9540
J . Phys. Chem. 1993,97, 9540-9546
Acidity and Basicity Scales for Polar Solvents W. Ronald Fawcett Department of Chemistry, University of California, Davis, California 95616 Received: April 12, 1993; In Final Form: June 18, 1993’
Acidity and basicity scales for polar solvents are examined and compared with the mean spherical approximation parameters derived from the Gibbs energy of solvation of the alkali metal and halide ions in 18 polar solvents, both protic and aprotic. On the basis of an analysis of data for the Gibbs energy of transfer of 1-1 electrolytes and standard redox potentials for simple reactions in a variety of these solvents, it is concluded that the most appropriate scales are the acceptor number A N and donor number DN introduced by Gutmann. The extrathermodynamic assumption for separating cationic and anionic contributions to thermodynamic quantities for electrolytes based on equal solvation of the tetraphenylarsonium and tetraphenylborate ions is reexamined. This assumption appears to be valid in aprotic solvents but questionable for protic ones.
Introduction It is well-known from thestudy ofthe thermodynamicproperties of electrolyte solutions that certain molecular properties of the polar solvent, more specifically, its acidity and basicity, are important in determining solution properties.’ For example, although nitromethane and dimethylformamide have dielectric constants which are almost equal, the extent of ion pairing in nitromethane is much greater than that in dimethylformamide. This observation is attributed to the weak basicity of nitromethane which poorly solvates cations. As a result, ion pairing is stronger in nitromethane in spite of the fact that long-range ion-ion interactions in the two solvents are approximately equal. A variety of physical propertieshave been proposed as measures of solvent acidity and basicity. The most popular basicity parameter is the donor number (DN) of Gutmann?~~ which is obtained by measuring the heat of reaction of the solvent with the strong Lewis acid SbClS when these reactants are dissolved in 1,2-dichloroethane.l An important defect of this parameter is that it cannot bemeasured for proticsolvents so that the basicities of often used protic solvents such as water, the alcohols, and the protic amides are not directly available. Another measure of solvent basicity is provided by the B parameter of Koppel and Palm.435 This scale is based on the red shift of the 0-D stretching vibration for CH3OD dissolved in a given solvent, an increase in the shift being attributed to an increase in solvent basicity. A third basicity parameter is provided by the B scale of Kamlet and Taft,6p7which is obtained by the solvatochromic comparison method. Their approach emphasizes the hydrogen bond accepting properties of the solvent rather than its electron donatingcharacter. These parameters and other methods of measuring solvent basicity were compared and discussed in detail for a large number of solvents ranging from polar to nonpolar by Marcuss and Makitra and Pirig.g A wide variety of parameters giving an empirical measure of solvent acidity have been described in the literature.10 A very popular measure of acidity is provided by the Dimroth-Reichardt ET parameterl1J2which is based on the energy associated with exciting an electron in a model dye compound, which has a strongly dipolar ground state with an exposed electron pair to an excited state for which the dipole moment is negligible. Mayer et al.13 introduced the acceptor number (AN), which is derived from the 3lP NMR shifts produced in triethylphosphine oxide by the electrophilic solvent interactions which lower the electron density at the phosphorus atom due to the inductive effect. Finally, Kamlet and Taft7.14 proposed the solvatochromicparameter a to ~~
~
Abstract published in Aduance ACS Abstracts, September 1, 1993.
measure the solvent’s hydrogen bond donating ability. Another acidity parameter is Kosower’s Z,15 which has a similar basis to the Dimroth-Reichardt ET. These parameters have been compared very recently by Marcuslo for a wide range of solvents both polar and nonpolar. It is clear from this analysisthat one requires two parameters to describe the ability of a solvent to stabilize Lewis bases using the Kamlet-Taft approach. One of these is the hydrogen bond donating ability a,and thesecond is thesolvent polarity defined by thesolvatochromicparameter T * . As a result, the parameters ET,AN, and Z can be written as linear functions of both a and ?r*.l0 In a recent paper, Blum and Fawcett16 showed that the parameter X/r, obtained from analysis of data for the Gibbs solvation energy of monoatomic monovalent ions in polar solvents within the mean spherical approximation (MSA) is directlyrelated to the solvent’s acidic or basic properties. In the MSA, X is the polarization parameter which is related to the correlation length in the solvent immediately adjacent to the ion and depends on whether the ion is a cation or anion; r, is the solvent radius in a spherical representation of this molecule. The MSA parameter and its temperature derivative” are available in 18 polar solvents both protic and aprotic. Since they are derived from thermodynamic properties which directly reflect ion solvation, it is especially interesting to compare the MSA parameters with the acidity and basicity parameters previously discussed in the literature. In the present paper, the relationship between the MSA parameter Xlr, and the acidity and basicity parameters mentioned above is considered in detail for polar solvents. A major goal of the present analysis is to derive basicity parameters for protic solventsand to reconsiderthe appropriate acidity scale for aprotic solvents. Solvent effects on the Gibbs energy of transfer of simple 1-1 electrolytes and on the standard potentials of simple redox couples of systems involving a molecule and either a monovalent cation or anion are also analyzed and discussed with respect to the popular acidity and basicity scales. Acidity and Basicity Parameters Based on tbe M S A Considering ion-dipole interactions only, the expression for the standard Gibbs energy of solvation of a monovalent cation within the MSA is
where NOis the Avogadro constant, zi the ionic charge, eo the fundamental electronic charge, eo the permittivity of free space,
0022-3654193f 2O91-954O%O4.00/0 0 1993 American Chemical Society
Acidity and Basicity Scales for Polar Solvents
The Journal of Physical Chemistry, Vol. 97, No. 37, 1993 9541
TABLE I: A Summary of Acidity and Basicity Parameters for Polar Solvents acidity
ET
AN
water (W) methanol (MeOH) ethanol (EtOH) 1-propanol (PrOH) formamide (F) N-methylformamide (NMF)
63.1 55.4 51.9 50.7 56.6 54.1
54.8 41.3 37.9 37.3 39.8 32.1
acetone (AC) acetonitrile (AN) benzonitrile (BzN) dimethylacetamide (DMA) dimethylformamide (DMF) dimethyl sulfoxide (DMSO) hexamethylphosphoramide (HMPA) N-methylpyrrolidone (NMP) nitrobenzene (NB) nitromethane (NM) propylene carbonate (PC) tetramethylene sulfone (TMS)
42.2 46.0 41.9 43.7 43.8 45.1 40.9 42.2 41.9 46.2 46.6 44.0
12.5 18.9 15.5 13.6 16.0 19.3 10.6 13.3 14.8 20.5 18.3 19.2
solvent
basicity
1.17 0.93 0.83 0.78 0.71
48.0 41.0 37.2 34.7 34.1 31.5
(0.0) Aprotic
e, the relative permittivity of the pure solvent, and ri the ionic
radius. Values of the ratio X/r, were extracted earlier16from the data for the Gibbs solvation energy for the alkali metal cations and halide ions.l* This quantity is significantly different for cations and anions in a given solvent, reflecting differences in the mechanism of ion solvation and thus the correlation distance. Defining the polar basicity B, to be the value of h/r, for cations, eq 1 may be rewritten
This relationship demonstrates that the Gibbs solvation energy of a cation is linear in the basicity provided that variation in (1 - 1/e8) with solvent is not large and that the ratio (1 riB,)-l is also linear in B,. Since the present discussion is limited to polar solvents, arbitrarily defined to be those solvents with a relativepermittivitygreater than 20,the factor (1 - l/eJ isalways close to 1,varying between 0.95 and 0.995. Values of B, extracted earlier for 18 polar solvents together with basicities on the DN and B scales are given in Table I. It is also easily shown that for typical cationic radii the ratio (1 B,,ri)-l is linear in B, for the observed range of this parameter. The relationship between the Gibbs energy of transfer of Na+ as tabulated by Marcus and B, is illustrated in Figure 1. It is apparent that a quite good linear relationship is obtained, the main deviations from the line being due to variation in the factor (1 - l/q,). However, it should also be kept in mind that an extrathermodynamic assumption, namely, equality of solvation of the tetraphenylarsonium cation and tetraphenylborate anion (TATB assumption)19is used to obtain the single ion thermodynamic parameters and thus the value of B,. Any failure of this assumption will have a relatively more marked influence on the Gibbs energy of transfer of a given ion than on the Gibbs solvation energy of the same ion and thus on B,. This may also contribute to the scatter seen in Figure 1. In the case of anions, the Gibbs solvation energy may be written as
0.08 0.19 0.0 0.0 0.0
0.0 0.0 0.0 0.22 0.0 0.0
B
BP
18.0 19.0 19.2 19.8 24 27
156 218 235 223 270 287
0.47 0.66 0.75 (0.80) (0.48) (0.8)
12.1 12.1 11.9 12.1 12.5 12.6
17.0 14.1 11.9 21.8 26.6 29.8 38.8 27.3 4.4 2.7 15.1 14.8
224 160 155 343 29 1 362 47 1 319 67 65 176 287
0.48 0.40 0.41 0.76 0.69 0.76 1.06 0.77 0.39 0.76 0.40 0.39
12.6 11.5 11.2 13.5 13.2 13.3 13.8 14.0 10.6 10.7 11.4 12.5
12
13
-
22.0 24.4 23.3 20.1 22.2 25.6 19.2 22.1 26.4 25.5 23.9 22.0
0.0
B
DN
A,
a Protic
40 0
-I
z
3 \
P
z v L
10
11
14
+
Figure 1. Plot of the Gibbs energy of transfer for Na+ ion from water to various nonaqueous solvents against the basicity parameter Bp. The points (0)are for aprotic solvents and ( 0 )for protic ones (see Table I). The solid line corresponds to the least-squares fit based on all 18 solvents considered and the broken line to that for aprotic solvents only.
+
where A, is the polar acidity of the solvent. Neglecting the variation in the factor (1 - l / e s ) with solvent, it is clear that G,(A-) is linear in A, provided that the ratio (1 riAp)-*is also linear in A, for the usual range of variation in this parameter. The relationship between these quantities for the C1- ion is shown in Figure 2. It is clear that a good linear relationship holds with
+
\
r 0 v
15
-5
I t
I 15
25
35
\'
1
45
55
I
A,
Figure 2. Plot of the Gibbs energy of transfer for C1- ion from water to various nonaqueous solvents against the acidity parameter A,. The designation of the data and linear correlations are the same as those defined for Figure 1.
scatter similar to that found for the Na+ cation. This can be attributed to the same causes as discussed above for the basicity parameter. When one tests for correlations between any two of the acidity parameters listed in Table I, quite good correlation coefficients are found. However, it isclear that thequality of thesecorrelations
Fawcett
9542 The Journal of Physical Chemistry, Vol. 97, No. 37, 1993 48
0
0
0
32
16
t I
I 10
14
12
16
20
18
AN
Figure 3. Plot of the acidity parameters ET (0)and A, (0)against the acceptor number AN for 12 aprotic solvents (see Table I).
12.6
!-
The Gibbs Energy of Transfer of 1-1 Electrolytes
A
0
11.8 17
the value 18.0 for the donor number of water is consistent with the donicities estimated from the data for Gibbs energies of solvation. Higher values for the donor number of water (DN = 3 l), the alcohols,and protic amides*are not at all consistent with the data for ion-solvent interaction energies.I6 From Figure 4, it is also clear that the correlation between Band B, for the protic solvents is much weaker. The main problem is that the value of B for water seems to be too low with respect to those for the other protic solvents. The failure of the Koppel-Palm parameter for protic solvents is probably due to the complexityof the IR spectra used to determine B. Since this parameter is based on the frequency shift associated with an 0-D vibration, it is certainly more complex when both interacting molecules are hydrogen bonding. Careful resolution of overlapping bands could undoubtedly help to improve the B scale for protic solvents. On the basis of the above comparisons, it is concluded that the DN and AN scales are the best for assessing the basic and acidic properties of polar solvents. This conclusion is largely based on the comparison with the B, and A, scales derived from the Gibbs solvation energiesof the alkali metal and halide ions, respectively, and therefore is not capable of assessing parameters used for weakly polar or nonpolar solvents.
18
23
21
25
27
DN
Figure 4. Plot of the basicity parameters B, (0)and B ( 0 )against the donor number DN (see Table I). The left-hand ordinate scale is for Bp
and the right-hand scale for B.
is largely determined by the protic solvents which are strongly acidic. When the data for protic solvents are removed, and correlations attempted between the parameters on the basis of the aprotic solvent data alone, only two acceptable correlations are found, namely, between the acceptor number AN and the Dimroth-Reichardt parameters ET and between AN and the MSA parameter A, (Figure 3). The range of variation of AN for these solvents is the largest, and therefore, this scale is preferred. It is also noted that these scales distinguish between the acidities of common aprotic solvents such as DMF, DMSO, and HMPA, ordering them HMPA < DMF < DMSO with respect to increasing acidity. On the other hand, the KamletTaft parameter a does not distinguish between the acidities of these solvents. The Kamlet-Taft polarity parameter ?r* does show that DMSO is more effective as a Lewis acid than HMPA or DMF, the relative ordering being HMPA DMF < DMSO. Since the parameter A, is derived directly from data for ionsolvent interactions, it seems that A, and the related scales AN and ET give better estimates of relative solvent acidity. In the case of the basicity scales, very good correlations are found between DN, B, and B, on the basis of the aprotic solvents only. The correlation between the Kamlet-Taft @ and any of the others is much weaker. However, the major problem with the basicity scales isassociatedwith the proticsolvents. Recent work20 indicates that these may be obtained using solvatochromic complexes, but the necessary data are still not available. Since the parameter Bp is determined from the Gibbs energies of ionsolvent interactions, it is a good reference for assessing basicity parameters for protic solvents on the other scales (Figure 4). The values of DN used for the protic amides are those given by Gutmann et al.,21and those for the alcohols are estimates made by Kanevsky and Zarubin.2z From the data presented in Figure 4, it is clear that there is a very good correlation between DN and B, on the basis of these choices. It is especially interesting that
-
Data have been collected for the solubility of selected 1-1 electrolytes in a number of nonaqueous ~olvents.~3-~~ When the solubility product is multiplied by the appropriate activity coefficient product, one may estimate the standard Gibbs energy of transfer of electrolyte CA from water to solvent S defined as follows: AGot,(CA) = Gos(CA) - Go,(CA)
(4) On the basis of the above analysis, it is reasonable to expect that the Gibbs energy of transfer can be expressed as a linear function of the solvent's acidity and basicity, that is,
AGOJCA) = AGO,,,(CA)
+ aA, + bB,
(5)
where AG0,o(CA) is a constant for the electrolyte CA, A, and B, are the chosen acidity and basicity parameters for the solvent, and a and b are the correspondingcoefficients measuringresponse to solvent acidityand basicity, respectively. A general relationship of this nature was proposed earlier by Krygowski and Fawcett31 for thermodynamic quantities related to ionic solvation. A more general relationship given by Koppel and PalmS applied to the present data is AGOJCA) = AGotr,o(CA)+ uA,
+ bB, + 7Y + T P
(6)
where
Y = (cs - l)/(Es + 2)
(7)
Y, which is calculated from the solvent's dielectric constant, measures solvent polarity, and P,calculated from the solvent's refractive index n, measures solvent polarizability. On the basis of the above discussion A, and B, reflect the properties of the solvent molecules immediately solvatingthe ions, whereas Yand P are nonspecific properties reflecting the long-range aspects of ion-solvent interactions. Although there are strong arguments for considering all of these parameters,lJ the precisioo of the available data does not permit a meaningful analysis 09 the basis of eq 6. However, theory clearly indicates that &at polarity Y is part of the Gibbs solvation energy for an ion througb the term (1 - l/es) in eq 1. Thus, the available data were fitted to
The Journal of Physical Chemistry, Vol. 97,No.37, 1993 9543
Acidity and Basicity Scales for Polar Solvents
TABLE II: Analysis of the Dependence of ACOdCA) on Solvent (Eq 9). salt
no. of solvents
AGO,.o(CA), kJ mol-’
v
b
u
0
standard deviation,kJ mol-’
6
-1.52 -2.88 200 9 38.0 0.53 0.44 0.03 LiCl 10 266.8 -1.23 -1.81 -338 0.57 0.36 0.07 NaCl 8 350.2 -1.04 -1.13 -553 0.55 0.31 0.14 KCl -1.23 10 422.7 -0.70 -737 0.38 0.42 0.20 KBr 10 612.6 -0.55 -0.91 -1153 0.33 0.34 0.33 CsBr -1138 10 57 1.7 0.17 -1.08 0.12 0.40 0.48 KC104 0.23 -0.95 -1157 0.16 0.35 0.49 RbC104 10 575.8 0.31 -0.23 -1147 0.31 0.12 0.57 (CHIWC~O~ 8 551.4 -0.13 -0.02 -715 0.26 0.02 0.72 (CzH34NI 10 357.6 -211 0.57 0.26 0.17 9 82.9 0.34 -0.28 (C6Hs)&I 1.59 -0.34 35.4 0.87 0.12 0.01 (C~HS)&(C~H~)~B12 -111.3 a The acidity parameter used was the acceptor number AN,” and the basicity parameter, the donor number DN.’
the equation
+
AGo,,(CA) = AGo,r,o(CA) aA,
+ bB, + qY
(9)
The resultingparameters AGotr,o(CA),a, 6,and q are summarized in Table I1 together with the standard deviations and correlation coefficients for the case that AN and DN are chosen to represent solvent acidity and basicity, respectively. Also included in this table are the relative partial regression coefficients if, 6, and 11. These are defined from the variances of the independent and dependent variables in the fitted equation where the variance of quantity Q is defined as
(13) The corresponding relative partial regression coefficients are defined by the equations
a=
0.997 0.997 0.998 0.984 0.952 0.933 0.921 0.852 0.937 0.701 0.959
dependence of AGO,, for single ions on the solvent. However, the quality of this fit to data examined here for AGO, of 1-1 electrolytes was definitely inferior to that based on eq 9. It is also important to point out that very good correlations were obtained for the alkali metal halides and (CaHs)&(C&)B (TATB) on the basis of a three-parameter fit involving acidity and basicity parameters only (eq 5). This is precisely because solvent polarity Y plays a minor role in determining the value of AGot,(CA) as can be seen from the values of 11 in Table 11. It is especiallyinstructive to examine the fit for TATB which is given by AGot,(TATB) = -94.6
Thus, the partial regression coefficients a’, b’, and q‘ are given by
2.5 1.8 1.7 4.4 7.2 6.1 6.1 6.1 2.9 5.3 7.3
correlation coefficient
+ 1.60AN - 0.346DN
(18) with a correlation coefficient equal to 0.959. The values of if and 6aresuchthat 88%oftheexplainedvariationin AGO,isaccounted for by solvent acidity and 12%by solvent basicity. According to the TATB assumption, these contributions should be equal. If one removes the data for the protic solvents from the analysis (W, MeOH, and F) and performs the regression with the remaining nine aprotic solvents, the values of the relative partial regression coefficientsare equal at 0.50. Thus, the present analysis shows that the TATB assumptionis only valid for aprotic solvents. If one analyzes the data further for AGot,(TATB) considering only the aprotic solvents with the condition that AGo,(TA+) be equal to ACot,(TB-), then the statistically best equations for the individual ions are
a’
AGo,,(TA+) = -30.2 - 0.346DN
a‘+ b’+ q’
(19)
and
b‘ a’+ b’+ q’
-
AGo,,(TB-) = -63.6
I
= a’+
;I)+
q1
This procedure effectively gives one regress-ancoefficients which can be compared to one another since they are multiplied by factors which compensate for the differences in the range of variation of the independent variables. Thus, the relative partial regression coefficientsgive the fraction of the explainedvariation in the dependentvariable due to each of the independentvariables. These are extremely helpful in interpretingthe results of a multiple linear regression. When eq 9 was fitted to the same AGO, data using either A, and B, or a and /Ias acidity and basicity parameters, poorer fits were found with higher standard deviationsand lower correlation coefficients. Thus, it is concluded that AN and DN are the best parameters for describing solvent acidity and basicity for the polar solvents considered here. The AGO,, data were also fitted to the Kamlet-Taft equation AGOJCA) = &Go,e(CA)
+ aa + bB + p r *
This relationship was used by Marcus et
al.18
(17)
to analyze the
+ 1.60AN
(20) Values of these quantities calculated according to eqs 19 and 20 are shown as a function of AGotr(TATB)/2 in Figure 5 . It is clear that the TATB assumption is approximately correct for the aprotic solvents but fails seriously for the protic solvents. In fact, according to the present analysis the cationiccontributionto AGO,(TATB) for the protic solvents is significantly more negative than that predicted by the TATB assumption. At the same time the anioniccontributionis significantly more positive. The present analysis clearly suggests that the TATB needs to be reexamined and that a better reference solvent for citing values of AGO,, would be an aprotic one such as AN or DMF. Standard Potentials of Simple Redox Reactions
The simplest systems which can be examined in terms of the acidlbase properties of the solvent are redox reactions involving one-electron reduction or oxidation of an organic molecule to form the correspondinganion or cation radical. Data were found €orseven systems in the literature.32-36 In the case of the reduction reaction M+e-*M-
(21)
Fawcett
9544 The Journal of Physical Chemistry, Vol. 97, No. 37, 1993 30 0 r
'-
E
I
-50 I -45
-35
-25
AG,(ex)
-15
/
-5
5
kJ mol-'
Figure 5. Plot of the estimates of the Gibbs energy of transfer of the tetraphenylarsoniumcation (TA+,A) and tetraphenylborate anion (TA-, V) estimated on the basis of eqs 19 and 20 against one half of the experimental value for the salt TATB. The straight line is drawn on the basis of data for the aprotic solvents alone assuming AGb(TA+) = AGb(TB-). The reference point for the solvent water (0,O)is indicated by the symbol
+.
the standard potential was given by the equation
E, = E,,
+ aAN
where EsO is the standard potential in a solvent with zero acceptor number. For the oxidation reaction M+M++e-
(23)
the relationship is
E, = E,,
+ bDN
The results of this analysis of eight systems are summarized in Table 111. The quality of the fits obtained on the basis of one parameter is quite good except for 1,4-diaminobenzene.34 When anion radicals are involved, the relevant parameter is solvent acidity, and when cation radicals are formed, solvent basicity. If parameters other than the acceptor or donor number are used, the quality of the fits is poorer. Data for redox reactions for 14 transition metal ion comp l e x e ~ were 3 ~ ~also ~ examined (see Table IV). These redox couples usually involved ions of higher charge and therefore are strongly associated with ions of the opposite charge in most solvents. As a result, analysis of thesedata required consideration of both solvent acidity and basicity. For the majority of systems, the fit was significantly improved when solvent polarizability was considered, the resulting equation being
E, = E,,
+ aAN + bDN + TP
E, = E,,
+ aAN + 6DN + QY
(25) When cations are involved in the reaction couple, the dominant term is that in solvent donicity which accounts for at least 50% of the explained variation in the standard potential. One exception is the C o ( ~ e p ) ~ +redox / ~ + couple,4*which is a cage complex and therefore is less sensitive to specific solvent effects. For three of the systems considered, namely, Co(bpy)3+/2+,37Co(phen)3+/*+,37 and F e ( b p ~ ) ~ + no / ~ significant +,~~ improvement in the quality of the fit could be obtained by considering more parameters than acidity and basicity. This result is undoubtedly due to the fact that the number of solvents considered was not as great as in the case of other similar systems. In the case of the two anionic redox couples, Fe(CN)6s/4 42,43 and and also for Fe(~hen)3~+/~+," the third parameter involved in the multiple linear regression was solvent polarity Y,the corresponding equation being (26) The dominant parameter in the regression analysis is solvent
acidity, but the quality of the fits obtained with the experimental data is somewhat poorer than for the other systems considered. It should be pointed out that the data considered here were referred to either the internal ferrocinium+/, or bis(biphenyl)chromium+/Oredox couples45in order to avoid problems with changing liquid junction potentials. Variation of the redox potential for the reference couple is included in the analysis and affects the value of the parameter b to an unknown extent. However, the influence of the reference couple is not expected to be large on the basis of the data obtained for the redox couples involvingorganic molecules and formation of anion radicals (Table 111). This follows from the fact that the quality of the fit to the data for these systems could not be improved by adding a term in solvent basicity. The present results show clearly that the data obtained for the organic redox systems are much simpler than those for the transition metal ion systems. This result is not unexpected because of the complex nature of some of the latter systems and the important role ion association is expected to play in their thermodynamics. Nevertheless, the quality of the fits obtained by the present analysis is clearly better than that obtained by Lay et al.,N who based their analysis on the Kamlet-Taft parameters.14 Theseauthors found theparametersp and 'K* tobemoreimportant for most redox couples and could not justify the addition of a for most of the multiparameter fits. Since the solvents involved in their study included both protic and aprotic systems, the resulting equation gives an incomplete description of the role of the acidic properties of the solvents. This work illustrates the problems involved in using a more detailed description of solvent acidity when the number of solvent systems studied is limited. By excluding the Kamlet-Taft acidity parameter a from the analysis, the hydrogen bonding donating ability of the protic solvents is ignored. It should also be noted that, in aprotic solvents, the standard potentials for reduction of 9,lO-anthroquinone32 and benzophenone33become more negative in the order DMSO < DMA < HMPA. This clearly indicates that their acidities increase in the order HMPA < DMA < DMSO so that the anion radical formed is most stable in DMSO and, therefore, most easily reduced in this solvent. This ordering of solvent acidities is reflected by the other acidity scales considered but most strongly by the acceptor number scale AN. Discussion The data analyzed here are all related to the solvation of ions in polar solvents. They show clearly that the empirical parameters developed by Gutmann' for solvent acidity and basicity give the best assessment of changes in the Gibbs solvation energy of ions with change in solvent. Comparisons of acidity'0.12 and basicity scale^*^^ have often involved a larger collection of solvents in which electrolytes are not soluble so that the conclusions reached on the basis of these assessments are sometimes different from those reached here. The major flaw with the Gutmann donor number is that it does not directly allow one to estimate the basicity of protic solvents, but methods of obtaining estimates that seem quite reasonable have been devised.20.22." Support for the present conclusions is obtained from the acidity and basicity parameters derived from the Gibbs solvation energies of alkali metal and halide ions in a variety of polar solvents. However, it must be remembered that the single ion quantities are usually obtained on the basis of theTATB assumption's which has been questioned above. On the basis of the present analysis, the TATB assumption is valid for the aprotic solvents but not for the protic ones. As a result, values of AGtr for single ions from water to aprotic solvents are in error by a constant amount but correct with respect to each other in a relative sense. This question can be assessed to some extent on the basis of the data presented in Figures 1 and 2. In the case of the Na*ion, the linear correlation
Acidity and Basicity Scales for Polar Solvents
The Journal of Physical Chemistry, Vol. 97, No. 37, 1993 9545
TABLE IIk Analysis of the Dependence of the Standard Potential for Simple Redox Reactions Involving Organic Molecules on Solvent reactant no.ofsolvents Ea,mV a b standard deviation, mV correlation coefficient 7 7 6 9 6 7 8 11
-1690 -1090 -1530 31.0 -1550 -1470 -2040 347
20.2 14.2 39.5
15 17 9 51 7 18 10 17
-12.3 25.5 21.6 25.9 -8.62
0.980 0.955 0.998 0.937 0.996 0.976 0.993 0.967
TABLE I V Analysis of the Dependence of the Standard Potential for Redox Reactions Involving Transition Metal Complexes on Solvent redox couplP
no. of solvents &,mV
Cr(b~yh(3+/2+)’~ 8 -714 Co(bp~)3(3+/2+)” 6 -36.2 12 -108.6 Co(en)3(3+/2+)38-39 8 1340 Co(salen)(O/ +)40 8 -1127 Co(salen)(O/-)a 6 9.4 Co(~ep)(3+/2+)~~ 9 168.5 Co((NOz)~-sar)(3+/2+)~~ Co( (NHC0CH3)~-sar)(3+/2+)~~ 6 -115.1 Co(CH3, COOC~H~-o~osar-H)(2+/1+)~~ 10 -829.3 8 29.0 C0(phen)3(3+/2+)~’ Fe(bp~)3(3+/2+)~~ 5 696.7 Fe( CN)6(3-/4-)42943 11 -8225 6 1240 Fe(~hen)3(3+/2+)~ Mt1(CN)6(3-/4)~~ 9 -9210 8 97.4 R~(NH3)6(3+/2+)”
b *or qb 1.92 4.12 380 1.23 -4.61 1.94 -15.3 -1640 -17.1 -17.0 802 27.8 6.0 7.1 2.75 -11.6 -2930 0.412 -23.4 -1086 2.86 -16.1 -1832 4.60 -12.3 -758 1.55 -5.38 4.00 1.70 31.7 0.28 (15470) 4.41 -0.80 (-1784) 32.4 4.02 (1590) 3.53 -30.8 -224 a
li
6
0.36 0.31 0.13 0.25 0.64 0.20 0.03 0.22 0.35 0.31 0.45 0.77 0.43 0.72 0.21
0.50 0.69 0.66 0.65 0.36 0.36 0.83 0.49 0.53 0.69 0.55 0.01 0.32 0.05 0.76
standard *or ;ib deviation,mV 0.14 0.21 0.10 0 0.44 0.14 0.29 0.12 (0.22) (0.25) (0.23) 0.03
7 6 69 46 41 48 65 6 18 4 10 130 16 102 27
correlation coefficient 0.988 0.974. 0.953 0.952 0.929 0.984 0.973 1.ooo 0.994 0.997 0.987 0.975 0.874 0.980 0.995
The followingabbreviations are used for the redox couples: bpy = 2,2’-bipyridine; en = ethylenediamine; salen = N,N’-bis(salicy1idene)ethylenediamine; sep = 1,3,6,8,10,13,16,19-octaazabicyclo[6.6.6]icosane;(NOz)z-sar = 1,8-dinitrosarcophazinewhere sarcophazine = 3,6,10,13,16,19-hexaazabicyclo[6.6.6]icosane; (NHCOCH3)z-sar = 1,8-diacetamidosarcophazine;COzCHzCH3, CH3-oxosar-H = 1-(ethylformato)-8-methyl-2-oxosarcophaginato; phen = 1,lO-phenanthroline.b The third independent variable in the fit was the solvent polarizability P except for the bracketed systems for which it was the solvent polarity Y. (I
between AGt, and the basicity B, extracted from the Gibbs solvation energy data (eq 2) is essentially the same whether one considers the data for the aprotic solvents alone or data for all solvents (Figure 1). However,inthecaseoftheCl-ion,a different correlation is obtained between AGt, and the acidity A, for the aprotic solvents alone with respect to that for all solvents (Figure 2). It is clear that the TATB assumption needs to be examined more carefully, especially for protic solvents. Because of the fact that the parameters A, and Bp are based on data derived using this assumption, and also because their range of variation is considerably less than those of AN and DN, they are not considered to be as reliable. The present analysis has shown clearly that specific solvation properties of solventsrelated to their molecular ability to stabilize individual ions in the polar environment are more important than bulk electrostatic properties such as the relative permittivity and index of refraction. This is very important because it provides chemists with a way of assessing electrolyte solubility, ion pairing, and other electrolyte properties on the basis of the solvent’s acidbase properties. In fact, it was also shown recently on the basis of an infrared study4’ that these parameters can be used to assess solute-solvent interactions in solutions of one polar solvent in another. In conclusion, the relationship presented some years ago by Krygowski and F a ~ c e t t 3 ’ 9provides ~~ an important starting point for analyzing solvent effects for electrolyte solutions and solutions of polar molecules. On the basis of the present results, this relationship is
Q = Qo+ CYAN+ j3DN
(27)
where Q is the thermodynamic property in question and Qo is its value in a solvent with zero acidity and basicity on the Gutmann scales. When data are available in a large number of solvents, terms in solvent polarity and polarizability can be added as described above. A very important way of confirming these
conclusions is by characteristic vector However, data sets are often incomplete so that the statistical analysis cannot be carried out. The acquisition of thermodynamic solvation data for the alkali metal halides in polar solvents would provide the necessary results. One could then address the question of the extrathermodynamic assumption needed to obtain single ion solvation quantities with a much more powerful tool.
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