Polarographic Measurement of Relative Strengths of Br$nsted Acids in Pyridine Dispersion and Solvation Effects in Acid-Base Equilibria. Analysis of Bransted Acid Mixtures Keiichi Tsuji' and Philip J. Elving The Unicersity of Michigan, Ann Arbor, Mich. A Bronsted acid in pyridine solution produces a le diffusion controlled polarographic wave per acidic function; d is controlled by equilibria involving the hydrogen-bmded nonionic pyridine-acid adduct, the corresponding ionized but undissociated ion pair, and the dissociated pyridinium and acid anion ions. When the background electrolyte consists of large univalent ions, separate but parallel linear correlations exist for each type of acid between EIjz and aqueous pK,; a leveling effect is seen for acids of pK, less than CQ. 3. Comparison with the potentiometric half-neutralization potentials indicates that the values are directly related to the pK, values of the acids in pyridine. On this basis, relative enhancement of acid strength (pK) in pyridine, compared to that in water, corresponds to 2.5 and 3.9 orders of magnitude for phenols and purines, respectively, compared to carboxylic acids; these changes are probably due to the contribution of the dispersion effect to the medium effect on free energy in connection with specific solute-solvent interaction. Mixtures of acids, depending on background electrolytes used, can be analyzed for total acid content or, depending on type and pK,, individually, SOLUTIONS of Bronsted acids in pyridine produce well defined polarographic waves, whose heights correspond t o a oneelectron (le) reduction per acidic group in the acid molecule ( I , 2); dependence of the half-wave potentials (El;*)on the pK,, values of the acids in water (pK,") varies with the background electrolyte--i.e., Bronsted acids of pKaaqless than 9 give waves with essentially identical E1/2 values (-1.36 + 0.03 V) in 0.1M LiC104, whereas in 0.1M EtdNC104, the Ell?values of nitric, benzoic, and acetic acids are -1.31, - 1.62, and - 1.72 V, respectively. Similar waves are produced by Lewis acids such as alkyl halides and AI(II1) ( I , 3-5). The waves are due to a l e attack on the pyridinium species resulting from reaction of an acid with the solvent pyridine ( I , 2, 4-6). The present study of the dependence upon pK,"", pK, in pyridine (pK,'IYr)and structural type of El,zin pyridine of a varied group of uncharged Bronsted acids, using 0.1M Et4NC104 as background electrolyte, indicates that El/z in pyridine for
Present address, The Institute of Physical and Chemical Research, Yamatomachi, Saitama, Japan. (1) M. S . Spritzer, M. Costa, and P. J. Elving, ANAL.CHEM., 37, 211 (1965). (2) J . E. Hickey, M. S.Spritzer, and P. J. Elving, Anal. Chim.Acta, 35, 277 (1966). (3) A . Cisak and P. J. Elving, J . Elecfrochem. SOC.,110, 160 (1963). (4) A. Cisak and P. J. Elving, Elecfrochim.Acfn, 10, 935 (1965). (5) R . F. Michielli and P. J. Elving, work in progress. ( 6 ) L. Floch, M. S. Spritzer, and P. J . Elving, ANAL.CHEM., 38, 1074 (1966). 286
ANALYTICAL CHEMISTRY
these acids is proportional to pK,"". Systematic parallel straight-line correlations exist for each type of acid studied [carboxyIic, phenolic, and nitrogen heterocyclic (purine)] between Ellz (pKTr) and pKaaq(Figure l), except for a levelling effect for acids of pKSaqless than ca. 3. The relationships including the relative enhancement in acid strengths in the series of carboxylic acid-phenol-purine can be related to the equilibria prevailing in a solution of a Bronsted acid in pyridine and to the contribution of the dispersion effect to the medium effect on free energy. POLAROGRAPHIC REDUCTION OF B R ~ N S T E DACIDS
Table I summarizes the essential data for the polarographic reduction at the dropping mercury electrode DME in pyridine (0.1M in Et4NC104)of the 29 acids studied (Kd' of -1.3 to 12.1), which produced 39 diffusion controlled waves. E, for nitric acid fits the smooth curve obtained on plotting El for the monocarboxylic acids against pK."" (Figure l), which levels off at lower pKa" values and is a straight line between pK, ' 2.9 and 5.2; the line can be expressed by E1 2 = -1.10
- 0.124 pK1'
(1)
Deviations such as those for the pyridinecarboxylic acids are subsequently discussed. For convenience, salicylic acid is included with the dicarboxylic acids, most of which produce two l e reduction waves; phthalic and salicylic acids give single l e waves and terephthalic acid produces a distorted wave of diffusion current constant equivalent to a 2e process, which clearly represents two partially merged waves. E, values were plotted (Figure 1) by assuming that the less negative wave I corresponds to the first pK,'" and wave I1 to the second P K ? ~the ~ ; resulting points cluster about the line for the monocarboxylic acids with those for wave I occurring more often below the line and those for wave I1 above the line (exceptions and deviations will be discussed later). The four phenols investigated produce single well defined le waves, which yield a straight-line plot us. pK,"', E1
2
=
-0.79
- 0.124 pKZaq
(2)
which is parallel to the straight-line portion of the similar monocarboxylic acid relation but is displaced by a distance equal to 2.5 pK,'" units--i.e., a phenol dissolved in pyridine gives a pyridinium reduction wave with an El identical to that of a hypothetica1 monocarboxylic acid, whose PK,'~is 2.5 units less than that of the phenol. The six purines studied gave one or two well defined l e waves, depending on the number of known dissociation constants for proton release from the originally neutral molecule
Table I. Polarographic Reduction Waves of Solutions of Brbnsted Acids in Pyridine (0.1M in Et4NC104) NO.^ 1
10 11
Acid HNOs CFSCOOH ClzCHCOOH ClCHKOOH HCOOH CsHaCOOH CHsCOOH (CH3)sCCOOH (pivalic) Nicotinic Picolinic Oxalic
12
Phthalic
13
Salicylic
14
Tartaric
2 3 4 5
6 7 8 9
15
16 17
PK."' -1.3 0.23 1.29 2.87 3.75 4.20 4.73 5.2 2.07 1.01
I 1.46 I1 4.40 I 2.96 I1 I 11 I I1 I I1 I I1 I
Terephthalic Succinic Adipic
I1 18
Fumaric
I
I1 19
Maleic
I I1
20 21 22 23 24
2,4-Dichlorophenol p-Chlorophenol Phenol 3,CDimethylphenol 6-Mercaptopurine
25
2,6-Dihydroxypurine
I I1 I I1
26 27
ZI
-
--EmV
16
1.33 1.35 1.38 1.49 1.57 1.59 1.71 1.74
1.79 1.92 1.90 1.97 2.00 1.85 2.04 2.02
51
1.53 1.53 1.37 1.78 1.35
2.15 1.87 1.79 1.67 1.71
3.46 1.71
89 119 64 73 64
1.40
1.90
1.90
66
1.42 1.65 1.53O 1 .6gC
1.76 1.77
3.53
70 72
1.50
1.59 1.56
mV
E1/4
57 76 86 85 85 82 78
5.51
2.97 13.00 3.03 4.37 3.54 4.46 4.21 5.64 4.41 5.28 3.02 4.45 2.00 6.26 7.85 9.38 9.89 10.3 7.4 10.84 7.74 11.86 8.93 8.94 12.10 9.16 9.83
d
d
3.69
1.93 1.65 1.76 1.46 1.78
83 70
3.15
d
d
3.29 1.82 1.45 1.83 1.57 2.03 2.01
d
2.01 1.76 1.94 2.01 2.06 1.61 2.02 1.70
65 150
3.27
6
3.40
60 104 89 99 92 80 88 87 59 96 81 74 166 116
1.90
1.74 1.44 1.27
2.71
/
f
2.11
Purine 1.66 1.74 6-Hydroxypurine I 1.72 1.61 (hypoxanthine) I1 2.15 1.17 2.78 28 6-Methoxypurine 1.74 1.35 29 6-Aminopurine 1.81 1.48 (adenine) a No. 1: nitric acid added as pyridinium nitrate; Nos. 2 to 10: monobasic carboxylic acids; Nos. 11 to 19: dibasic carboxylic acids; Nos. 20 to 23: phenols; Nos. 24 to 29: purines. Diffusion current constant, I = ir/Crn2/3t1'6. c Measured, assuming that the observed wave consists of two waves of equal heights. d The two waves merged or nearly merged. e Anomalous wave; see text for detail, Saturated solution was polarographed because of low solubility of the compound. Based on wave height, the concentration was about 0.7 m M . f
(7). A plot of Eli2 for the nine waves observed us. pKaE9 gives a straight line, Eli2 =
-0.62
- 0.124 pK.""
(3)
which indicates that, relative to the carboxylic acids, the acid strength of these compounds seems to be enhanced by 3.9 pK units in pyridine. NATURE OF DIFFUSING AND REDUCIBLE SPECIES
The principal equilibria in a dilute solution of Brgnsted acid in pyridine may be written as (7) (a) G. Kortum, W. Vogel, and K. Andrussow, Eds., "Dissociation Constants of Organic Acids in Aqueous Solutions," Butterworths, London, 1961; (b) A. Albert, in "Physical Methods in Heterocyclic Chemistry," A. R. Katritzky, Ed., Academic Press, New York, 1963, Vol. I, pp 2 et seq.
pyr
+ HA I
$ pyr-HA,
I1
pyrH+A-
I11
pyrH+ IV
+ A-
(4)
where pyr is pyridine, HA the monobasic uncharged Brpnsted acid, pyrH+ the pyridinium ion, and A- the acid anion. Species I1 represents the hydrogen-bonded, nonionic pyridineacid adduct and species I11 the ionized but undissociated ion pair: I1 and I11 represent two extremes of the state of the associated species. Barrow (8), by infrared spectrophotometry, estimated the association constant between HOAc and pyridine to be 70 in CHC1, and 220 in CCI,. Because the dielectric constant of pyridine (12.4) exceeds those of the latter solvents (4.8 and 2.2), the association constant in pyridine is expected to be
(8) G. M. Barrow, J . Amer. Chem. SOC.,78, 5802 (1956). VOL. 41, NO. 2, FEBRUARY 1969
287
- 2.2 - 2.0
I
I
I
I
1
I
I
I
I
I
I
II
I
I
27
I6ll 0
/ /
/
/
- 1.8 z W
-1.6
24 I*
/
/
A26
- 1,4 "I
I
- 1.2
0121
0
10
5
PGq
Figure 1. Relation between halEwave potentials of waves given by solutions of Bronsted acids in pyridine containing 0.1M tetraethylammonium perchlorate a t 25" C and the aqueous pK, values of the acids 0 Nitric and monocarboxylic acids
Salicylic and dicarboxylic acids Phenols A Purines Numerals refer to the acids as listed in Table I smaller. However, under polarographic conditions, the concentration of the acid in pyridine is so small that association would be extensive-e.g., even for a n association constant as low as 1, only 7% of the acid would be unassociated in 1 m M solution. The situation with other weak acids would not be very different. The dissociation constant is conventionally defined by K , = a ~ +. ~ A - / ~ E A (5) In the present study, acid concentration in pyridine is so low (ca. 1mM) that concentrations may be regarded as equal to activities. In Equation 5 , it is understood that the solvent term is omitted and that the species may be solvated (7a). Consequently, K, is actually similar to the dissociation constant of combined I1 and I11 to the right in Equation 4. Dissociation constants of Bronsted acids in pyridine are smaller than in water, as expected on the basis of dielectric constants. pK, values of HC104, H N 0 3 , and HI in pyridine have been conductometrically determined (9) to be 3.12, 4.30, and 3.23, respectively; pK, in pyridine, relative to that of "OB, were potentiometrically determined (IO) to be for HCI, +1.60; HBr, +0.30; HI, -0.60; HC104, -0.78. Those of 2,6-dinitro-3,4-xylenol (pK,: 4.92 in 50% EtOH), : 5.22), and ethyl hydrogen isopro2,4-dinitrophenol (pKSaQ pylidene-malonate (pK,"": 3.36) were found by spectrophotometry to be 2.5, 3.1, and 7.7, respectively (11); the latter is ( Y M . M. Davies, Trans. Faraday SOC.,31, 1561 (1935). (10) L. M. Mukherjee and J. J. Kelly, J . Phys. Chem., 71, 2348 (1967). (11) E.J. Corey, J. Amer. Ckem. SOC.,75, 1172 (1953). 288
ANALYTICAL CHEMISTRY
the only carboxylic acid whose dissociation constant in pyridine has been published. When an acid of pK;' exceeding 7 is dissolved in pyridine to 1m M concentration, less than 1 is dissociated into pyridinium ion and acid anion. Many of the Brgnsted acids in the present study have pK? values exceeding 3.36; pKd"' for these acids should exceed 7.7 if the order of acid strengths in pyridine is assumed not to be drastically different from that in water; as subsequently shown, this assumption is not entirely true but is effective in the present case. Consequently, for acids of pK," 2 3.4, the concentration of associated species I1 and I11 in pyridine nearly equals the analytical concentration of the acid. It is these weaker acids that produce waves whose are dependent on pKC" (Figure 1 ; Equations 1 to 3). Because the polarographic waves produced by the acids in pyridine are diffusion-controlled and proportional to their analytical concentration, it is reasonable to attribute the diffusing species for acids in the category just discussed, to the associated species I1 and 111. The additiveness of the wave for polyprotic acids and for mixtures of acids, subsequently discussed, also supports the conclusion that the diffusing species is I1 or 111, rather than IV. For Bronsted acids, which are appreciably dissociated in pyridine, it can, accordingly, be assumed that the species, whose diffusion controls the current, are the pyridinium ion and the associated species. It is evident from Figure l that E , , , for these acids approach a constant value with decreasing pK,", indicating reduction of a common species-ie., pyridinium ion.
This discussion of the relation of the polarographic wave to the equilibria in the pyridine solution of an acid, has assumed that the background electrolyte does not affect the equilibria. This is essentially correct when the background electrolyte consists of large symmetrical unicharged ions whose participation in association phenomena would tend to be small-e.g., in the use of EtaNC104-it is not necessarily valid for an electrolyte containing a small ion, such as Li(1). The effect of Li(1) as a levelling agent on the polarographic reduction of pyridinium ion in pyridine due to ion exchange and association phenomena will be subsequently reported (12). Attack of electrons on the pyridinium species of Equation 4 probably occurs at the carbon-nitrogen bond system in the ring, although the site of electron addition is not necessarily connected with those of free radical dimerization or of ring fission, because the latter reactions may occur following electronic rearrangement subsequent to electron addition-e.g., cf. electrochemical reduction of Lewis acid-base adduct between AI(II1) and pyridine ( 4 ) . Shift in electron density in the pyridinium species may possibly favor electron attack on the 4 position of the pyridine ring. DEPENDENCE OF E112 ON pK,""
The dependence of polarographic half-wave potentials of reduction waves due to Brpnsted acids in nonaqueous media upon their pKanU values has been often reported (13). Coetzee and Kolthoff (14) found a spread of 1.6 V between the HOAc and HCIOr waves in acetonitrile (Et4NC104background electrolyte); no definite mechanism was presented for the electrode reaction except to indicate that the reduction might be that of solvated proton. of proton combined with uncharged base, or of proton combined with an anion. The order of El!zvalues for acid waves in 80% dioxane and in diluted pyridine (MerNBr electrolyte) seems to be affected by either dissociation constants or electronic structure of the acids; the waves were classified as due to reduction of solvated proton, undissociated acid or hydronium ion (15). The polarographic wave observed for pyridine solutions of acids has been ascribed to a l e attack on the pyridine ring of the pyridinium species (1, 4 ) . However, it has not been explained why the electron addition is facilitated as acid strength increases; facts pertinent to this question are discussed in the following paragraphs. Barrow (8) concluded on the basis of infrared absorption that the associated species between pyridine and acid in CHCll and CC14solutions does not take on the character of the pyridinium ion paired with the acid anion continuously as the acid strength is increased, but that there is a tautomeric equilibrium between hydrogen-bonded and ion-paired species. In a more recent infrared study of solid 1 :1 pyridine-acid complexes, Johnson and Rumon (16) concluded that the complexes are predominantly ionized when pK, of pyridinium ion (5.23) exceeds that of the acid by 3.7 and predominantly unionized when it is not; they claimed that crystal forces are not the deciding factor in determining the shape of the potential functions of the bonds in the complexes, because dissolution of the complexes in acetonitrile had no significant effect on the (12) K. Tsuji and P. J. Elving, work in progress. (13) P. J. Elving and M. S. Spritzer, Tulunta, 12, 1243 (1965). (14) J. F. Coetzee and 1. M. Kolthoff,J. Amer. Chem. Soc., 79,6110 (1957). (15) Y. Okazaki, Yukugukuzasshi, 81, 1618 (1961); ibid., Japan A d y s t , 11, 991 (1962); ibid., Reu. Polurugruphy (Kyoto), 14, 307 (1967). (16) S. L. Johnson and K. A. Rumon, J . Phys. Clzem., 67,74 (1965).
essential absorption bands-Le., those for 0-H and N-H, although C=O is somewhat sensitive to this medium. It would, consequently, be reasonable to assume that Brpnsted acids, which are not appreciably dissociated in pyridine and which show systematic dependence of their EI/Zon pK,"", belong to the weaker of the two categories of acids, whose complexes with pyridine are predominantly hydrogen-bonded in the solid state. Although species 111 and IV are equivalent in regard to reduced electron density in their nuclei, when compared with 11, IV would be more favorable for direct reduction because of its positive net charge. The essential part of the reaction thus may be expressed as follows :
-
pyrH+ pyrH O
+ e --+ kof.h
pyrHo
inactive product
(6)
(7)
where kof.his the forward heterogeneous rate constant for irreversible reaction 6, whose irreversibility may arise from instantaneous electron rearrangement within the molecule after electron transfer or may be due to the rapid conversion of pyrHo to inactive product, which may be a dimer (1). The slopes of the reduction waves are not regularly dependent on F,z, which means that the negative shift of Ell2with decreasing acid strength is not due to a regular decrease of the transfer coefficient a. Since kDl,hshould be equal to all acid waves if the above scheme is correct, the origin of the dependence of EI,Zupon acid strength has to be sought in a preceding chemical step. Involvement of an undissociated species in the electrode process is supported by the fact that protonation of the ketyl radical, produced on polarographic reduction of benzophenone in pyridine in the presence of 2,4-dimethylphenol as proton source, involves the undissociated acid (17). For the weaker category of the BrQnsted acids, which form hydrogen-bonded complexes with pyridine and produce waves with E112 dependent on acid strength, the diffusing species is predominantly species I1 and the preceding chemical step is Kd
pyr-HA e pyrH+
+ A-
(8)
It is apparent from what has been said concerning Equation 4 that Kd is virtually the acid dissociation constant-Le., K T . Although the equilibrium of Reaction 8 may be largely to the left, it is sufficiently rapid that the limiting current is controlled by diffusion. E112 of typical irreversible polarographic waves is given by (9) where CY is the transfer coefficient, n, the number of electrons transferred in the controlling step, t the drop time, and 0,the diffusion coefficient of the electroactive species. In order to adapt Equation 9 to the mechanism postulated, kol,h can be replaced by kol,hKd/CoA-to account for the preceding equilibrium (Equation S), where COA-is the concentration of the acid anion at the electrode surface; an analogous situation for fast preprotonation preceding electron transfer is treated on pages 246-8 of Ref. 18. Since t and Do are effectively constant, Equation 9 may be rewritten as 17) R. F. Michielli and P. J. Elving, J. Amer. Chem. Soc., 90, 1989 (1968). (18) L. Meites, "Polarographic Techniques," 2nd ed., Interscience Publishers, New York, 1965. VOL. 41, NO. 2, FEBRUARY 1969
289
where E' is a constant potential. Although the experiments in the present study were not specifically designed to keep CoAeffectively constant, the deviation of Eliz for this reason may be assumed not to be very much different from one acid to another. It is apparent that an increase in Kd shifts E , ~ z toward more positive potential, as observed. The effect of C'A- on Ell2postulated in Equation 10 is supported by the following experiment: addition of 8mM tetraethylammonium benzoate to 3mM benzoic acid in pyridine (O.1Min Et4NC104)made Ellafor the benzoic acid wave more negative by 50 mV (2). The calculated shift is (33/0()mV, which would indicate a reasonable value of 0.66 for 01. The discussion comprising Equations 4 to 10 seems to support the view that E!,z of the acid waves are dependent on pK. of the acids in pyridine. Consequently, it would follow that the systematic shift of the relations for phenols and purines from that for monocarboxylic acids (Figure l), as well as the deviations of the data points for the dicarboxylic acids, may be regarded as due to the effect on the dissociation of acids of the solvent change from water to pyridine. The above supposition is also supported by the result of comparing the El 2pKa" relationship with another known potential-pKasq relationship, as discussed in the next section. Comparison with Eh,,-pKanq Relationship. Streuli and collaborators, who extensively studied acid-base titratiocs in pyridine (19-21) and other nonaqueous solvents, observed that, with BudNOH in CeHs-MeOH as titrant, the half-neutralization potentials, EI,,,,, of fifteen metu andparu substituted benzoic acids (pK," : 3.42 to 4.92) in pyridine can be expressed by Ehnp
=
0.647
- 0.156 PK,"
when Ehnpof benzoic acid is taken as zero (the sign of Ehnpused by Streuli et a/. has been reversed to be consistent with general usage-e.g., pages 294 et seq. of Ref. 22). An identical relation was found for six aliphatic monocarboxylic acids (pK."' : 4.69 to 5.05). For two strong acids, p-toluenesulfonic and naphthalenesulfonic, Ehnplevelled off at about -0.43 V. A similar relation was found for fifteen phenols (pK,": 7.14 to 10.68),
For two stronger phenols (2,4-dinitro- and 2,4,6-trinitro-), the potential also levelled off at about -0.43 V. It was indicated that the difference between Equations 11 and 12 represents a relative enhancement of 3.4 pK,"' units in the acidity of phenols in pyridine as compared to water. Relations similar to these, though often less consistent, have been found for various acids and bases in acetic acid, acetic anhydride, acetonitrile, n-butylamine, N,N'-dimethylformamide, acetone, methyl isobutyl ketone, nitrobenzene, nitromethane, 2-nitropropane, chloro- and bromobenzene, 1,2-dichloroethane, and some mixed solvents (21-23).
C. A. Streuli and R. R. Miron, ANAL.CHEM., 30, 1978 (1958). C. A. Streuli, ibid., 32,407 (1960). R. R. Miron and C. M. Hercules, ibid., 33, 1770 (1961). G. Charlot and B. TrCmillon, "Les Reactions Chimiques dans les Solvents et les Sels Fondus," Gauthier-Villars, Paris, 1963, Chapter VI et seq. (23) C. A. Streuli, ANAL.CHEM.,30, 997 (1958); ibid., 31, 1962 (19) (20) (21) (22)
(1959). 290
ANALYTICAL CHEMISTRY
/
i 0.1
B 0.0 -0.1
-0.3
I
- 1.3
- 1.5
- 1.7
-1.9
Figure 2. Correlation between titrimetric half-neutralization potentials ( E h n p ) (Refs. 19 to 21) and polarographic half-wave potentials (Eli2)of acids in pyridine Dashed line represents a 1 : 1 relation 0 Monocarboxylic acids Dicarboxylic acids 0 Phenols Numerals refer to the acids as listed in Table I Kolthoff and Chantooni (24), in discussing the meaning of half-neutralization titration points in acetonitrile, demonstrated that the simple equation,
where UH is the hydrogen ion activity and KEAthe dissociation constant of the acid H A in acetonitrile, holds at the half-neutralization point, despite complications arising from formation of the hydrogen-bonded complex AHA-. Assuming that Equation 13 holds in pyridine and that the glass electrode in nonaqueous solvents responds to hydrogen ion activity similarly to the hydrogen electrode (an unproved but widely accepted view), Ehnp values in pyridine may be regarded as measures of pK,"" values. Comparison of Equations 1 to 3 with Equations 11 and 12, and of Figure 1 with Figure 2 of Reference 20, makes it clear that El,*and Ehnp are interrelated through their relations to pK,". Thus, a plot of E h n p against El,*for the monocarboxylic and dicarboxylic acids and phenols, for which both values are known, produces a close to 1 :1 correlation (Figure 2); the discontinuities present in both E112-pK,Ya and Eh,,-pK,'" reiationships between the monocarboxylic acids and phenols are minimized ( E h n p values for the second dissociation of dicarboxylic acids are not given in Ref. 19, but can be calculated by adding the figures which appear as (HNP2-HNP1) in Table I11 of Ref. I9 to the AHNP values in Table 11, which are actually for the first dissociation as is evident from the pK vaiues listed; the sign of the figures has been reversed as previously mentioned). These results strongly suggest that both potentials are related to the pK,"" values of the acids. The correlation between Eli2and Ehnp is somewhat unexpected in view of some of the uncertainties involved-e.g., the overall irreversible nature of the polarographic waves, which decreases the thermodynamic significance of E! ?, and ~~
(24) I. M. Kolthoff and M. K. Chantooni, J. Amw. Chern. Soc., 87, 4428 (1965).
Table 11. Cyclic Voltammetric Peaks at HMDE for Bronsted Acids in Pyridine (0.1M in EtdNC104)
Acid (concn) rnM Nitric acid
(2.0) Benzoic acid (2.0) Phenol (2.0)
Scan rate V/sec 0.2 0.4 0.8 0.2 0.4 0.4*
1.37 1.40 1.47 1.72 1.77 2.25
Cathodic - E p 2, V 1.28 1.30 1.35 1.60 1.62 2.02
0.4c
2.25
2.02
-Ep,
v
Anodica ip, PA
18.7 26.0 35.0 16.5 25.5 22.5
-Epr V 0 25 0 24
0.22 0.33 0.33 I 0.25 11 0.46
23.0
I 0.27 I1 0.50d
-Ep12, V
i,, P A
0.35 0.32 0.31 0.46 0.47
1.8 3.2 6.2 4.5 6.2 3.0
0.60
4.0
12.2
Peak due to product of reaction producing cathodic peak. 0.0 to -2.35 V. Range scanned: 0.0 to -2.50 V. Appears as a bump on peak I.
* Range scanned:
the still not well understood nature of the response of glass electrode in nonaqueous solvents. Some portion of the deviation from a perfect ElI2-Ehnp correlation may be attributed to the effect of the different environments-;.e., the presence of background electrolyte in polarography and of benzene and methanol in the titrations. It is unlikely that charge transfer is a significant factor in the observed El/, relations. If stabilization by intermolecular charge-transfer were an important factor in the formation of the pyridine-acid complexes, Ellzwould vary from acid to acid, depending on the properties of the acids as electron acceptors-e.g., the linear relation found for some X - A complexes (25, 26) between the wavelength of the charge-transfer absorption band, which depends on the difference between the ionization potential of the donor and the electron affinity of the acceptor, and the polarographic However, chargetransfer phenomena cannot account for the fairly regular El,zpKanqrelationship for the monocarboxylic acids, which includes acids of varying acceptor strength and for the nearly 1 :1 correspondence of and E h n p , because the latter does not involve an electron transfer process. consequently, the variation of EIIzof the acid waves can be only related to ionic dissociation. Rationalization of Deviations in E1,z-pK8auRelation. If El in pyridine is directly related to pK,"", deviations from the regular El rz-pK,n' relationships can be, at least partially, considered in terms of the effect of solvent change on the order of acid strengths. Solvent effects on the overall dissociation of electrolytes can be classified as electrical and nonelectrical. The former, which is the primary factor in the solvent effect (29, is related to the dielectric constant of the solvent and is equal for acids of the same charge type. The decrease in dissociation constants of acids with decrease in solvent dielectric constant is, qualitatively, larger for a negatively charged acid of the type HA--/A*- than for the uncharged type HA/A-. This is in accord with the present observation of the E1,2-pKaaqplots for the second waves of dicarboxylic acids appearing above the line for monocarboxylic acids (Figure 1). The dielectric effect, however, cannot account for the other types of deviations and the nonelectrical effect must be considered. DICARBOXYLIC ACIDS. The effect on the dissociation constants of dibasic acids of stabilization of the monoanion by (25) M. E. Peover, Trans. Faraday SOC.,58, 1656 (1962). (26) Ibid., p 2370. (27) G. C. Pimentel and A. L. McClellan, "The Hydrogen Bond", W. H. Freeman, San Francisco, 1960, pp 181 et seq.
intramolecular hydrogen bonding has been discussed--e.g., Ref. 27; frequently, K, is increased and KZis decreased beyond what they would be in the absence of this effect. Because, unlike water, pyridine cannot act as a hydrogen donor in hydrogen bonding with monoanion to stabilize the open form of the monoanion, the cyclic form of the monoanion would gain additional stabilization in pyridine. Consequently, the effect of intramolecular hydrogen bonding on the dissociation constants of dibasic acids would be more marked in pyridine than in water. In fact, the first dissociation constant of phthalic acid in pyridine is comparable to that of trifluoroacetic acid, as indicated by their Eliz values; the absence of the wave corresponding to the second phthalic acid dissociation probably points to an extreme weakening of that dissociation. On the other hand, terephthalic acid, whose geometric structure is unfavorable for formation of intramolecularly hydrogen-bonded monoanion, produces two merging waves, whose El;zare close to the monocarboxylic acid E1,z-pK,nQ relationship. This effect accounts for E1,2of wave I of oxalic, salicylic, tartaric, and succinic acids being below the monocarboxylic acid line; those of fumaric and adipic acids fall on the line, indicating the inability of their monoanions to form stable intramolecularly hydrogen-bonded ring structures. Maleic acid forms a stable monoanion in water and would be expected to do so in pyridine. Unfortunately, its wave I in pyridine is anomalous-;.e., it starts at - 1.O V, and may involve reduction of double bond, although the possibility of an easily reducible charge-transfer complex being formed in the bulk of the solution or at the electrode surface cannot be eliminated. Data points for wave I1 of oxalic, succinic, fumaric, and maleic acids appear well above the monocarboxylic acid line, which could be partly due to the dielectric effect. (The second maleic acid wave cannot correspond to its second dissociation, if the first wave is due to the reduction of its double bond.) However, the fact that the points for wave I1 of adipic and terephthalic acids, which are unlikely to form stabilized monoanions, fall on the monocarboxylic line shows that the effect of increased monoanion stabilization is more pronounced than the dielectric effect. Nonappearance of a second wave for salicylic acid is probably due to the wave being beyond the potential of background discharge; the second dissociation constant in water is too small (pK," : 13.0) to produce a wave in the available potential range, even without the dielectric effect and the effect of monoanion stabilization. VOL. 41, NO. 2, FEBRUARY 1969
291
PYRIDINECARBOXYLIC Acids. Deviation of the two pyridine-carboxylic acids from the regular monocarboxylic acid EI/z-~K.”‘line can be interpreted in terms of the effect of the basicity of the solvent. These acids are zwitterions in water; pK,89 values are given in Table I. Dissociation of the carboxylic groups in water occurs in the pH range where the nitrogen atom is protonated and positively charged; this positive charge is transmitted to the carboxylic group, facilitating dissociation. The apparent weakening of the strengths of these acids, relative to other monocarboxylic acids, by the solvent change from water to pyridine can be attributed to the lack of the above effect in pyridine; the very large excess of pyridine, whose nitrogen is of nearly the same basicity as the nitrogen in the acids, would not allow these acids to be protonated. ENHANCEMENT OF RELATIVE ACIDITY WITH ACID TYPE
The magnitude of the solvent effect on acid behavior, if in pyridine (0.1 M i n Et4NC104)does reflect p K T , is seen in the hypothetical example that three acids-one each being carboxylic, phenolic, and purine in type-of identical pK. in water, would have the following relative pK. values in pyridine: carboxylic acid, pK.‘; phenol, (pK,‘ - 2.5); purine, (pK,’ - 3.9). This enhancement of the acid strengths of phenols and purines relative to carboxylic acids by the solvent change from water to pyridine as summarized in Figure 1, presents an interesting problem on the effect of solvent on acid strength. The causes of the analogous situation involving the existence of two parallel but distinctly separate relations between E h n p and pKan0of carboxylic acids and phenols in pyridine seem not to have been considered. Electrostatic effects depending solely on the dielectric constants of the solvents can be eliminated as the principal cause, because these should be essentially comparable. Similarly, differences in change of activity with the three types of acids on solvent change are not likely to be so great-Le., acid concentrations in the present study were cu. 10-3M and background electrolyte concentration was 0.1M. An interpretation based on the electron-acceptor properties of the acids, assuming charge-transfer complex formation with pyridine, can be rejected for the reasons previously cited. The cause of the systematic difference between the three groups of acids, therefore, must be sought in the effect of the nonelectrical type of solvent-solute interaction on the process of ionic dissociation of the acid-pyridine complexes. Dispersion Effects in Acid-Base Equilibria. Grunwald and Price (28) found that the acid strength of picric acid relative to acetic acid increases by almost two orders of magnitude in the solvent series HzO, MeOH, EtOH, while that of trichloroacetic acid remains nearly constant. These results were shown to be qualitatively consistent with a dispersion effect with the dominant dispersion term coming from the interaction of the delocalized oscillators of the picrate ion with dispersion centers in nearby solvent molecules. The latter are localized, and their effectivedensity increases in the sequence HOH < MeOH < EtOH. Grunwald and Price point out that, although information is not available for a precise calculation of the dispersion energy of solvation for each solvent, the relative effectiveness of solvents as sources of dispersion energy can be readily ascertained. The results obtained in the present study are entirely consistent with the nature of dispersion effects due to the solvent environment in acid-base equilibria and their variation with (28) E. Grunwald and E. Price,J. Amer. Chem. SOC.,86,4517(1964). 292
ANALYTICAL CHEMISTRY
molecular structure. Thus, Grunwald and Price (28) conclude “that the contribution of the dispersion effect to the medium effect on AFo can range up to several kilocalories per mole.” The differences in relative acid strengths in pyridine as compared to water for phenols and purines relative to carboxylic acids correspond, as discussed, to 2.5 and 3.9 pK units, which, in turn, correspond to 3.4 and 5.3 kcal/mole, respectively. The order is consistent with the fact that, whereas the negative charge of the carboxylate anion is considered to be fairly well localized on the carboxylate group, that of the phenolate ion and, even more so, of the purine-derived anion must be comparatively spread out over the molecule. Solvation Number and pK,. A different but apparently compatible approach, which is operational in nature, is based on Glover’s interpretation of the solvent effect by solvation number (29). He successfully interpreted the variations of the dissociation constants of several protonic acids in dioxane-water and other solvent-water mixtures, by considering the role of the solvent in the dissociation rather than the dielectric effect. He defined a “true” dissociation constant K of an acid, which is independent of solvent, involving reaction 14, by Equation 15:
nS
+ HA ;=: S,H+ + S,A-
(14)
where S is the solvent, HA the acid, x and y the solvation numbers of proton and anion, respectively, and n the sum of x and y . (The symbol style differs slightly from that of Glover.) The constant K is related by Equation 16 to the conventional dissociation constant k , as usually expressed by Equation 17, where it is understood that the ions are solvated and k includes the solvent term [SI”:
(16 4
K = k/[SIn
- n log [SI
(16b)
[H+] [A-l/[HAl
(17)
pk = pK k
=
Application of Glover’s approach to the present problemLe., assuming that the relative enhancement in acidity is operationally solely due to the effect of the change in solvation, yields the following equation for phenols, 1 . 6 ( ~ l ”-~ n28q) =
- n?)
(~1’~’
+ 2.3
(18)
where the numbers of solvent molecules involved in the dissociation of carboxylic acids are n? in water and n? in pyridine; n? and nFr are similarly those for phenol. For purines with a single acid function, 1.6 (nlSQ- n?)
= (nlRyi-
ny)
+ 3.6
(19)
where n T a n d n? are the number of solvent molecules involved in the purine dissociation. The differences in Equations 18 and 19 are, at the same time, the differences between the solvation numbers of the carboxylate and phenolate ions in Equation 18, and between those of the carboxylate and purine anion in Equation 19, because the solvation number of the proton is constant in a given solvent (assumed equal to 1 in foregoing discussion), Although these results cannot be verified on the basis of present knowledge of the solvation of anions, some qualitative comments can be made. Because the dominant factor in the solvent-acid anion interaction in water is hydrogen bonding, the order of the strength (29) D. J. Glover, J. Amer. Chem. SOC.,87, 5275, 5279 (1965).
0.6
t iI 1.P
I.4
1.6 I.8 POTENTIAL, V
2.0
2.5
Figure 3. Polarogram of a mixture of 0.923 mM nitric acid (wave A) and 0.600mM 6-mercaptopurine (waves B and C ) in pyridine (O.1Min EtrNC104)
of the interaction would be carboxylate > phenolate > purine anion, because the more strongly localized negative charge on the anion would favor the hydrogen bonding. On the other hand, the interactions in pyridine lack the hydrogen bonding and would be much weaker than in water; this view is supported--e.g., by the very much lower solubilities of lithium benzoate and acetate in pyridine than in water (12). At the same time, the order of the strength of the interaction would be the reverse of that in water, because its main factor would be the dispersion force, which is stronger for delocalized anions. Consequently, the differences of solvation numbers in pyridine would tend to be smaller than that in water in Equations 18 and 19. ANALYTICAL APPLICATIONS
/It has been previously shown ( I ) that the Bronsted acid content of a sample can be collectively determined by dissolving the sample in pyridine, which is O.1Min LiC104,and measuring the pyridinium reduction wave of Elizequal to - l .36 i 0.03 V, to which wave all Brgnsted acids of pK,"" less than 9 contribute. This procedure can even be applied to aqueous samples since a moderate amount of water, up to several volume %, can be tolerated in the polarographic test solution (6). The results of the present study--e.g., Figure 1 and Table I-indicate that in the presence of Et4NC104 (or, presumably, other tetraalkylammonium perchlorates) the potential for the pyridinium reduction wave depends on the structural type of the parent Bronsted acid and the magnitude of its pKaBa. This fact has two major analytical advantages. First, it allows the analysis of acid mixtures in terms of the individual acids or groups thereof, depending on the nature of these acids. For example, mineral acid content of a sample could be readily differentiated from organic acid content where the latter were of pKaaqexceeding 4 or 5 , as is frequently the case. Second, it offers an alternative for determining an acid in a sample containing other polarographically reducible compounds-e.g., a carboxylic acid of pK? of ca. 5 could be determined ca. -1.3 V, using LiC104 background or at ca. - 1.17 V,using R4NCI04background. A number of acid mixtures were examined, particularly from the viewpoint of interaction effects between successive pyridinium reductions. A mixture of benzoic and nitric acids produces two well separated waves. On addition of up to 1.2mM H N 0 3 to 0.8 m M benzoic acid, Eliz for the latter's wave shifts slightly (- 1.60 to - 1.63 V) and il decreases somewhat (1.78 to 1.66 P A ) for 0 to 0.4 m M nitric acid and then
remains constant. The presence of benzoic acid has no effect on the prior pyridinium nitrate wave. Three waves are obtained on addition of HNOs to 0.60mM 6-mercaptopurine (Figure 3). Eliz for both 6-mercaptopurine waves becomes more negative on H N 0 3 addition--ex., by 47 and 40 mV at the 0.92 m M nitrate level. The wave I height remains constant, but that of wave I1 decreases by ca. 10% at 0.92mM nitrate. The prior pyridinium nitrate wave is not affected. In general, the components of mixtures of acids give separate waves as long as their Elizvalues are well separated; wave heights are nearly additive. This is true for several mixtures which were not systematically investigated-Le., nitric acid, benzoic acid, and phenol, 6-mercaptopurine and benzoic acid, and 6-mercaptopurine and phenol. EXPERIMENTAL
Chemicals. Pyridinium nitrate was prepared as described (1). Tetraethylammonium benzoate (Southwestern Analytical Chemicals) was repeatedly recrystallized from acetone-ether mixture to remove free benzoic acid. 6-Mercaptopurine hydrate (Mann Research Laboratory) was dried at 130 "C. under 20 mm pressure for 3 hr; loss of water was quantitative. Other chemicals, which were mostly reagent grade, were used without further purification. Nitrogen and argon were used for deoxygenation of polarographic solutions. Nitrogen was passed through vanadous chloride solution, calcium hydroxide suspension, Drierite, and, finally, pure pyridine kept at the same temperature as the polarographic solution ; only Drierite and pyridine were used for argon. Triple distilled mercury was used for polarography. Reagent grade pyridine was purified by treatment with adsorption alumina (30) or by fractional crystallization (31). Apparatus and Procedures. All measurements were made at 25 f 0.2 "C. (except as stated), using 0.1M EtdNC104 solutions in pyridine as background. Potentials are reported GS. the normal silver electrode (Ag/lM AgNOJ in pyridine (NAgE), which has a potential of 0.09 V us. aqueous SCE (liquid junction potentials included) (3). Dissociation constants of BrQnsted acids were taken from authoritative publications such as Ref. 7. POLAROGRAPHY. A Leeds & Northrup Type E ElectroChemograph was used in conjunction with an operational amplifier-based iR compensator (32). Three-electrode systems were employed for polarography and coulometry. T i e polarographic cell, and counter and reference electrodes have been described (2). The DME (12-cm length of marine barometer tubing) had m = 1.203 mg/sec and t = 5.10 ( w ~ * ' ~ t=* / ~1.332) at 60 cm mercury pressure in 0.1M Et4NC104 with the electrode polarized at -1.40 V. Values of m213t1/6for the calculation of diffusion current constants were based on t values at the potential where the current was measured. CYCLICVOLTAMMETRY. The polarographic cell was used with a hanging mercury drop electrode (HMDE) or pyrolytic graphite electrode (PGE). The HMDE consisted of one drop of mercury delivered from the DME and hung from the lower end of a glass tube into which a 0.4-mm platinum wire was sealed. The 4-mm diameter PGE was prepared and used as described (33). A triangular voltage sweep was furnished by a unit consisting of a function generator (HewlettPackard Model 202A) and an operational amplifier-based potentiostat ; an Electro Instruments Model 320 X-Y recorder was used. (30) W. M. Banick, JR.,ANAL.CAEM., 34, 296 (1962). (31) D. A. Hall and P. J. Elving, A n d . Chim. A d a , 39, 141 (1967). (32) R. Annino nnd K. J. Hagler, ANAL.CHEM., 35, 1555 (1963). (33) L. Chuang, 1. Fried, and P. J. Elving, ibid., 36, 2426 (1964). VOL. 41, NO. 2, FEBRUARY 1969
293
CONTROLLED POTENTIAL COULOMETRY. A three-compartrnent cell, similar to that used in polarography was used with a spirally wound 1-mm platinum wire cathode (10 cm long), coated with mercury and rotated during electrolysis, a 2-cm2 platinum foil anode immersed in 0.1714 Et4NC104 and a NAgE reference electrode. The potentiostat consisted of a Heathkit EUW-19 operational amplifier manifold and auxiliary circuits. Current was recorded with a Heathkit EUW-20 recorder. Ten milliliters of deoxygenated 0.1M Et4NC104 solution was preelectrolyzed in the cell for 20 min at the potential to be used in the electrolysis; the circuit was interrupted; 1 ml of stock acid solution was added; the solution was deoxygenated for 5 min; electrolysis was resumed. After 40 min, electrolysis was discontinued and a portion of the solution was removed and polarographically analyzed for residual acid by the standard addition method. The electrolysis current was graphically integrated from the recorder chart. Polarographic Behavior. Essential experimental data are summarized in Table I. Because E1/2 for some acids is slightly concentration-dependent, it was measured for the concentration range of 0.9 to 1.4mM. PYRIDINIUhl NITRATE AND MONOCARBOXYLIC ACIDS. The behavior of pyridinium nitrate in pyridine is obviously that of anhydrous nitric acid in pyridine; its E112 and diffusion current constant (0 values agree with previously reported values (2). The monocarboxylic acids give well defined waves with Ell2 values from -1.33 to -1.74 V and I values between 1.79 and 2.02. Wave slopes, calculated as (E114 E3,Jr are between 51 and 86 mV, compared to the 56 mV expected for a reversible l e wave, except for slopes of 89 and 119 mV for the two pyridinecarboxylic acids. Data for acetic and benzoic acids agree with previous data (2), except that I for benzoic acid is 1.85, (previously found: 1.40 =t 0.22). The effect of acid concentration was studied for nitric and benzoic acids. E,/zfor H N 0 3 shifts from -1.353 to -1.333 V on stepwise concentration increase from 0.20 to 1.60mM; I is within 1.79 + 0.02. The benzoic acid wave is unaffected by a concentration increase from 0.24 to 1.30mM; Ellz = -1.612 0.006 V and I = 1.85 0.04. DICARBOXYLIC ACIDS. The patterns observed are evident from Table I and the previous discussion. Reference need be made only to the behavior of maleic and fumaric acids, each of which produces two approximately equal waves, whose heights are proportional to concentration. However, only the first (less negative) wave of maleic acid and the second (more negative) wave of fumaric acid have unambiguous concentration-independent Ei,s values. Maleic acid wave I, which starts at about - 1.1 V at 0.49mM concentration and at about -1.0 V at 1.41mM, is drawn out and does not reach a current plateau until about -1.6 V; with increasing concentration, the wave is more clearly seen as two waves (Elis= -1.19 and -1.46 V at 1.41mM). Fumaric acid wave I1 is also drawn out, covering the potential range of -1.5 to -1.9V; El,zis -1.74Vat0.49mMand -1.78V at 0.96mM. PHENOLS.The waves produced by solutions of phenols in pyridine are generally more drawn-out than those of the monocarboxylic waves, as is evident from their (E114- E3/4) values. PURINES.The number of the waves equals the number of “proton release” dissociation constants. Diffusion current constants are generally lower than those of the carboxylic acids and phenols-e.g., I is between 1.35 and 1.74 for the three compounds with only one “proton release” constant; I for the sum of the two waves for compounds with two “proton release” constants is between 2.71 and 2.78. The behavior of 6-mercaptopurine was investigated in some detail. Ell2for wave I shifts from -1.58 to -1.61 V
*
294
ANALYTICAL CHEMISTRY
*
on increasing the concentration from 0.20 to 0.50mM, but
is not affected by further increase up to 1.20 mM. El/% for wave I1 is not appreciably affected by concentration. Slopes
of both waves are concentration-dependent-e.g., (E114 E3,J values are 110 and 53 mV at 0.20mM, and 80 and 88 mV at 1.20mM, respectively. 6-Mercaptopurine gave a well-defined anodic wave (Eliz= 0.300 i 0.005 V ; I = 1.51), which was not further investigated. Effect of Drop-Time and Temperature Variation. Plots of log it US. log h (height of the mercury reservoir) gave straight lines for each of the waves of nitric and benzoic acids, phenol, purine, adenine, and 6-mercaptopurine (both waves examined), whose slopes correspond to the current being proportional to 0.50 f 0.05 power of the mercury height; theoretical value for diffusion-controlled currents is 0.50. E112becomes slightly more positive with increasing drop-time, which is usually indicative of an irreversible wave. The temperature coefficient of the current for 0.8mM benzoic acid, calculated after Meites (18), is 1.03 between 11 and 25 “C; and 1.01 between 25 and 49 “C. These values are in the range expected for diffusion-controlled currents. becomes more positive (0.4 mV per degree) as temperature is increased. Cyclic Voltammetry. The behavior of 0.1M Et4NC104 background electrolyte solution and solutions of several acids in presence of background were examined, mainly in regard to the reversibility of the electrode reactions. Cyclic voltammetry at the HMDE of solutions of nitric acid, benzoic acid, and phenol produces cathodic peaks, whose E, potentials at a scan rate of 0.4 V/sec agree within h0.03 V with their respective Ell! potentials at the DME (Table 11); for an electrochemically reversible reaction at a stationary electrode at 25 “C,
Ep = Ele2 - (0.029jn).
(20)
The overall reactions producing these cathodic peaks are irreversible-Le., the products of the cathodic reactions give rise to anodic peaks at potentials slightly more negative than the anodic discharge potentials, which peaks are probably due to oxidation of mercury on reaction with the acid anions, liberated by the cathodic electrode reaction, to form sparingly soluble salts, because these anodic peaks do not appear at the PGE. Voltammetry of phenol between 0.0 and -2.35 V produces a cathodic peak at of the DME phenol wave; two smaller anodic peaks (I and I1 in Table 11) appear on the return scan, which do not appear when the negative limit of the sweep is -2.20 V, indicating that these peaks result from the reaction at the cathodic peak. Coulometry. Coulometry at potentials on the crests of the nitric acid and first oxalic acid waves, gave results for l e reductions, in accord with previous coulometric results ( I ) of le, le, and 2e reductions for nitric, benzoic, and sulfuric acids in 0.1M LiClO?, respectively, The fact that the diffusion current constant for thallium(1) in pyridine ( 3 ) of 1.94 =k 0.17 is close to those of the nitric acid and monocarboxylic acid waves supports the conclusion of l e reduction for each single acid wave. ACKNOWLEDGMENT
The authors thank Michael S. Spritzer for help with experimental techniques and David A. Hall for purifying some of the pyridine used. RECEIVED for review October 3, 1968. Accepted November 12, 1968. Work supported by the National Science Foundation and the Petroleum Research Fund of the American Chemical Society.
