Acid-base equilibriums in dipolar aprotic solvents - Analytical

vents has been used with correct results for the identification of synthetic food dyes in cakes. This result proves that the technique presented here allows classification of chromatographic systems into groups or genera with similar characteristics, and that a combination of well-chosen individual systems from the different groups is a rational way of selecting an identification method. As noted above, it is not impossible that careful visual inspection of the data would allow the same result to be obtained. I t should be kept in mind, however, that the example given here uses a relatively small data set. For really large data sets and particularly for sets in which the number of possible combinations is high, the visual method is out of the question. The combination of the numerical taxonomy classification and calculation of the information content is an example of a recent trend in analytical chemistry-ie. the tendency to try and obtain a more formalized view of analytical chemistry (see also the already cited articles on system analysis, information theory, and operational research as applied in analytical chemistry). One of the principal aims of developing such an overall view is to develop methods that allow a rational choice among the various options which are usually open to the analytical chemist who has to elaborate a complex analytical procedure or program. I t is the belief of the authors that such an approach may prove

particularly valuable in separation chemistry, where the number of possible combinations and schemes is sometimes enormous. An application in which numerical taxonomy was used with success is the classification of 226 stationary phases for gas-liquid chromatography (see also introduction). The results will be published elsewhere (21). A warning against overbelief in these methods is in order: they always represent a simplification of reality. The analytical chemist should retain, therefore, the possibility of using his own judgment. The numerical taxonomy classification allows this.

ACKNOWLEDGMENT Discussions with A. Dijkstra and his collaborators and with members of the Nederlandse Studiegroep voor Laboratorium Optimalisering were very helpful. The authors also thank N. Harford for help in the redaction of this article.

RECEIVEDfor review February 8, 1974. Accepted July 8, 1974. The authors thank the Fonds voor Fundamenteel Wetenschappelijk Onderzoek for financial assistance. (21) D. L. Massart, M. Lauwereys, and P. Lenders, J. Chromatogr. Sci., in press.

Acid-Base Equilibria in Dipolar Aprotic Solvents' 1. M. Kolthoff Department of Chemistry, Universityof Minnesota, Minneapolis, Minn. 55455

A classification of organic solvents is proposed. The main emphasis is on the effect of homo- and heteroconjugate formation by hydrogen bonding on acid-base equlllbria and on conductomelric and potentiometric tltration curves in dipolar aprotic solvents. The relation is discussed between resolution of acid strength and transfer activity coefficients of ions and molecules. A brief review is presented of analytical uses of protophobic solvents for the titration of very weak bases and of protophillc solvents for the titration of very weak acids.

In this review are considered acid-base equilibria which are fundamental for an understanding of titration curves of acids and bases in dipolar aprotic solvents of intermediate dielectric constant ( e of the order of 40). In such solvents, tetraalkylammonium salts in dilute solutions ( c of the order of 0.01M or less) can be considered to be completely ionically dissociated. There are several good books in which detailed procedures for nonaqueous acid-base titrations are presented (1). In this connection, reference is made This review is based upon a lecture at the ACS meeting before the I. M. Kolthoff 80th Anniversary Symposium in Los Angeles, April 4, 1974. (1) (a)J. S. Fritz, "Acid-Base Titrations in Nonaqueous Solvents," Allyn and Bacon, Boston, Mass.. 1973; (b) I. Gyenes, "Titrationen in nichtwasserigen Losungen," F. Enke Verlag, Stuttgart, 1970; (c) see also "Titrations in Nonaqueous Media" in Anal. Chem., Fundamental Reviews, 1964, 1966. 1968, 1970. 1972, 1974.

1992

only to a recent comprehensive monograph by Fritz ( l a ) in which essential theory and practical applications of nonaqueous acid-base titrations are described with references to the literature. In our own work, Dr. M. K. Chantooni, Jr., and I have concentrated on the derivation of expressions for acid-base equilibria in the above type of aprotic solvents, as this type of solvents is being used more and more generally in analytical procedures. A subdivision of this type of solvents into two classes is given in the following section. A separate section is devoted to a discussion of hydrogen bonding, as this kind of reaction plays a major role in nonaqueous acid-base equilibria. Classification of Organic Solvents. Brinsted (2) proposed a classification of organic solvents and distinguished between 4 types on the basis of their acid and basic properties. Davis ( 3 ) extended the Brdnsted classification and distinguished in each class between solvents with a dielectric constant, e , greater and smaller than 20. Hence, she has 8 classes in her tabulation. She specialized on equilibria in inert solvents of low dielectric constant in which ionic equilibria are quite involved. Since it is difficult to memorize which type of solvents belongs to a certain number, it is preferable to refer to them by name and not by number. This has been done in the classification in Table I. No clas(2) J. N. Br@sted, Chem. Ber., 61, 2049 (1938). (3) (a) M. Maclean Davis, "Acid-Base Behavior in Aprotic Solvents," Nat. Bur. Stand. (U.S.) Monogr., 105, Washington, D.C., 1968; (b) "The Chemistry of Nonaqueous Solvents," Vol. 111, J. J. Lagowski, Ed., Academic Press, New York, N.Y., 1970.

ANALYTICAL CHEMISTRY, VOL. 46, NO. 13, NOVEMBER 1974

Table I. Classification of Organic Solvents Type no.

Neutral

) Protogenic Amphiprotic \

Dipolar Protophilic

Aprotic

Dipolar Protophobic Inert

a

€0

Relative

Relative

acidity b

basicityb

ila

+

+

+

lb

-

+

+

(2a

+

1

Examples a

water (78), methanol (33), ethylene glycol (38) tevt -butanol ( l l ) ,cyclohexanol (15)

++

++

k

-

HzSO,, H F , HCOOH (58) HAC (6)

i

*

++

N-methylacetamide (165), DMSO (46), tetramethylurea (23), formamide

(3b

-

+

++

ethylenediamine (14), tetramethyl guanidine (11.5). NH, (17)

4a I4b

+

-(*I

I

-

-

++(+I

j 5a

4-

- (*)

-

(5b

-

-

-

5c

-

-

-

1%

*

(100)

DMF (36). DMSO (44) pyridine (12), dioxane (2), t e t r a hydrofurane (7). e t h e r (4) n i t r i l e s , [acetonitrile (36)]. ketones, acetone (21), nitromethane (36) methyl isobutyl ketone (12), methylethylketone (17) aliphatic hydrocarbons, CC1, (3), benzene (2), etc.

+ under c means dielectric constant greater than 20. Numbers between parentheses in the column "Examples"

f indicates considerably weaker and

++ indicates much stronger acid or base than water.

sification is perfect, and this is the case also with the proposed one. We adopt Bransted's terminology amphiprotic to signify that the solvents have both acid and basic properties. The prototype is water, and we call solvents which have similar acid and basic properties as water has, neutral solvents. Solvents much stronger acids and much weaker bases than water are protogenic and those much stronger bases and much weaker acids than water are protophilic. The difficulty in this classification is that it is impossible to draw a sharp line between solvents which are aprotic and those that are protic. In the literature, solvents with extremely weak acid properties are often referred to as aprotic. A critical reader may ask why classify solvents like ammonia and ethylenediamine as protophilic amphiprotic and a protophilic solvent like N-N-dimethylformamide (DMF) as aprotic. It seems reasonable to call solvents which have a stable lyate ion amphiprotic a n a others aprotic. On this basis, dimethylsulfoxide (DMSO), which forms a stable lyate ion called dimsyl ( 4 ) , should be classified as protophilic amphiprotic. However, in the literature, DMSO is often referred to as aprotic, and to avoid confusion with the literature we will discuss acid-base equilibria in this solvent under aprotic solvents. In this respect, it is of interest to add that solvation of cations and anions is similar in amphiprotic protophilic and dipolar protophilic solvents. Davis' class 8, called aprotic by her, we denote as "inert" soloents, acid-base properties of hydrocarbons and halogenated hydrocarbons being hardly demonstrable, their dipole moments being zero (pure hydrocarbons) or small (several halogenated hydrocarbons) and their dielectric constant usually considerably less than 10. Thus, we distinguish between amphiprotic (neutral, protogenic, protophilic), dipolar aprotic (protophilic, protophobic) and inert solvents. Examples in each class are given in Table I. Hydrogen Bonding. Homo- a n d Heteroconjugation. (4) G.C. Price and M. C. Whiting, Chem. Ind., London, 775 (1963).

refer to the value of

c.

Hydrogen bonding is an important self-association (autocomplexation) reaction of solvent molecules in amphiprotic solvents and association of solute anions and molecules with solvent or solute in all solvents. There exists a very extensive literature on hydrogen bonding (5-8 ). According to the simple valence theory, the hydrogen atom is univalent but, in hydrogen bonding, it is formally divalent. Atoms in compounds B with electronegativity greater than hydrogen have the capability of forming AH- - -B hydrogen bonds, in which B has an unshared pair of electrons (base) and is the hydrogen bond acceptor, AH being a Brdnsted acid and the donor. AH may also act as a hydrogen bond acceptor, e.g., water and alcohols. Atoms with electronegativity greater than hydrogen (2.1) are F (4.0), C1 (3.0), N (3.0), C1 (3.01, Br (2.8),I ( 2 . 5 ) , and Se (2.4). The numbers refer to Pauling's electronegativity scale (9). In "neutral" amphiprotic solvents like water, alcohols, there is considerable association (polymerization) of solvent molecules by hydrogen bonding, the solvent acting as a hydrogen bond donor and acceptor.

The structure of water is quite involved and incompletely understood. In mixtures of water and alcohols, hydrogen (5)

G.C. Pimentel and A. L. McClellan, "The Hydrogen Bond," W. H. Free-

man, San Francisco, Calif.. 1960. (6) D. Hadzi and W. H. Thompson, "Hydrogen Bonding," Pergamon Press, Oxford, 1959. (7) W. C. Hamilton and I. Ibers. "Hydrogen Bonding in Solids," W. A. Benjamin, New York, N.Y., 1968. (8) P. A. Kollman and L. C. Allen, Chem. Rev., 92, 283 (1972). (9) L. Pauling, "The Nature of the Chemical Bond," 2nd ed., Cornell University Press, Ithaca, N.Y., 1940, p 60.


1993

bonded complexes of both species are present. Solutions of water in inert solvents contain mainly intermolecular hydrogen-bonded water molecules and, to a minor extent, water hydrogen-bonded to the solvent if the latter has weak basic properties, like benzene (10).Self-association of alcohols in nonpolar solvents has been studied by Fletcher and Heller (11). However, when the solvent is a poor hydrogen bond donor orland acceptor, water or alcohols as solutes can be present as monomers. For example, Muney and Coetzee (12) concluded from spectrophotometric studies that, in acetonitrile, water is monomeric to a concentration of about 1M. Solubility of water in nonmiscible inert and other types of protophobic solvents which also contain a hydrogen bond donor or acceptor can be greatly increased by hydrogen bonding, and equilibrium conditions then may become quite involved. For example, the solubility of water in inert solvents is increased by carboxylic acids, and hydrogen bond complexes between water and acid are also formed. Salts with a large organic cation ( e . g . , tetraphenylarsonium) and small anion with a localized charge (e.g., chloride or carboxylate) increase the solubility of water in nonmiscible inert solvents because of hydrogen bonding of water with the anion (hydration). These types of reactions are especially important in the interpretation of extraction analysis and of the effect of water and alcohols on the pH of mixtures of an acid and its salt in polar protophobic solvents (uide infra). Quite generally, it is safe to assume (13) that all proton transfer reactions take place along a hydrogen bond with the proton forming a full bond to one base as it breaks its full bond to another. Thus, we can assume that the "simple" dissociation of an acid of any charge type in a solvent S (base) occurs with the intermediate formation of a hydrogen bond complex; e.g., for an uncharged acid: AH

+

S

e AH---S

T--* A----HS'

A-

+

3

SH'(so1vent is base) (2)

S H + can hydrogen bond with S to form SH+- - -S,the solvated protons H,+. Especially in an amphiprotic solvent, HS, several molecules of HS can be added by hydrogen bonding to SH+- - -(SH),. For example, in water the proton is present mainly in the form of H+(H20)4. Quite generally, in all protophilic solvents, the proton is strongly solvated by hydrogen bonding. In water and alcohols, the solvated proton distinguishes itself by a very high mobility in an electric field. In an oversimplified way, this is accounted for by a jumping (transfer) of the proton from one water molecule to another. A lyate ion like OH- in water, -0CH3 in methanol, is also hydrogen bonded to the solvent and has a high mobility compared to that of other ions. The high mobility of the proton in alcohols is greatly decreased by even very small amounts of water by the formation of H30+ (and H+(H20),(ROH),). The stability of the solvated proton increases with basic strength of the solvent. For example, the stability of the solvated proton in various solvents decreases in the order ammonia, ethylenediamine > pyridine > dimethylsulfoxide > water or alcohol > acetone or acetonitrile > sulfolane or nitromethane. Weak acids, HA, like carboxylic acids, phenols, are stabilized by hydrogen bonding in solvents which have basic character. The stability of such acid solvates in different solvents decreases in the same order as that of the solvated proton. The order of acid-base strength in the gas phase often is quite different from that in a solvent. For example, (10) See e.g., L. Odberg, A. L. Lofvenberg, E. Hogveldt, and F. Fredlund, J. horg. Nucl. Chern., 34, 2605 (1972). (1 1) A. N. Fletcher and C. A. Heller, J. Phys. Chem., 71, 3742 (1967). (12) W. S. Muney and J. F. Coetzee, J. Phys. Chem., 86, 89 (1962). (13) J. Hine, J. Amer. Chern. SOC.,94, 5766 (1972).

1994

Table 11. K f ~ * *in - AN, DMF, a n d DMSO Acid

AN (15)

Acetic Benzoic Salicylic

5 x 103 4 x 103 2 x 103

DMSO (E)

DMT (16)

-3 x 10'

4 x 102

2 . 5 x 10'

-6 x 10'

-3 x 101

in the gas phase, toluene is a stronger base than water. Quite generally, hydrogen bonding is especially important in inert solvents and the overall equilibria may become quite involved: HA

+

B

AH---B

A-HB* 3 A-

+ BH'

(2a)

In solvents of low dielectric constant, interionic reactions with formation of ion triplets and quadruplets make the equilibria even more complicated. A lucid discussion of acid-base interactions in inert solvents is given by Davis ( 3 ) .The equilibria are much simpler in dipolar aprotic solvents with a dielectric constant greater than about 20 than in inert solvents. Even in solvents which are very weak bases, like acetonitrile, acetone, sulfolane, nitromethane, hydrogen bonding with acids is strong enough to make dimerization of acids very small and virtually negligible in dilute solutions. Particularly in these protophobic solvents hydrogen bonding between an anion A- and its conjugate acid HA has a large effect on the shape of titration curves: A'

+ HA

f A----HA

+ nHA

9 A-(HA),,,

(3)

Hammett and Van Looy (14) were among the first to recognize this type of complexation of anions in a solvent which is or is not a very poor hydrogen bond donor. The complex HAa-(or A-(HA),+l) has been called a homoconjugate, while hydrogen bonding with a nonconjugate acid HR has been called heteroconjugation (15): A-

+

HR

(4 )

A----HR

Formation constants of homo- and heteroconjugates are much greater in protophobic than in protophilic aprotic solvents. The latter are stronger bases than the former and form stronger hydrogen bond complexes (solvates) with HA (or HR) than the protophobic solvents do. Thus in any solvent there is competition between reactions 3 or 4 and 5 A----HA(HR)

+ s a S---HA(HR) +

A-

(5)

For the sake of simplicity only one HA(HR) is written, but more than one molecule HA(HR) often participates in the conjugation reactions (A-- - -(HA)2, etc.). An illustration of the difference in values of the formation constant K f ~ a , in a protophobic solvent, acetonitrile (AN), and two protophilic solvents, dimethylformamide (DMF) and dimethylsulfoxide (DMSO) is presented in Table 11. In nitrobenzene, homoconjugates are more stable than in the stronger base acetonitrile. Pawlak ( 1 7 ) reports the following values for K f ~ ~X, 21, 8.7, 0.14,0.10,0.10, 7.7, and 0.30 of dichloroacetic, monochloroacetic, diphenylacetic, phenylacetic, acetic, 3,5-dinitrobenzoic, and benzoic acids, respectively. Heteroconjugation with chloride ion of carboxylic acids and phenols is pronounced in protophobic (14) H. van Looy and L. P. Hammet, J. Arner. Chern. Soc., 81, 3872 (1959). (15) I. M. Kolthoff, M. K. Chantooni, Jr., and S. Bhowmik, J. Amer. Chern. SOC., 90, 23 (1968). (16) I. M. Kolthoff, M. K. Chantooni, Jr., and H. Smagowski, Anal. Chem., 42, 1622 (1970). (17) 2.Pawlak, RocznlkiChern., 48, 249 (1972) (in English).


ple, values of Kfl for the equilibrium constant of the reaction

Table 111. Hydrogen Bond Accepting Properties of Anions Expressed by Kfl (for n = 1) in Methylene Chloride [Taylor a n d Kunz (23)] Anion

Phenol

10 16 400 >5,000

BFdc10,c1-

so4*-

nAH

*4

... 4*1 25 + 2 >5,000

solvents. In AN, the following values are reported for K f ~ ~ c and 1 - Kf2(H,4)C1-:acetic 3.5 X lo2 (18);benzoic 1.6 X lo2, Kf2 1.2 X lo2 (19); 3-nitrobenzoic 3.9 X lo2, Kf2 1.2 X IO3 (19); salicylic 5 X lo2,Kf2 1 X lo2 (20); 4-bromophenol 2.4 X lo2, Kf2 1.8 X lo3 (21). In acetone, Pawlak (17) reports K f ~ ~ c Xl 50, 6.7, 3.2, 2.4, 1.0 for dichloro, monochloro, diphenyl, phenyl, and acetic acid, respectively, while in the much weaker base nitrobenzene Kf~*c1-of 5.8 X lo6 was found for dichloroacetic acid. In DMSO the values of Kf~*c1-of substituted acetic acids are of the order of 1 or less. In a given acid series, the stability of the 1:1 chloride heteroconjugate increases with increasing acid strength of HA. In fact, linear Hammett plots of log us. a were obtained for non-ortho substituted benK zoic acids in acetonitrile (AN) (19). On the other hand, only a slight increase in K f ~ ~ in, -AN was found with increasing acid strength of HA as basic strength, and therefore hydrogen bond accepting capacity of A- decreases. Quite generally anions with a localized charge form stable homo- and heteroconjugates with hydrogen bond donors in aprotic protophobic solvents, the stability decreasing with basic strength of the solvent. On the other hand, conjugation becomes very small for ions with a delocalized charge where there is a dispersion of the charge comparable to resonance, presumably by London dispersion forces (22). This, for example, is the case with picrate and 2,6-dinitrophenolate ions: f

~

~

~

~

+ B-

E (AH),---B-

(6)

Water

-

in which n is the number of proton donor molecules and Ban anion in methylene chloride, are presented in Table 111. These various constants were determined by Taylor and Kuntz (23) using infrared and NMR techniques, with phenol or water as hydrogen bond donors. As was to be expected, phenol is a stronger hydrogen bond donor than water. Hydrogen bonding has a large effect on the properties of a salt composed of an ammonium ion and an anion with a localized charge. When the base or the acid, or both, are too weak to give rise to proton transfer in an inert solvent with formation of an ion pair, they react in an inert solvent with formation of a hydrogen bonded complex AH- - -B. As shown by Yang and Taft (24) by lgF-NMR and pH measurements, the extent of ion pair formation of amines and other very weak bases with the strong acid p-fluorobenzenesulfonic acid in methylene chloride is of the same order as that of the dissociation constants of the amines in water. On the other hand, the extent of hydrogen bond complex formation in CH2C12 between the above series of bases with the relatively weak acid p -FCsH*OH is not directly related with basic strength in water, strength of hydrogen bonding apparently also depending upon acid and/or base structure. The ionic dissociation of an ion pair R3NH+- - -A- composed of an ammonium ion and an anion with a localized charge is counteracted by intermolecular hydrogen bonding R$T"H---A-

__

R3NH'

+ A-

(7)

In isodielectric solvents, this dissociation increases with increasing basicity of the solvent, the base solvent competing with the base A- in being hydrogen bonded to R3NHf. For a salt, like triethylammonium 3,5-dinitrobenzoate (Et3NH+A-), the ionic dissociation constant K d in acetonitrile (e = 36) is 1.2 X ( 2 5 ) (25O), while in DMSO ( t = ,- ,' 0 ' \ \ 44), the salt is practically a strong electrolyte, the latter sol4 N m 0 2 vent being a good hydrogen bond acceptor for R3NH+. On purely electrostatic grounds alone, the dissociation constant of an ammonium salt of a homoconjugate anion is The homoconjugation constant of the picrate ion, K f ~ ~ , - , much greater than that of R3NHfA-. Thus, in AN, as compared to 1.2 X lop5 for K d ~ t 3 " + ~ ~ ,is- 3.0 X in acetonitrile is only about 2 (16), and of 2,6-dinitrothe unconjugated 3,5-dinitrobenzoate (25). No hydrogen phenolate, close to zero. From an analytical viewpoint, conbonding, and therefore no stabilization, occurs between a jugation of such acids and anions is negligible. Use of this is tetraalkylammonium ion and an anion, e.g., K d of tetraethmade in the preparation of well buffered solutions of ylammonium 3,5-dinitrobenzoate in AN being 5 X mixtures of picric acid and tetraalkylammonium picrate for For a salt with a given anion which is a poor hydrogen bond the calibration of the glass electrode in dipolar aprotic solacceptor K d appears to be of the same order of magnitude vents. Visually the effect of homo- or heteroconjugation for primary, secondary, and tertiary ammonium salts. For can be strikingly illustrated with tetraethylammonium example, Kraus et al. (26) report in nitrobenzene ( t = 36; a 3,5-dinitrophenolate. A dilute solution of this salt is red in protophobic aprotic solvent) for pKd of the picrates of acetonitrile but turns yellow upon addition of very little of NH4+, BuNH3+, Bu2NH2+ and Bus"+ values of 3.84, the free acid (homoconjugate) or p-bromophenol or with 3.83, 3.81, 3.72, respectively. In solvents of low dielectric less sensitivity water or methanol (heteroconjugation). The constant (inert solvents, methyl isobutyl ketone) concenhydrogen bond accepting capacity of inorganic univalent trations of unconjugated ion pairs can be very large. In ions is usually in the order of the so-called Hofmeister sebenzene as a solvent, Davis (27) reports a formation conries. Quite generally, divalent anions in which the charges stant of 15.5 for the ion pair RNH3+- - -BPM-E- (bromoare at close distance from one another are much stronger phthalein magenta E) hydrogen bond acceptors than univalent ions. As an examM. K. Chantooni, Jr., and I. M. Kolthoff, J. Phys. Chem., 77, 527 (1973). M. K. Chantooni and I. M. Kolthoff, J. Amer. Chem. Soc.. 92, 7025

(1970). I. M. Kolthoff and M. K. Chantooni, Jr., J. Amer. Chem. SOC., 93, 3843

(1971). I. M. Kolthoff and M. K. Chantooni, Jr., J. Amer. Chem. SOC., 91, 4621

(1969). E. Grunwald and E. Price, J. Amer. Chem. Soc., 86, 4517 (1964).

(23)R. P. Taylor and I. D. Kuntz, J. Amer. Chem. SOC.,94,7963 (1972). (24)H. B. Yang and R. W. Taft, J. Amer. Chem. Soc., 93, 1310 (1971). (25)I. M. Kolthoff and M. K. Chantooni, Jr., J. Amer. Chem. SOC., 85, 426 ( 1963). (26)C. R. Witschonke and C. A. Kraus, J. Amer. Chem. SOC., 69, 2472 (1947). (27) M. M. Davis and H. B. Hetzer, J. Res. Nat. Bur. Stand.. 46, 496 (1951).


1995

8‘

BT

0

COOC,H,

Homoconjugation can even occur in neutral (amphiprotic) solvents, like water and alcohols; however, K f ~ ~ is, very small. The increase of solubility of benzoic acids in fairly concentrated aqueous alkali benzoate solutions (“salting in”) has been attributed to homoconjugation (28, 29). The degree of dissociation of salts, BHA, of cationic acids in general also increases (slightly) in protophobic aprotic solvents (AN) by homoconjugation of BH+ with the free base: BH’ -t B

--+

BH’---B

(8 )

Formation constants K f ~ 2of~ a+number of aliphatic and aromatic amines in AN have been determined by Coetzee e t al. (30).Values of K ~ B , H + in general aie smaii, for noiisterically hindered primary and secondary aliphatic amines of the order of 20, for sterically hindered secondary amines 5 to 0, and zero for tertiary amines. Values of Kfg,H+ of aromatic amines are smaller than those of aliphatic amines, e.g., 4 for pyridine and zero for aniline and p-toluidine. On the other hand, Morman and Harlow (31) reported very stable BzH+ conjugates formed with amine oxides in acetonitrile and sulfo!ane. Analytical use for standardization of acids and bases in nonaqueous media of stable salts of the type B2HC104 has been made by Alessi e t al. (32a)and by Busev e t al. (32b). A summary of properties of homoconjugate and heteroconjugate cations in inert and aprotic solvents is given by Davis (ref. 3, p 77 f f ) . Analytical Significance of Homo- and Heteroconjugation. In this section, illustration of the analytical importance of conjugation is confined mainly to acetonitrile (AN) as a solvent, which is a typical representative of a dipolar aprotic protophobic solvent with an intermediate dielectric constant of 36. Qualitatively, in solvents of the same class, like sulfolane, nitromethane, acetone, etc., the effects are similar to those in AN. Conjugation and Solubility. Consider the ionic dissociation of a slightly soluble ion pair M+A-:

with a solubility product KSP = a M + -CIA-. In the presence of HA or HR (an acid much weaker than HA), the equilibrium in Equation 9 is displaced to the right by homo- or heteroconjugation. From the increase in solubility, it is a relatively simple matter to calculate K f ~ ~ of, - K f ~ ~ knowing KSP and Kd of M+A-. For example, the solubility of potassium 3,ti-dinitrobenzoate (KA) in AN is 0.31 X 10-3M. In the presence of 0.006,0.01,0.019 and 0.347M HA (28)E. Larsson. Z.Phys. Chem., 153, 466 (1931). (29)I. M. Kolthoff and W. Bosch, J. Phys. Chem., 36, 1685 (1932). 130) , la\ ~ J., F. . Coetzee. G. R. Padmanabhan. and G. P. Cunninaham, Talanfa. 11, 93 (1964);(b) J. F. Coetzee and G. R . Padmanab-han, J. Amer. Chem. SOC., 87, 5005 (1964);(c) J. Phys. Chem., 69, 3193 (1965);(d) W. S.Muney and J. F. Coetzee, J. Phys. Chem., 66, 89 (1962). (31)D.H. Mormanand G. A. Harlow, Anal. Chem., 39, 1869 (1967). (32)(a) J. T. Alessi, D. G. Bush, and J. A. Van Allan, Anal. Chem., 46, 443 (1974):(b) A. I. Busev, 8. E. Zaitsen, V. K. Akisnov, Ya. Chelikhovskii, and F. Kopetski, Zh. Obshch. Khlm., 38, 534 (1968);English Translation, p 523. ~

1996

solubilities were found (25) of 2.45, 2.94, 4.52, and 7.4 X 10-3M, respectively. From these data, a value of K f ~ ~=, 1.7 x lo4 was derived. Carboxylic acids are extremely weak acids in aprotic solvents, like acetonitrile (AN), acetone, sulfolane, nitromethane, etc. This means that their anions are fairly strong bases, and it is a simple matter to titrate carboxylates in such solvents with perchloric acid (in a suitable solvent) as reagent. Alkali carboxylates are slightly soluble in aprotic protophobic solvents, the solubility being greatly increased by homo- or heteroconjugation. Thus, in AN alkali carboxylates have been titrated accurately with perchloric acid (in water-free acetic acid) by dissolving the salt in a little acetic acid and diluting with AN (33). Effect of Conjugation on Conductometric Titration Curves. Conductometric titration curves in an aprotic protophobic solvent of carboxylic acids and several other types of acids with an amine exhibit a pronounced maximum in the neighborhood of 50% neutralization when the acid-base reaction is quantitative or close to quantitative. Qualitatively the explanation of this shape of the curve is simple. In a previous section, it was mentioned that, because of hydrogen bonding, the dissociation constant Kd of an ammonium carboxylate, e.g., in acetonitrile, is very small, while that of its homoconjugate is several hundred times greater. The conductance of a carboxylic acid HA is practically equal to zero and increases sharply upon addition of an amine B as a result of the formation of BH+HA2- which is a strong electrolyte in AN. When the proton transfer between acid and base is quantitative and K f ~ ~is, large, the concentration of the homoconjugate salt has a maximum value at 50% neutralization and then decreases as a result of the formation of the slightly dissociated salt BH+A-. A low conductance is attained a t the equivalence point. Upon further addition of base, the conductance remains constant or increases slightly if there is BzH+ formation. When dissociation constants of the normal and homoconjugate salts, homoconjugation constant, and ion mobilities are known, it is possible to calculate the shape of the conductometric titration curve. An example is given in Figure l of the titration in acetonitrile of 3,5-dinitrobenzoic acid with triethylamine ( 2 5 ) . When the acid concentration is smaller than O.O2M, the agreement between calculated and experimental points is quantitative. When proton transfer between acid and base is not quantitative, the maximum (in Figure 1) is displaced to the right and may even occur far beyond the equivalence point. An example is given in Figure 2 of titrations in AN of 3,5-dinitrobenzoic acid with various substituted pyridines, the substitute in curve B being the strongest base in water ( p K d ~= 6.6) and unsubstituted pyridine (curve E) the weakest ( p K d = ~ 8.8). Knowing the various constants and ion mobilities, it is even possible to calculate the shape of the curves ( 3 4 ) .Such titrations are of no analytical significance. Presence ‘of hydrogen bond donors which are such weak acids as to give negligible proton with the base in a titration as in Figure 1 may ~transfer - , greatly affect the shape of the conductometric titration curve. An example of the effect of resorcinol in the titration of the system in Figure 1 is given (35) in Figure 3. The maximum is eliminated as the anion A- now heteroconjugates with the hydrogen bond donor. It is gratifying that the calculated and experimental points on the curves in Figures 1, 2, and 3 are in good agreement. The shape of the (33)I. M. Kolthoff. M. K. Chantooni. Jr.. and S.Bhowmik, Anal. Chem., 39, 1627 (1967). (34)I. M. Kolthoff and M. K. Chantooni, Jr., J. Amer. Chem. SOC., 87, 1004 (1965). (35)I. M. Kolthoff and M. K. Chantooni. Jr., J. Amer. Chem. SOC.,85, 2195 (1963).


I

7I -

‘“I

L

I

!

14-

I

i

0 0

20

80

60

40

100

I

80

40

I20

120

160

200

% Titrated

% Titrated

Figure 1. Conductometric titration of 3,5dinitrobenzoic acid with triethylamine

I, 0.0187M acid: 11, 0.0619M acid: A experimental points; A corrected for viscosity in II; 0 calculated points

Figure 3. Conductometric titrations of 0.0187 M 3.5dinitrobenzoic acid with triethylamine in the presence of resorcinol I, no resorcinol present: 11, 0.286M in resorcinol: V. experimental points; V, calculated: 111, 0.532M in resorcinol: A, experimental points: A, calculated, IV. 0.750M in resorcinol: 0, experimental points; 0 , calculated Viscosity correction applied to all experimental values 4 ,

, Y , 20

60

I00

1 I40

,

I

I80 220”

,

I

I ;

1000 5000 l0,OOO 0.005

% Titrated grm.

Figure 2. 0.0187M 3,5-Dinitrobenzoic acid with various pyridine bases (A), Et3N. (B), 2.4,6-trimethylpyridine; (C), 2,4dimethylpyridine: (D), 4methylpyridine: (0, pyridine

titration curve as in Figure 1 may become considerably more complex in various dipolar aprotic protophobic solvents, which are still weaker bases than AN, probably because of formation of various homoconjugate ions A-- - HA, A-(HA)2. Bryant and Wardrup (36) determined a host of conductometric titration curves of carboxylic acids and phenols with amines in acetonitrile, acetone ( e = 20) and nitrobenzene ( e = 36). Especially in the latter solvent, several curves exhibited two maxima which probably must be accounted for by the formation of homoconjugates like A-(HA)3 and A-(HA)2 at concentrations greater than about 0.05M when homoconjugate salts can no longer be (36) F. J. R. Bryant and A. W.

H. Wardrup, J. Chem. Soc.. 169, 895 (1957).

0.010

c.020

mols. base

Figure 4. Conductometric titration of dichloroacetic acid with triethylamine in nitrobenzene 20 ‘ C . c = 36 (Wardrup and Bryant). Molar concentration of acid: I, 0.20: 11, 0.10; 111, 0.050; IV, 0.034: V, 0.05

considered as completely dissociated. Examples of titration curves of dichloroacetic acid with triethylamine in nitrobenzene are given in Figure 4. Maryott (37) was the first to observe and interpret maxima of the above nature in inert solvents, while several interesting titration curves of substituted phenols in toluene with tetrabutylammonium hydroxide (in isopropanol) as titrant have been reported and interpreted by Harlow and Bruss (38).A detailed discussion of conjugate ions in inert solvents is presented by Davis ( 3 ) . (37) A. A. Maryott, J. Res. Nat. Bur. Stand., 38, 527 (1947). (38) G. A. Harlow and D . B. Bruss, Anal. Chem., 30, 1836 (1958)


e

1997

n -4

-73 1

\\

4

1

20

'

40

report half neutralization potentials (HNP) in potentiometric titrations with the glass electrode of uncharged acids with some tetraalkylammonium hydroxide solution as titrant in polar aprotic solvents. They plotted the H N P us. p K d of ~ the ~ acids in water. Although the shape of the neutralization curves of uncharged acids with a strong base in aprotic protophobic solvents can be quite different from that in water (see Figure 51, it is shown very easily that in solvents in which the tetraalkylammonium salts can be considered to be completely dissociated the numerical value of pH a t 50% neutralization is equal to P K ~ H Apro, vided no other homoconjugate than HA2- is present, and all species are monomeric. Neglecting activity coefficients for the sake of simplicity the following relations exist at the HNP: [HA]

+

[HA,-]

(10)

C, =

[A-]

+

[HA,-],

(11)

'

60

80

% Titrated

Figure 5.

C, =

c , and c , being the analytical concentrations of acid and

salt. Thus a t the HNP, [HA] = [A-] and

Calculated potentiometric titration curve of HA with

Et4NOH for various values of capHAz=

(1) tHA,-

lo3,(2)IO2,

(3)lo', (4)1, (5)simple acid dissociation, Le.,

=0

When the anion has not a localized charge, like in picrate, homoconjugation becomes negligible. For this reason, the conductometric titration curve of picric acid with an amine in a protophobic aprotic solvent does not exhibit a maximum, the conductance increasing until the equivalence point, to become constant on further addition of base (provided there is no B2HC formation). The titration line resembles that of acetic acid with ammonia or an aliphatic amine in water. Conductometric titrations in aprotic solvents of uncharged acids with tetraalkylammonium hydroxide are of no analytical use. There is no maximum in the lines as in Figure 1 since the dissociation constant of the tetraalkylammonium salt is only slightly smaller than that of the homoconjugate salt. No sharp break in the conductance line is observed at the equivalence point, as the mobility of the hydroxyl ion is not much different from that of other anions. In a protophilic solvent like DMSO, homoconjugation is so small that conductometric titration curves of acids with a weak base resemble those observed in aqueous media. Again, in such a solvent the mobility of the hydroxyl ion is not much different from that of other anions and no sharp break in conductance is observed in the titration of acids with tetraalkylammonium hydroxide. On the other hand, extremely weak acids can he titrated conductometrically with the sodium lyate of DMSO called sodium dimsyl (uide i n f r a ) ,provided the sodium salt of the acid is slightly soluble. Hiller ( 3 9 ) found a large dissociation constant of the order of of sodium dimsyl in DMSO and titrated conductometrically such weak acids as water and alcohols. In the titration of water, the conductance initially increases and soon becomes constant as a result of precipitation of sodium hydroxide. A sharp increase in conductance is observed at the equivalence point. Denoting the lyate (dimsyl) ion by s-: Na'

+

S-

+ H,O(HA)

-

HS

+ NaOH(NaA)

+ PPt + Effect of Conjugation on Potentiometric Titration Curves. Many years ago several authors (40-43) started to (39)L. K. Hiller, Anal. Chem., 42, 30 (1970). (40)J. Fritz and S. Yarnarnura, Anal. Chem., 29, 1079 (1957).

1998

=

["IHNP

(12)

KHAd

This simple relation does not hold in solvents of low dielectric constant like pyridine or methyl isobutyl ketone ( 4 4 ) , in which dissociation of tetraalkylammonium salts is far from complete and also not in protophobic solvents of larger dielectric constant (about 30 or larger) in titrations of HA with an amine (B), the BH+A- ion pairs having a smaller dissociation constant. The shape of potentiometric titration curves of HA with a tetraalkylammonium hydroxide is characterized by the product of the homoconjugation constant K f ~ ~and , - the concentration, c,, of the acid:

e H' + A-

HA A-

+

2HA

(H'

= solvated proton Hs+) (13)

HA f HA,H' t HA2-

===k

Note than in a mixture of HA (in excess) and its tetraalkylammonium salt, [H+] decreases 10 times with 10-times dilution when K f ~ ~ is, -very large and ( e , e,) of the order of or larger. Consider a situation in which K f ~ ~=, lo4 - and c , = 0.1M. At 10%neutralization (no volume change), practically all of A- is present as HA2-. Under these conditions [HA] = 0.08M, [HAz-] = 0.01M, and [H+] = 6.4 X lo3 X K d ~as~compared , to 9 X K d ~ ~ when there is no homoconjugation. Similarly we find a t 90% neutralization c , = [A-] = 8 X 10-2M, [HAz-] = 10-2M, [HA] E 1.2 X and [H+] = (10-3/6.4) X K d ~ ~ . When there is no homoconjugation, pH changes by about 2 units between 9 and 91% neutralization, but in the above example about 7.6 units. Exact calculations of pH at different values of K f ~ ~( c, , - c,) have been made and the corresponding neutralization curves are presented in Figure 5 ( 4 5 ) . The curves in this Figure can be representative of a given acid at different dilutions. At large dilutions, the curves approach those observed in water. Neutralization curves of acids with a small K~HA?-, like picric acid, are similar to those in water. In protophilic aprotic solvents

+

+

(41)G.A. Harlow and G. Wyld, Anal. Chem., 30, 69 (1958). (42)R. Miron and D. Hercules, Anal. Chem., 33, 1770 (1961). (43)L. Chatten and L. Harris, Anal. Chem., 34, 1495 (1962). (44)J. Juillard and I. M. Kolthoff, J. Phys. Chem., 75, 2496 (1971). (45)I. M. Kolthoff and M. K. Chantooni, Jr., J. Amer. Chem. Soc., 87, 4428 (1965).


6 [ I

5 -

4

0 x

3 t

Q

0

7 .4 .8

1 1.2

1.6

--

0

.4

.8 I 2

I .6

Molartty o f Additive

Flgure 7. Effect of additives on pH of benzoic acid-tetraethylammonium benzoate mixtures -4

-3

-2

-I

0

+I

t2

+3

14

Left hand figure, 3.6 X 10-3M HBz-3.05 X 10-*M Et4NBz, pH at A pH = 0.23.40. Right hand figure, 6.5 X IO-*M HBz 2.18 X 10-3M EtrNBz, pH at A pH = 0, 16.80. -x- dimethyl sulfoxide as additive, -.-n-butanol, -@-water, -U-methanol and -A-p-bromophenol

+

PH- PKHn

Figure 6. Calculated buffer capacity plots as a function of pH and capHA2-in mixtures of HA and Et4NA ; A ) simple dissociation; (6) capnA2-= lo3, (C)lo2,(D)10, (81

(DMSO), K f ~ * , - values are much smaller than those in protophobic solvents, and neutralization curves in the former in general deviate but little from those in water. As has been observed by various authors (40, 41 ), it is seen that several curves in Figure 5 exhibit an inflection a t the midpoint, indicating a minimum buffer capacity. Plots of the buffer capacity 0 us. values of p H - p K d ~ * for different 2 presented in Figure 6. Two maxivalues of c, X K f ~ ~are ma in p at various distances from the midpoint are observed, the difference becoming larger with increasing values of c,Kf~**-.Equations have been derived ( 4 5 ) for the calculation of K f ~ ~and , - also the buffer capacity from the shape of experimental neutralization curves. Effect of Hydrogen Bond Donors and Acceptors on pH of Mixtures of an Acid and Its Salt in AN. Hydrogen bond donors and/or acceptors can have a large effect on pH in protophobic solvents when the neutralization curve has a shape like that in curves 1 and 2 in Figure 5 . For example, in mixtures of benzoic acid with a large excess of tetraethylammonium benzoate in AN hydrogen bond donors greatly decrease the p H as a result of heteroconjugation (complexation, solvation) of the benzoate ion with the donor. The effect of water, alcohols and p -bromophenol is illustrated in Figure 7 (left hand Figure) (46). The effect of tert- butanol is about one half that of methanol. Dimethylsulfoxide, which virtually is not a hydrogen bond donor has no effect on the pH, at least up to a concentration of 1M. Picric acid has such a small homoconjugation constant that its neutralization curve in AN is like that in water, the picrate ion being practically not a hydrogen bond acceptor. Thus, in picrate buffers in AN water and alcohols up to 0.5M have no effect on pH. On the other hand, in mixtures of a univalent anion acid HA- with its tetraalkylammonium salt BzA, the effect of hydrogen bond donors can be much larger than in the benzoate mixture in Figure 7. This happens when the charge in A2- is localized as the charges in bicarboxylates are at a short distance (oxalate, biphthalate, succinate). For example, in A S in a mixture 3.6 x (46) I. M. Kolthoff and M. K. Chantooni. Jr., Anal. Chem., 39, 1080 (1967).

10-4M in Et4NHS04 and 2 X 10-3M (Et4N)2S04, the pH decreased from 26.6 to 22.0 by the presence of 0.9M methanol. In a benzoic acid-benzoate mixture in AN, which contains a large excess of benzoic acid, the anion is present mainly as the homoconjugate HA*-, and the relatively weak hydrogen bond donors and acceptors, water and alcohols, up to 1M concentration have hardly any effect on the pH (right hand side in Figure 7). On the other hand, the much stronger hydrogen bond donor p - bromophenol decreases the pH considerably in its competition with the free acid for conjugation with the benzoate ion. Dimethylsulfoxide, being a fairly strong hydrogen bond acceptor, heteroconjugates with the free benzoic acid and increases the pH, as illustrated in the right hand side of Figure 7 . Small anions with a localized charge, like chloride, are good hydrogen bond acceptors in a protophobic solvent and can affect the pH of a mixture of an acid and its salt without proton transfer. For example, addition of 0.1M chloride to a mixture 4.8 X 10-3M in salicylic acid and 1.06 X 10-3M in tetraethylammonium salicylate in AN increases the pH from 15.1 to 17.4, the ionic strength being kept constant with tetraethylammonium perchlorate. In aprotic protophilic solvents, homo- and heteroconjugation constants are much smaller than in the protophobic solvents. For this reason, the effects of hydrogen bond donors and acceptors on the shape of titration curves in such solvents are much smaller in the protophilic than in the protophobic solvents. Resolution of Acid Strength and Its Relation with Transfer Activity Coefficients. Analytically, resolution of acid strength in dipolar aprotic solvents is very important as it often allows the individual titration of each acid in a mixture of two or more acids whose dissociation constants in water (or alcohols) differ too little to allow separate neutralization of each acid. For acids of a given class, the resolution R is given by the relation bKdH.41 -

PKdFIA)S1 = R(pKd,,i

- PKd,,)@

(17)

in which the left hand side is the difference in pKd between, e.g., a non-orthosubstituted and unsubstituted benzoic acid or phenol, HA1 and HA, in a dipolar aprotic sol-


*

1999

vent SI, while the right hand side is the difference in Sp (usually water or methanol) multiplied by R. As shown in a previous section, the H N P is a measure of pH1/2 (half neutralization), the latter being equal to p K d in solvents S with a dielectric constant of the order of 30 or greater. From the H N P of substituted benzoic acids, Miron and Hercules (42) found the following values of R (with reference to water) in the aprotic solvents acetonitrile 2.6, 2-nitropropane 2.3, 0-nitrotoluene 2.4, nitrobenzene 2.5, dimethylformamide 2.4. These values are in good agreement with that of 2.4 from a plot of pH1/2 us. pKd, (or the Hammett u function) in AN, DMF and DMSO ( 1 9 ) .Even in the low dielectric constant solvents, pyridine, methyl isobutyl ketone, 2,6-dichlorobenzene, and bromobenzene, Miron of 2.2, 2.6, 2.4, and Hercules found values of R = p&pw 2.6. For non-orthosubstituted phenols, we found a value of R = PAN/Pw = 2.24 in AN and 1.9 in DMSO with reference to water. Apparently resolution of acid strength for a given group of substituted acids is closely the same in protophobic and protophilic aprotic solvents. With reference to methanol instead of to water, the R value for substituted benzoic acids is 1.4 instead of 2.4. Methanol (M) is close to isodielectric with AN, DMF, and DMSO, and the Born effect upon PYA- between M and these solvents is small enough to neglect. For theoretical purposes, we have often referred resolution in aprotic solvents with reference to methanol. For analytical purposes, R with reference to water is more important. The difference between P K ~ HinA water and a solvent S,S A w p K d ~can ~ , be expressed in terms of transfer activity coefficients of the various species: w ~ S p ~ d=H~A~ 7 % + P'

p~ = 0.733AG0(25")

pWySHA (18)

(19)

The transfer activity coefficient y allows one to express the conventional activity of a species in a given solvent on the activity scale in another solvent, e.g., water. There is no uniform agreement on the sign convention. By our definition, a value of pwys of +2 means that, a t a given concentration (or rather conventional activity), the activity of the species in the solvent S is 100 times greater than when referred to that in water as the standard state. If pwys = -2, the activity is 100 times smaller than that with reference to water as the standard state. In general, values of y of uncharged compounds can be determined accurately. Thermodynamically it is impossible to determine the activity coefficient of a single ion yl, but it is possible to determine exactly ~ c + Y A - , yc1/yc2+and yA1-/YA2-, c+being a cation, A- an anion. Extrathermodynamic assumptions must be made to derive the value of a single yi. I t is beyond the scope of this review to discuss the various assumptions, and reference is made to an extensive critical review by Popovych (48). In our own work, we used the assumption that the transfer activity coefficient of tetraphenylphosphonium cation, YpPh4+ (49) or of tetraphenylarsonium, YAsPh4+ is equal to that of tetraphenylborate anion, YBPh4- (50, 51 1. 147) . , See e.o. R. G. Bates. "Determination of OH."J. Wilev, New York. N.Y., 1973, 21 1 ff. (48) 0.Popovych, Crit. Rev. Anal. Chem., 1, 73 (1970). (49) E. Grunwald, G. Baughman, and C. Kohnstam, J. Arner. Chem. Soc., 82. 5806 - - - 119601. ~ (50) 0. Popovych and A. J. Dill, Anal. Chem., 38, 588 (1966). (51) R. Alexander and A. J. Parker, (a) J. Arner. Chem. Soc., 89, 5539 (1967); (b) J. Amer. Chem. Soc., 94, 1148 (1972); (c) B. G. Cox, G. R. Hedwig. A. J. Parker, and D. W. Watts, Austr. J. Chem., 27, 477 (1974).

2000

The transfer coefficient of an uncharged molecule is easily obtained from the ratio of its solubility in the two solvents, a t least when the solubility is not too large. I t is fair to consider that PYHA is composed of two parts, a "neutral" part pyn and a hydrogen bond component p y ~ , , ? ~being , a measure of the hydrogen bond accepting capacity of the solvent.

~ ~ ' ~ A -

in which py denotes +log y. The transfer activity coefficient is closely related to AGO, the transfer energy for 1mol of the species, expressed in kcal mol-l ( 4 7 ) .

--.

Based on this assumption, Parker et al. ( 5 1 ) have reported a large number of y values of univalent cations and anions in a host of organic solvents and water, using acetonitrile as reference standard state. In this laboratory (521, we reported pwysi or pMySi,W and M denoting water and methanol, respectively, and S usually being AN or DMF or DMSO. For example, for the proton we report pWyA"+ = +8.1, p W y D M F ~=+ -2.6, p W y D M S o ~=+ -3.5, and for Wy'~+ = f1.9. Thus a solution with a hydrogen ion activity of 1 in water corresponds to an activity of in acetonitrile, while a value of aH+ in DMSO of l corresponds to [aH+] = 10-3.5 in water. These figures also indicate how much weaker a base AN is and how much stronger bases DMSO and DMF are than water is. From Expressions 17 and 18, it appears that the resolution R is independent of basic strength of the solvent or p y ~ as +

P'TJHA'

= P

w s y,

pW?HaS

(21)

Values of pWySnhave been estimated ( 5 3 ) from solubility of the methyl esters of various substituted benzoic acids and, knowing p w y s ~ values ~, of p w y S ~ .have been estimated to be -0.7, -1.1, -0.6, $0.8, $0.9, +1.2, and +3.8 for S being M, DMSO, DMF, AN, acetone, methyl isobutyl ketone and nitrobenzene, respectively. The following relation has been proposed ( 5 4 ) for PYA-

PYA-,, denoting the electric contribution to PYA-. Introducing Expressions 21 and 22 into 20, we obtain

The value of pwys~-,,of any anion is determined mainly by its hydrogen bonding capacity with water plus the energy involved in its ion-dipole interaction with this solvent. Aprotic solvents are practically no hydrogen bond donors, while anion- (not cation-) dipole interaction is extremely small as the positive pole is buried within the molecule of these solvents. Thus the resolution of acid strength of HA is determined mainly by the right hand side difference in Equation 23. As an example (53b), we mention the following values for the anions of 3,4-dimethyl-, unsubstituted, 3,4-dichloro-, and 3,s-dinitrobenzoates p"yAN~-: +6.6, $6.9, +5.0, and +4.2, respectively, and p"yAy~-,,: +9.6, +9.2, +8.0, $6.9. Evidently the solvation of these anions in water (or methanol) decreases with their decreasing basicity or increasing strength of their conjugate acids. (52) I. M. Kolthoff and M. K. Chantooni, Jr., J. Phys. Chern., 76, 2024 (1972). (53) M. K. Chantooni, Jr., and I. M. Koithoff, (a) J. Phys. Chem., 77, 527 (1973); (b) J. Phys. Chem., 78, 839 (1974). (54) M. Aifenaar and C. L. DeLigny, Red. Trav. Chirn. Pays-Bas, 86, 929 (1967).


Resolution of acid strength of ortho-nitro-, and halogensubstituted benzoic acids is considerably less than that of the non-ortho-substituted acids. This indicates enhancement in acid strength in water of the ortho-substituted acids (and anilinium ions) as compared to that of the metaand para-substituted acids. The very large free energy of hydration in water of the ortho- as compared to that of the non-ortho-substituted benzoate ions, combined with steric effects, accounts for the large difference in resolution between these groups of acids ( 5 3 b ) . Acids, the anions of which are not hydrogen bonded in amphiprotic (hydrogen bond donating) solvents, do not exhibit resolution of acid strength between amphiprotic and aprotic solvents. This is the case with carban acids. From p K d values ~ ~ in methanol and DMSO of some fluorenes and fluoradene by Ritchie ( 5 5 ) it may be concluded that the difference in p K d between ~ ~ the two solvents is mainly determined by the difference in basicity (PYH+) between the two solvents and that the difference in electrostatic free energy of solvation of the anions in M and DMSO is negligibly small. Difference in resolution of acid strength between water and aprotic solvents between H2A and HA- has been made analytical use of for many years (40, 41, 4 3 ) . The decrease ~ - that in water and a protophobic solvent in K d ~between ~ . statement is is very much greater than that of K d ~ 2This true when the two charges in A2- are not too far separated from each other. For example, pK2 of sulfuric acid in DMSO = 14.5, in DMF = 17.2, and in AN = 25.9 ( 5 6 ) ,as compared to a value of 2 in water. Thus SAWpK2 is 23.9 for AN, 15.2 for DMF, and 12.5 for DMSO, as compared to 16.5 (AN), 8.1 (DMF) and 6.9 (DMSO) for ApKd of benzoic acid. On the other hand, the difference in pKd2 between AN and DMSO is 11.4, close to a value of about 10 for p K d of~ uncharged ~ acids and to 11.6 for pDMSoyAN~+. The large resolution between pK1 and pK2 is to a very large extent to be attributed to the much stronger solvation in water of A2- as compared to that of HA-; in other words, pWys~2->> p w y s ~ ~(S- = aprotic solvent). For example, - pwyA"so4- is calculated to be 15.8 (56).At pCVyANso42present Dr. Chantooni in this laboratory is engaged in an extensive study of K1 and K2 of a homologous series of dicarboxylic acids in AN and DMSO and of K ~ H of E their monoprotic esters (HE). For several reasons, the results are very interesting and will be reported at the conclusion of the experimental work. As an illustration, we report only the following data for succinic acid in AN: pK1 = 17.6, pK2 = 29.0, p W y A N ~ 2 s u=c c+1.20, pWyAN~succ= +6.5, and = +21.9. From (pK2 - pK1) in AN of 11.4, as pWyANSucczcompared to (5.6 - 4.2) = 1.4 in water, it is seen that the resolution is large. This decreases with increasing number of CH2 groups. These studies are particularly of theoretical interest as they provide valuable information on intramolecular hydrogen bonding in HA-. Resolution of acid strength of cation acids BH+ between water and aprotic solvents is very much smaller than that of uncharged acids HA. Analytical Uses of Dipolar Aprotic Solvents. Protophobic S O h ? n t S . TITRATIONS O F BASES AND BASIC STRENGTH. B

iH,'

a BH,'

(24)

From Equation 24 in which H,+ denotes the solvated proton, it is evident that the base B and the solvent compete ( 5 5 ) C. D. Ritchie, J. Amer. Chem. Soc.. 91, 6749 (1969). (56) I. M. Kolthoff and M. K. Chantooni, Jr., J. Amer. Cbem. (1968).

for the proton. Thus, the reaction to the right becomes more quantitative, the weaker base the solvent is. The hydrogen bonding of BH+ to the solvent is a great factor in the energy of solvation of the proton. For these reasons, titration of weak bases is carried out in aprotic protophobic solvents as the formation constant K&+ increases and Kdg~+ decreases with decreasing basic strength of the solvent. Protophobic solvents are also very useful for the de+ such weak bases which in aqueous termination of K f g ~ of medium hardly exhibit basic character. For example, basic strength of carboxylic acids can be determined using Hammett indicators in sulfuric acid containing little water, a solvent quite different from water. In a protophobic solvent, like acetonitrile, the constant K f ~ ~can~ be~de-~ 2 + termined spectrophotometrically in dilute solutions of perchloric acid or conductometrically in dilute solutions of a fairly strong acid like methanesulfonic acid. Some values of K f g ~thus + found in AN ( 5 7 ) are compared with values reported in water-sulfuric acid mixtures in Table IV. Values of p K f g ~ of + some substituted benzoic acids (not reported in the table) were found to be the same as that of the unsubstituted acid, while K ~ HofAthese acids varies considerably with substituent. The value of K f g ~ of + hydrogen sulfide cannot be found in water-sulfuric acid mixtures because of reduction of sulfuric acid. As expected, the acid is a considerably weaker base than water. It is of interest that -7 for carboxylic acids, phenol, and acetone ( p K f ~ ~ + ) w ( p K f g ~ +is) equal ~ ~ to 7.1 f 0.1 and of the same order of magnitude as that (7 to 8) reported by Coetzee and Padmanabhan (30a, b, c ) for aliphatic amines and for pyridine by this laboratory ( 3 4 ) .For aromatic amines, Coetzee et al. find a difference of the order of 6, the same as we find for benzamide and its substituents ( 5 7 ) .For the sake of completion, reference is made to pioneer work by Hall (58)who titrated potentiometrically (glass electrode) a large number of amines in nitromethane, ethylenedichloride, ethyl acetate, nitrobenzene, and acetonitrile. Titrations of many weak bases have been carried out in the protophobic solvents acetonitrile and acetone ( I ). Sulfolane, which has a ( p K f g ~ + ) value w of f12.9 (59),is a considerably weaker base than acetonitrile with a ( p K f ~ ~ + ) w +9.5 (60). Sulfolane as a solvent for acid-base titrations was introduced by Morman and Harlow (31) who titrated weak bases with perchloric acid dissolved in dioxane as solvent. Since sulfolane is a considerably weaker base than AN, bases which are too weak to yield a good end point in AN were titrated by Coetzee and Bertozzi (61) with anhydrous perchloric acid in sulfolane. These authors titrated conductometrically perchloric acid with water (61b ) and obtained a well defined end point when H30+C104- formation was complete. Alcohols and ketones could also be determined in this way. Benoit and Pichet (62) titrated with perchloric acid in sulfolane a host of bases with a ( p K d g ~ + ) in w water varying between -0.3 ( 0 - nitroaniline) and 11.1 (piperidine). They found a straight line in a plot of H N P us. ( p K d g ~ + ) w with a slope of 0.073 VIpK, which is practically the same as that of 0.078 in AN and 0.075 in nitromethane reported by Streuli (63).Apparently there is practically no resolution of basic strength in the protophobic solvents [see also Hall ( 5 8 ) ] Many . authors have used a solution of perchloric acid in anhydrous acetic acid as a ti-

SOC., 90, 5961

(57) l. M. Kolthoff and M. K. Chantooni, Jr., J. Amer. Cbem. SOC., 95, 8539 (1973). H. K. Hall, Jr., J. Phys. Cbem., 60, 63 (1956). S. K. Hall and E. A. Robinson, Can. J. Chem., 42, 1113 (1964). N. C. Den0 and M. J. Wisotsky, J. Amer. Chem. SOC.,85, 1735 (1963). J. F. Coetzee and R. J. Bertozzi, (a) Anal. Chem., 43, 961 (1971); (b) Anal. Cbem., 45, 1064 (1973). (62) R. L. Benoit and P. Pichet, J. Electroanal. Cbem., 43, 59 (1973). (63) C. A . Streuli. Anal. Chem., 30, 997 (1958); 31, 1652 (1959).

(58) (59) (60) (61)


2001

~

~

Table IV. Protonation Constants of Some Very Weak Bases in AN Base

log ( P K ~ ~ H +

log (PK~BH+

Table V. pKd Values of Some Acids (BH+,HA, HzA, HA-) in DMSO A

Acid

P Kd

BH' Ammonium 10.5" Acetic acid -6.1 cl.1 7.0 Triet hy lam monium 9.0a Benzoic acid -7.3 +o. 0 7.3 4.0b Tribenzylammonium Phenol -6.7 1-0.4 7.1 HA 2,6-Dinitrophenol 4.9" 2 -Hydroxyphenol ... +0.3 o -Hydroxybenzoic(salicylic) 6.8" Acetone -7.2 -0.1 7.1 3,5 -Dinitrobenzoic acid 7.4" Benzamide -2.1 +3.8 5.9 p -Nitrophenol 11.0" 0.0 +6.1 6.1 DMF Benzoic 11.1" 0.0 1-5.8 5.8 DMSO Acetic 12.6 ... +O. 5 Phenol 16.4." 16.9' H2S 9 -Cyanofluorene 8.46 H20 (-6.7) +2.2 Nitromethane 15.97b16.5' CHBOH -2.3 +2.4 Diphenylamine 23.6" Urea 25.1' trant in protophobic solvents. However, in this solvent, the Dichloro-2.4 -aniline 25.3c strong acid is mainly present as an ion pair (salt) (64) Water 28.ZCgd CH&OOHz+ClOd-, and the very weak base glacial acetic Triphenylmethane (30.0)d acid (Table IV) introduced with the titrant interferes in the H2A and HA- Oxalic pKi = 6.2' p K , = (14.9)" titration of very weak bases in protophobic solvents. Coeto -Phthalic 6.2' 16.0' zee and Bertozzi (65) recommended the use of anhydrous Succinic (9.5)e (16.4)e perchloric acid in sulfolane as a titrant, using the glass elecMalonic (4.5)" (18.9)" trode as p H indicator. In dilute solutions the perchloric Fumaric (8.3)e (12.l)e acid is considered to be completely dissociated, its P K ~ H A a Ref. (15); Ref. (69); ( 7 1 ) ; value probably too low because of in sulfolane being 2.7 (66). Considering the difficulty and precipitation of NaOH; e estimated by Kolthoff from E1 2 values the danger of explosion involved in the preparation of the reported by J . A . Martin and J. Duperis, Bull. SOC. Chim., 1968, anhydrous acid, use of HSbC16 as a titrant is suggested, this 138 in titrations with 40% (in water) tetrabutylammonium hyacid being completely dissociated in sulfolane (66). Nitrodroxide. methane may be preferable as a solvent over sulfolane since it is much less viscous than and is an equally weak base as and Buisson (68) find that trifluoromethanesulfonic acid is However, a separate study must sulfolane ( p K f ~ =~ $13). + completely dissociated in DMSO, while values of K d of ~ be made of the stability of solutions of strong acids in nipicric, methanesulfonic, hydrochloric, trifluoroacetic, and tromethane before a definite recommendation can be sulfuric are -0.3, f1.76, +2.0, +3.45, and 1.4. The glass made. Coetzee e t al. (65) found solutions of perchloric acid electrode is suitable for pH determinations in DMSO, but a in sulfolane to be stable. On the other hand, the aH,+ of sosteady potential is slowly attained a t p H greater than 15. lutions of perchloric acid in acetonitrile decreases rapidly Ritchie e t al. (69) used it to a pH of 25 with cesium dimsyl on standing, although the total acidity does not change as titrant. Courtot-Coupez e t al. (70) used the hydrogen (67). As a matter of fact, the aH, of solutions of all strong electrode and sodium dimsyl for obtaining solutions of p H and moderately strong acids in AN decreases rapidly on as high as 35. She reports an autoprotolysis constant pK, of aging. 33. Because of this very large value, many substances which Protophilic Solvents. TITRATION OF WEAK ACIDS. do not exhibit acid properties in water or alcohol can be tiHomo- and heteroconjugation constants in protophilic soltrated in DMSO (vide i n f r a ) . Dissociation constants of a vents are much smaller than those in protophobic solvents host of acids have been determined in various laboratories. and neutralization curves of uncharged acids of the former A select list is in Table V. resemble those in water much closer than in the latter. For Price and Whiting ( 4 ) introduced sodium dimsyl (NaS) analytical use N,N- dimethylformamide (DMF), pyridine, in DMSO as a titrant in this solvent, using triphenylmethdimethyl sulfoxide (DMSO), and to a lesser extent ethylane as an indicator in the titration of extremely weak acids. enediamine (EDA) are popular solvents for the titration of The color change from colorless to red a t the end point is weak acids and mixtures of acids. Extensive studies of acidvirtually instantaneous. Excellent results were obtained in base equilibria have been made in DMSO. For this reason the titration of such weak acids, like nitromethane, aceand also for the reason that it forms a stable lyate ion, the tone, alcohols, ethylene glycol, diethylene glycol and cyclofollowing discussion is mainly confined to DMSO. EDA pentadiene, which behave as monoprotic acids while diethalso forms a stable lyate ion, but because of its small dielecylene glycol was titrated as a dibasic one. Steiner, Gilbert, tric constant ( E = 14), equilibria are much more involved in and Whiting (72) in several instances found great differthis solvent than in DMSO. As discussed in the last section, ences in end point between titration results with sodium there is no difference in resolution of acid strength of carand potassium dimsyl. With sodium dimsyl, glycerol gave boxylic acids between any of the protophobic and protoan end point after addition of 1.5 mol of sodium dimsyl, philic dipolar solvents, except of course for the leveling efbut 2 equivalents with potassium dimsyl. On the other fect in protophilic solvents, in which acids like hydrochlohand, water, ethanol, n- butanol, tert- butanol and l-meric, sulfuric, and picric are strongly dissociated, but weakly in protophobic solvents. From conductometric data, Benoit (68)R . L. Benoit and C. Buisson, Electrochim. Acta, 18, 105 (1973) (64)S. Bruckenstein and I. M. Kolthoff, J. Amer. Chem. Soc., 78, 2974 (1956). (65)J. F. Coetzee and R. J. Bertozzi, Anal. Chem., 41, 860 (1969). (66)R. L. Benoit, C. Buisson and J. Choux, Can. J. Chem., 48, 2353 (1970). (67)I. M. Kolthoff and M. K. Chantooni, Jr., Chem. Anal. (Warsaw), 17, 841 (1972).

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ANALYTICAL CHEMISTRY, VOL.

(69)C. D. Ritchie and R . E. Uschold, J. Amer. Chem. Soc., 89, 1721 (1967). (70)J. Courtot-Coupez and M. L Demezet, C. R. Acad. Sci., 266, 1438 (1968) ( 7 1 ) J. Courtot-CouDez and M. L. Demezet. Bull. SOC. Chim. Fr.. 1033 (1969). (72)E. C. Steiner, J. M. Gilbert, and M. C. Whiting, J. Amer. Chem. SOC.,85, 3054 (1963).

46, NO. 13, NOVEMBER 1974

~

thoxy-2-propanol were found to react a t the end point with 0.64, 0.36, 0.45,0.33, and 0.54 equivalent of potassium dimsyl, respectively, but with 1 equivalent of sodium dimsyl. No explanation of the difference between sodium and potassium dimsyls is offered. We suggest that the difference is due to a difference in solubility (and partly of dissociation constants) between the sodium and potassium salts, the sodium salts, in general, being less soluble in DMSO than are potassium salts. This interpretation is substantiated by a recent study by Exner and Steiner ( 7 3 ) . Considering the wide spread in pK values in Table V, it should be possible to make a wide use of differential titrations in mixtures of very weak acids. Since the glass electrode is extremely sluggish a t high pH, such titrations might be tried with the hydrogen electrode which would also indicate the p H [Courtot-Coupez (70)]or possibly one of the many metal electrodes (platinum, gold, bismuth, tin, carbon) which have been used empirically in titrations in nonaqueous media. Moreover, it is suggested that research be carried out to find a group of indicators with pKd values in DMSO between 16 and 30. Such indicators may be useful in the titration of mixtures of weak acids with different pKd. Nitroamines and nitrodiphenylamines may be found useful. Ethylenediamine (EDA) was introduced by Moss et al. ( 7 4 ) for the titration of weak acids using sodium aminoethoxide as a titrant. Relatively recently Heumann et al. ( 7 5 ) introduced the lyate ion in the form of lithium 2-aminoethylamide as a titrant in this solvent. They estimated that the p K d of water is of the order of 38. They used the platinum electrode as p H electrode in their titrations and obtained excellent breaks in titrations of such acids as weak as water, aniline, diphenylamine. I t is remarkable that the end-point break in the titration of water is greater than that with aniline or p - phenylenediamine, as in DMSO the dissociation constant of the latter two is greater than (73)J. H. Exner and E. C. Steiner, J. Amer. Chem. SOC.,96, 1782 (1974). (74)M. L. Moss, J. H. Elliott, and R. T. Hall, Anal. Chem., 20, 784 (1948). (75)(a) W. R. Heumann, A. Bouchard, and C. Trembley, Can. J. Chem.. 45, 3129 (1967);(b) W. R. Heumann. A. Bouchard, and D. Rochon, Anal. Chem., 40, 1529 (1968).

that in water (see Table V). I t is quite possible that this is explained by insolubility of some of the alkali salts of the acids, and partly by small dissociation constants. This interpretation is substantiated by the fact that Heumann et al. (76) found the length of the potential jump at the end point with various alkali lyates in the order K > Li > Na. Undoubtedly the dissociation constant as well as the solubility of the salts formed will be quite different in a solvent with a dielectric constant of 14 [See also ( 7 3 ) ] .The much greater basicity of EDA than of DMSO is an analytical disadvantage because the leveling effect of acid strength is much greater in the former than in the latter. For example, the difference in E 112 in the titration of benzoic acid on the one hand and phenol and water on the other was reported (75a) to be 80 and 180 mV, respectively. Assuming that the platinum electrode obeys the Nernst equation for pH, these differences would correspond to differences in pH,/, of only 1.3 and 3.0, respectively. It is clear, therefore, that for differential titrations of very weak acids the DMSO-dimsyl couples are more useful than EDA-lyate systems. In addition to dimsyls, potassium tert- butoxide may be very suitable for the titration of many weak acids and their mixtures in DMSO (77).

ACKNOWLEDGMENT Sincere thanks are expressed to M. K. Chantooni, Jr., the coauthor of all papers from this laboratory referred to in this review, who carried out all experimental work and who shares equally in the interpretation of the results. His constructive comments on this paper are also greatly appreciated.

RECEIVEDfor review June 3, 1974. Accepted September 9, 1974. Grateful acknowledgment is made to the National Science Foundation which has supported all the work in this laboratory referred to in this review. (76)W. R. Heumann, A. Bouchard, and.B. Safarite, Can. J. Chem., 47, 3509 (1969). (77)S. Ehrlich-Rogozinsky and H. R. Bosshard. Anal. Chem., 45, 2436 (1973).


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Acid-base equilibriums in dipolar aprotic solvents - Analytical

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