aqueous solution were calculated. The first pK. di-. 3. but nothing seems to be known about their stability. Steric effects are expected to be small. is close to the observed value but this is probably accidental. of the acid produced on hydrolysis in Fig.93 (43). Chem.- actually happens in aqueous solution (33). Using one third of the observed free energy change for complete hydrolysis as the free energy change per step. + Methyl Borate ~ r o mthe free energies of formation for trimethyl borate and boric acid in Table 1 and the usual assumption concerning the acid strengthening effect of replacing hydroxyl by methoxyl. of 11. which should show a decrease in resonance upon ionization. Data from the literature permit the calculation of the overall free energy of hydrolysis of dimethyl carbonate as -2. orthosilicate in acidic solution has been measured (42) but is subject to an uncertainty of 2 kcal mol-' because of uncertainty concerning the nature (colloidal solution or amorphous precipitate) of the silica produced (42). class of hydrolysis reactions. the fit to the previously reported line is very good. [l] and are included in Table 1. which is a measure of the importance of resonance delocalization upon the acidity of nitric acid. [8] which is believed to represent what I 7~ 181 I H3B03 e H + H3B03 + HZB03- + H. Methyl Esters of Carboxylic Acids Equilibrium constants for hydrolysis of methyl formate and acetate have been measured. the free energies of hydrolysis can be calculated for each step.31 mol-'. respectively.' and a calculated pK. The calculated pK. which leads to a pK.3 and 11. From. It should be noted that this refers to the hypothetical process shown in eq. The predicted value for the overall free energy of hydrolysis for process [6] is -8. This leads to a pK. values for acids. Clearly.4 by 13. for boric acid of 9. it is necessary to esti- 2351 mate the free energy of transfer because of the rapid hydrolysis of alkyl nitrites. [ l ] is valid for orthosilicic acid and its esters. so it should lead to anomalously low pK. value of .O e H' + B(OH). This procedure. a free energy of hydrolysis of $0. The difference of 12 log units may be attributed to the effect of resonance delocalization in the anion upon the acidity of nitrous acid. which is to be compared 2.com by UNIV GUELPH on 10/16/14 For personal use only. such as boric. values for Brmsted oxygen acids which can exist in water and therefore it seems appropriate to conclude that we have a general method for calculating the equilibrium constant for a defined. this differs from the observed pK.78 kcal mol-' can be obtained. the values in Table 1. [I] leads to a predicted pK. on going from acid to ester would be the same as for formic acid. The agreement is within the uncertainties of the quantities concerned.6. The free energies of hydrolysis derived in this work (Table 5). Downloaded from www. The correlation holds for the entire range of pK.GUTHRIE Can.0. it was then assumed that the increment in AG.78 kcal mol. are plotted as a function of the pK. If pK.) From the free energies of formation of the gaseous acid (50) and the hypothetical aqueous acid (calculated from the free energy of formation of nitrite ion and the pK. values of 11. These species are obligatory intermediates in the hydrolysis of trimethyl borate. These lead to pK. Free energies of formation of the mono-. must lead to considerable uncertaintv in the final value of the free energy of formation of the aqueous ester. for those acids where resonance effects are not important. HARKER. 14.J. I.34 (1961). 70. 6.J . Am.097 & 0. Phys.RUSS.Trans. J . 47. with neutral reactants and products. (b) J. J. B. GUTHRLE. + Acknowledgements Financial assistance from the National Research Council of Canada and the Alfred P. Trans. Phys. 10. negative than the values for the corresponding methyl esters and must reflect the very powerful hydrogen bonding of strongly acidic protons to water. J. J. 394. Educ. E. J. =Thiswork. San Francisco. E. the line is calculated using the slope points for compounds and intercept reported in ref. Test of eq. Chern. F. Russ. 13.J . KOSSIAKOFF and D.1 1 1 k 0. C. 176. 31. RUSS. values of the equilibrium constant of 0.2701 (1969). J . 48. COVINGTON. . Sloan Foundation is gratefully acknowledged. (0) points for inorganic acids without resonance. 57. (84) v a l ~ l e0. P. ~ e n e r achemistry. Chem.3. Chern. in aqueous solution. RLCC1. G.260(1963). 7. Chern. p. and T . V. HNO. 37. J. X-OH FIG. R. Phys. Chem.. Phys. A. "Free energy o f hydrolysis. . T. ZARAKHANI and M. K . Chern. W. . Soc. integrating the methyl signal relative to the solvent peak. 5. SCHWARTZENBACH. Experimental The solubility of dimethyl carbonate in water at 25°C was determined by nmr analysis of a saturated solution. 1126 (1957).com by UNIV GUELPH on 10/16/14 For personal use only. The solvent w a s 0. [I]. Chern.0 kcal mol-'. ( ( I ) T ..(b) N. Chern. Faraday Soc.989 (1973).SO. P. 2. SANDERSON. V. H.A. Downloaded from www. 60. MAIOROVand N. 27. C.003 M-') a n d 0. ( A ) points for acids in which resonance is important. REILLY. WALRAFEN. 898 (1975).133 (1936). HOODand C. AKITT. G. J . Data for Fig. (The uncertainties reflect the uncertainty in AH:(g).006 M-' for acetic acid plus methanol were obtained. Chem. Can. I thank Dana Zendrowski for technical assistance. VOL. the free energies of transfer from the gas phase to aqueous solution can be calculated: HCIO. dAverage AG" per step based on AGrOvalues. CA.) These values are much more + + 1 . 32. l Freeman. 2275 (1968). D. A.. 3. CHEM. PAULING. A m Chern.J . G. D. Phys.2352 C A N . J.001 N aqueous HCI.J . 99. 1978 TABLE5. GUTHRIE.21 4 kcal mol-'. DUERST. Phys. 65. Chem. 127 (1960). 2. LIBROVICH. 3 PK~ AG"" Can. 1°9(1948). 1947. 47. G. LILLEY. M.122 0. 2 : (0) previously reported in ref. 12. G.2 (1945).3991 (1977). 8. L . Soc. B. MAIOROVand N. J . *Reference 2. 56. Am. Chern. J. (a) R. 2047 (1938). Phys.nrcresearchpress. HOODand C. YOUNGand J. Sot. 53. A. 9. 1295 (1973). Chern. W. VINNIK. -7. Equilibrium constants for ester formation in water at 25°C were determined by nmr analysis as previously described (83).015 M-' for formic acid plus methanol (lit.19 2 kcal mol-'. Z. J . Faraday Soc. REILLY. FREEMAN.J . 4. corrected for steric and symmetry effects. LIBROVICH. Soc. 42. Acta Chern. J. E. J. 47. 199 (1972). Chern. Am. D. 2nd ed. (b) C. I V . C. 68. and H. CHARLOT and B. Soc. 3777 (1971). 18.J.CATCH tables for silicon 63. 1198 (1958). V.)Circ. KIRBY and M. PEDLEY compounds. G. 353 (1947). 23. l(1960). 30. and G. J. Chern.J .78. DENNIS. 76. E. SCOTT. Am.729 (1969). Chern.J. H. I 31. 2nd ed. J . 30. 3293 (1960). Scand.S.com by UNIV GUELPH on 10/16/14 For personal use only. 2537(1950). K. 618(1976). I . S. P. 1750 (1962). E . KIEHLMANN. McGraw-Hill. 59. (1964). A. GILLESPIE. R.Tetrahedron. Phys. 78. I. Chern. W. 40. R. Soc. B. 727 (1970). D. M. 20. G. B. 83. 52. A. 1969. Am. BRANCH. Czech. Chern. OLDHAM. Chern. SMITHand A. Plenum Press. 39. J. 62. DESSEIGNE.. Amsterdam. W. BRUCKENS~EIN and I . Mern. 1 . Vol. Vol.. P. J. 29. p. J.917(1970). New York. J. G. 608. SOC. BRUCKENSTEIN. OGG. COVINGTON and R. S. 1976. Chern. J. and L . Chern. Vol. Phys. Chern. J .J. Downloaded from www. R. 141 (1953).Natl. 50. University of Sussex. TULCHENSKII. New York. 64. Soc. 1. Acta Chern. NY. 32. W.J . MARTIN Chern. SCOTT. London. Tr~it~slated by P. 66. J. PARKE and W. 34. F. POPEIKIN and A. H. Prentice Hall. 5 3 . F. G. 4 4 . Chern. B. Chern. J. OH. 66. M. ANNESSA. ~ J. A. RAY and R. LEVITT. J. W. J .Therrnochernical kinetics. THOMPSON. GERSHON. J. A. 2092 (1958). Chern. KO and R. 546 (1958). D.I. ALBERTand E. L. ROBINSON. 85. BUNTON. ( a ) A . W. H.K. Chern. W. 95. Chern. JENCKSand J . J. 51 1 and 533. 1969. ROBERTSON. BERKHEIMER. M. Soc. W. W. E. MEHROTRA. Soc. B. 83.Catalysis In chemistry and enzymology.. G. Chern. Soc. Am.Anal. 1952. Fr. p. J.213(1967).nrcresearchpress. KEVILLand A. D. H. D. Chern. E. Chern. 84. 0. . 1962. C. LEWIS. C. Inorg. MARTELL. Acta Chern. Pergarnon Press. (a) Ser. J. 2924 60. 27. p. VERNON. Soc. Recl. Oxford. A. 267. Soc. 55. M. D. MORTIMER. Soc. B. Chern. S .757 and C. R. G. L. New York. Geochern. A. 500(1952). PILCHER. E . McGraw-Hill. 1. Can. Chern. 63. R. 45.55 (1970). and G. CHARTON. M. KLUEPPEL.5083 (1971). S. Chirn. 53. E . C. Engelwood Cliffs. J.435(1966). SWANICH. LEVITTand B. Can. NJ.99(1967). and C . HALLand E. Ithaca. E . GILLESPIE. Organornet. 9 4 7 (1961). Chemical reactions in solvents and melts. 51. BESSIERE. DAVIS.K. Soc. DIPPYand F.Catalysis in chemistry and enzymology. Am. 52. Int. 4. Chern. 1 . EVANS. 44. 1972. F. FERSHT. Ryss and V. Cornrnun. P.The proton in c h e r n ~ s t ~2nd y . Chern. Am. H. 1 1 13 69.39220d (1970). Chern. 1st ed. Stand. Cornell Unlversity Press. J. C. T .and E. Buss. (a) W. The oxidation states of the elements and their potentials in aqueous solution. N. R. WILKINS. P. J. E. R. COFFEY(Editor. Phys. stants.. Can. Trotrnan-Dickenson. ( b ) A . 24. Chem. 1969. 74. ed. 1596(1959). KOLTHOFFand S. Chern. 709 (1903). J.Ind. Chern. and W. J. O'NEALand M. 1 I72 (1970). Soc. 27. 1855 (1971). 11. T . 29. GRAYand P. G. 4. J. Sci. (b) Ser. Soc. (U. HOGFELDT. J. 35. J. and E. J. 2025 (1953). J . TANG. S ~ N I O R Can.In Comprehensive inorganic chemistry. 191. H . l(1956). R. CERFONTAIN and B. NY. 26. Chem.J.517(1947). 603 (1974). and J. (b) D. KIRBY.15. Soc.2210 (1953). J. H.J. S. Chern. L. Akad. and W. Abstr. R. Eng. Scand.L. DOAK. J. 93. 23.D.J. SOC. ROBERTSON. E. K. Soc. ROSSINI. 42. Chern. SERJEANT. J . P. A. Soc. J. D.M. . SMITH. J. T. 54. PRICE. GRIFFIN. 5 . J. 73. ROBINSON. 1968. (1976). R. 48. SCHNITGER. Soc. JR. 1973. Academic Press. D. A. Soc.59(1948). Scand. p. 80. WANG. Chern. W. N. 65. RUSSELLand J . McGraw-Hill. 6 . RAY and A. J. K. Cornrnun.785 (1963). Chem. ROGNE.434 (1972). 17 Can. S W A I Nand C. H. 26. ISAND. A. Vol. B E S S I ~ RBull. 1970. Wiley. WARDLAW. J. 1222 (1964). Chern. Chern. 93. D. 11. Solution Chern. Phys. Vol. pp. C. 29. A. PEEL. C. P. p. STULL. S K I N N E RJ. 55. 85. K. Chern. BRADLEY. 1259 (1973). 81.J. Am. R. 2. ROBERTSON. 91. Data. T . Chern. ROGNE. NY. M. NAGMAN. HINZE. A. S. R. Chern. Chern. 1976. Trav. Acta. D. 25.Therrnochernistry of organic and organornetallic compounds. H . S. S.). N.J. Soc. J. Handbuch der organischen Chernie. N. BENSONand J. Soc. 75. JENCKS.I n o g . ANDERSON. 57. B. J. ELAGGAN. Pergarnon Press. J. Am. 148 (1963). Vol. B. 1 28. CHARNLEY. Soc. 90. WEBSTER 3233 (1933). GUTHRIE. V. Sober (Editor). C . B. Ionization constants of acids and bases. A. NY. Brighton. 2974 (1956). In Handbook of 72. Eng.2380(1953).642 (1954). (1974). 36. E. W. JAFFE. Chern. Oxford. Chern. TAFT. NY. Org. Am. (c) S h . J. R. DINIUSand G. P. R. 3356(1969). J. biochemistry. Soc. 41. B E S S I ~ RBull. T . Coll. WILLIAMS. 42. 0. Nauk SSSR. 71. Chern. 3. 161 (1934).292 (1964). RYZHENKO. BENSON. 43. J .78. J. A. M. H. 81. KONTTINEN. S . LATIMER. 17. HAYESand G. HORYNA. C. 39. Chern. 1165 (1970). M. OLDHAM. 1965. New York. J . DENOand H. K. KRESGEand Y. H I N Eand A. Chern. 3 106(1975). BUNTON. Chem. J. 21. 50. 19. A. C. 4. D. Chemical Rubber Publishing Co. 46. TREMILLON. H. Soc. Cleveland. SOC. R. Soc. 272 (1941). 57. Elsevier. E.Can. C. JAFFE. WARDLAW. A.J . 77.202(1976). A. E . Prog. Chern. p. 1973. D. Chern. WHITEHEAD. SALOMAA. S K I N N E RJ. YOUNAS. Org. Edited by A. 96. 73. Catalysis in chemistry and enzymology. B. 52. 5. poudres. BRADLEY. J. NY. Harvey. GUTHRIE. 3353 (1969). 3574(1958).3562(1977). 61. NY. 0 . Chern. and I . 1969. J. Chern. 56. 1 .Chern. A. CHOPPIN. W. STREITWIESER. P. 24. New York. REGENSTEIN. JR. BEILSTEIN. Methuen. A. MHALA. Am. 1181 (1953). 1. 75. Anal. (a) D. 49. KOLTHOFF. M. 1598 (1968). 66. Soc. Org. MIKHAILOV. FREEDMAN. 7 2 2 1 (1950). 2nd ed. Can. Abstr. J . F. p. 54. J.J . 2975 (1974). 33. 67. K H A Nand A. Vol. Org. T. V. and B. 55. DAVIS. J. JAFFE. A. SMITH. W. Chirn. A. Phys. W. VERNON. 58. GUTHRIE. 1 1 1 . Am. D. and H. P.3504 (1971). p. Am. Chern. Chirn. 37. FLITCROFT and H. P. and C. 1459 (1969). Chern. Cox and G. Rodd's chemistry of carbon cornpounds.6999 (1973). BELL. 16. J. (d) Ser. Am. 271 (1941). Chern. JENCKS. R.268 (1962). 65. New York. 22. 38. C. LLEWELLYN. J. E. Bur. 82. J. RING. 1. (c) S. RUSS. Dokl. Chern. Fr. 0 MXKITIOand V.J . JENCKS. 1522 (1959). LEIMER and P. FOX. LEVINE. Critical stability con75. 79. 3355 (1956). 1555 (1943). 70: E . HELGESON. M.S. 1 B. and tricoordinate arsenic were needed.78 . 'Estimated as described in the Appendix. For the cases of dimethyl sulfate a n d tetraethyl orthosilicate it was necessary to draw the best lines through plots of In p vs.77 Can. and EA is a correction for hydrogen bond formation between solute and water. 'Calculated as described in the text. EAwas assumed to be equal to the value calculated from the solubility and parachor for the analogous orthoester.01 3P . hThis work. type. VOL.5' -3. only the boiling point at atmospheric pressure was available so that it was necessary to estimate the vapor pressure using the heat of vaporization (60) and the heat capacity of vaporization taken as .' mol. 1/T based on data from ref.79 -1. J.5' 0. using C H ( O C H 3 ) (65) ~ as the model for evaluating the effect of hydrogen bonding. This method is based upon a relationship between solubility and the parachor expressed as log (cI/c2) = 0.0096* 1 .EA where c. see Experimental.5. RInterpolated from a plot of In p vs. or HC(OR). Estitnatio~of Solubilities Since many of these inorganic esters hydrolyze rapidly. Chem.13.78 -0. using C(OCH2CH3)4(2) as the model for evaluating the effect of hydrogen bonding. P is the parachor of the solute.5gh 0.nrcresearchpress. and AsF.B (CH3CH20)4Si (CH3O). and AsC1.) and are . respectively.35' 3. I n the case of dimethyl carbonate. these were calculated from the available entropy data (51. and BF.36* 9. cCalculated from the equation relating log p to T given in ref. CHEM.12 cal deg-I mol-I (546). 52) but in some cases no parameters were available and it was necessary to employ the atomic contributions scheme (51). For each inorganic ester of the M(OR). Free energies of transfer from the gas phase to aqueous solution Compound (MI Vapor pressure (Torr) AGt (kcal mol-I) (CH3O)zSOz (CH30)3As (CH.CAN.. 53) (for perchloric acid. with the same R and n. 61. 39.7.. c2 is the molar solubility in water. bCalculated by extrapolation of a line through vapor pressure data from Beilstein (806 and c)..22" 1. wherever possible this was done using bond contributions (51. Downloaded from www. . Parachor values were calculated from density a n d surface tension data found in Beilstein.92" 61.CO 0. it is not possible to determine their solubilities experimentally. dCalculated from the equation relating log p and T given in ref.'. For this purpose terms for tetracoordinate chlorine.. 1/T (in the case of tetraethyl orthosilicate using only data at low pressure) and so estimate the vapor pressure at 25'C. 56.O). is the concentration of the liquid solute in itself.35.20 -2.com by UNIV GUELPH on 10/16/14 For personal use only. The vapor pressures are found in Table 6.1. tricoordinate boron. 81. Solubility EReference 80.3. Estimation of Vapor Pressures The vapor pressures of the esters were taken wherever possible from published equations relating log p to T. and . 454 132' 1 . Solubilities were estimated employing a modification of the method of Deno and Berkheimer (54). BCl. 1978 TABLE 6. The solubility values so estimated are found in Table 6. J. C(OR). . this was done using the additivity schemes proposed by Benson and Buss (51). CCalculatedas described in the text.2 cal deg. Appendix Estimation of Entropies Standard entropies for the gaseous esters had to be estimated in most cases.