Russell S. Drago University of Illinois Urbono, 61801
A Modern Approach to Acid-Base Chemistry
A very common criticism of the undergraduate course in inorganic chemistry is that, in comparison to organic chemistry, there are few underlying concepts that enable one to tie the descriptive chemistry together. This is particularly prevalent i n the chemistry of the nonmetals which most texts treat in such an encyclopedic manner that reading the material is about as stimulating as reading a hone book. In treating,transition metal ion chemistry, chemical reactivity is often avoided and emphasis is placed upon describing the physical properties of these materials and the models that have been developed to understand these properties. A wide disparity exists in our excellent understanding of the physical properties when compared to our poor understanding of the reactivity. The slow development of unifying concepts governing chemical reactivities of inorganic compounds is in part unavoidable due to the wider variety of elements encountered in the study of inorganic chemistry as compared to organic chemistry. However, the situation is not nearly so bad as one would infer from reading several of the standard textbooks. In many presentations, one shortcoming which is a partial cause of the above difficulty is either the complete absence or an inadequate presentation of Lewis acid-base theory and nonaqueous solvents. These topics can provide a framework for presenting a good deal of the descriptive chemistry and accordingly are important ideas to be presented in any introductory course in inorganic chemistry. It is the purpose of this article to summarize the current status of our knowledge of acid-base interactions. After discussing the scope of Lewis acid-base considerations, it will he shown how these and other thermodynamic factors are necessary for a full understanding of chemical reactivity. We shall show how the existence of quantitative information regarding a reactivity requires us to modify the qualitative acid-base concepts of HSAB and Donor Numbers that are currently "in vogue." Qualitative procedures for employing the ideas that have evolved from our quantitative treatment will be briefly summarized and key literature references for using these ideas in discussing descriptive chemistry will be provided. Scope of Lewis Acid-Base Interactions
In modern usage, a Lewis acid is defined as any substance capable of accepting electron density and a Lewis hase as any substance capable of donating electron density. Many substances are capable of heing either one or the other, and some materials are capable of being both. (Water, for example, is a Lewis base when it coordinates to Na+ and a Lewis acid when it hydrogen bonds to C1-.) A Lewis acid-base interaction requires coordination of the two so that the bonding electron density is shared (via electrostatic and covalent mechanisms) by both the acid (acceptor) and the base (donor). With this definition, there are only a few types of reactions that do not involve Lewis acid-base interactions in at least some step of the process; outersphere electron transfer quickly comes to mind as one of the few reactions that does not qualify. Many examples of reactions which can be classified as involving Lewis acid-base interactions, but which often are not described in this way, have been summarized (la). 300
/ Journal of Chemical Education
For example, it is shown ( I b ) how the presentation to freshmen o f the concepts of hydration, hydrolysis, acid and base ionization and amphoterism can he greatly simplified and unified by using this approach. In addition to the many synthetic applications of this model, Lewis acid-base interactions are involved in chemistry which is very important and relevant to everyday life, e.g., homogeneous and heterogeneous catalysis, carbon monoxide and oxygen binding to hemoglobin, the hydrogen bonding of hase pairs in DNA, etc. Lewis acid-base interactions also play an important role in understanding many "physical" properties, e.g., solubility, wetting of surfaces, properties of polymers, colors of transition metal ion complexes, etc. With little effort, these lists can be expanded, and the reader will profit by thinking about the relevancy of these interactions in his area of immediate interest. Clearly, any concept of such widespread utility should be thoroughly and quantitatively understood, and it is the purpose of this article to summarize and to provide a key to the literature of recent developments in this area that have not yet found their way into most textbooks. Many of the chemical and "physical" properties described above are very complicated phenomena in which Lewis acid-base interactions are but one of many different energy terms. Indeed, a common shortcoming of many approaches in this area has been the attempt to explain very complicated phenomena, such as a reaction or process which has contributions from many different independent effects, (e.g., lattice energies, solvation, etc.), with one or two quantum mechanically based bonding concepts. One way to enumerate all of the energy terms influencing any of these phenomena is to construct a thermodynamic cycle which converts the observed reaction to the gas phase. This has been done in Figure 1 for a simple reaction in which an addition compound is formed in a polar solvent.
Step 1 in Figure 1 corresponds to the measured enthalpy of the reaction in a polar solvent, i e . , the enthalpy contribution to the observed chemical reactivity; step 4 corresponds to the strength of the acid-base interaction as manifested by the enthalpy of forming the adduct in the gas phase; steps 2 and 3, to the enthalpies of desolvating the acid and base, respectively; and step 5, to the enthalpy of solvating the adduct. It is step 4 that can he interpreted in terms of the electronic structure of the acids and bases. Since a state function is independent of path, i t can be seen that the enthalpy change measured in a polar
Figure 1. Bcra,v,-
Enthalpy cycle tor formation of AB,..I,,
tram A,,,,,,,
+
Table 1. Summary of Calorimetric Results for Hydrogen Bond Complexes of m-Fluorophenol with Different Bases in Various Solvents at 24 1%
+
-. .--. -
Ethyl
acetate
K"
AH^
34 f 3 192C1
5.2?c0.1
6
K'
6 . 7 2C 0 1
10.3f0.6 4 . 7 f 0 . 1 5.02C0.1 4 . 0 f 0 . 1 2.5f0.1 3.7+0.2
'In ""its
Dmethyl sulfmide
470i71 321i59 2542C15 73fS
AH^
7.2'10.1 6.72C0.1 6.1-tO.1 54320.1
Midine
K '
262rt11 106323 116f10 532C2 32f3
methykmine
AH^
KO
8.42C0.1 7.5-tO.l 6.92C0.1
...
6.33-0.1 64320.1
...
15Sf25 120-tl0 32&S
--AH'
n-Butyl ether -AH"
K"
9.8-tO.2 1 7 . 0 & 0 . 2 6.51.0.1 ... 11.1 + 0 . 2 6.0 + 0.1 9.3-tO.l 7 . 4 + 0 . 1 5.74Z0.2 8.6+0.1 .. . ... S . S i 0 . 1 3 . 3 2 C 0 . 1 4.54Z0.2
of 1mole-1.
In "nib of kcsl mole-1.
solvent, AHl, has contributions to it from many different independent effects, i.e. AH,
=
AH,
+ A H , + AH, + AH,
(2)
In order to interpret enthalpies measured in polar solvents, enthalpies for all these steps must he known. Often values for steps 2 or 3 and 5 are of the order of magnitude of those for step 4. When one attempts to explain equilibrium constants or free energies for chemical reactions, the enthalpies and entropies for all of the steps in a cycle of the type in Figure 1 must he determined. The relative stabilities of complexes in water, the pKB values of bases, and pKh's for acids are free energy considerations and contain enthalpy and entropy contributions from all the above factors and, where ionization occurs, many others. Consequently, these systems do not provide quantitative data about the bond strength in acid-base interactions and will remain uninterpretable until we discover a way to factor and obtain all the essential energy terms. Of course, the eventual aim of any program aimed a t understanding chemical reactivity is to obtain understanding and to make reliable predictions of interactions in polar media where most synthetic and relevant chemistry occurs. A semiquantitative attempt a t explaining the complex reactions that occur when solutes are dissolved in various solvents provides us with an example of one method of approaching complicated reactions. We have labeled this approach the Coordination Model. When, for example, dilute solutions of iron(1II) chloride are examined in various solvents, S, the species FeCl3.S; FeCl&+, F e C k ; FeS5C12+, C1- and FeSo3+, CI- form depending on the solvent employed (2). We wish to understand what solvent properties govern the extent of anion displacement. The overall process can be represented by a series of steps, each of which is exemplified by the general reaction
where (solvated) refers to interactions in the metal containing species outside the first coordination sphere. As described above, converting the reaction to the gas phase employing the thermochemical cycle (Fig. 2) elucidates important enthalpy contributions to the equilibrium written above. The enthalpy contributions to the position of this equilibrium are determined by the solvation of Si,, (step 3). the difference in the heats of solvation of MS,X(,, and MS+,+l,,, (step 5-step 2), the solvation of X-I,, (step 6) and the difference in donor strength of X-(,, and Si,, as measured by the difference in the gaseous heats of formation of MS,X + S and MS+,+l + X-I,, (step 4). Of course, the extent of chloride ion dissociation is a free energy consideration. However, one can examine
The selection of the enthalpy of adduet formation, as an approximation of the change in internal energy of the donor and acceptor upon addition compound formation, results from the thorough discussion by (4) J. E. Leffler and Grunwsld.
Figure 2.
Enthalpy contributions to halide displacement
whether the trends in estimated enthalpy contributions parallel the observation and, if they do, one can be assured that entropy either goes the same way or the changes are not significant enough to cause reversals in the enthalpy predicted behavior. When entropy terms dominate the difference in observed systems, interpretations will be very difficult because of our poor quantitative understanding of the magnitudes of contributions to AS. However, for related solutes, the application of quantitative information about donor strength together with qualitative estimates of solvating ability of solvents can be employed to produce a good semiquantitative description, with predictive power, of the complicated factors represented by the above cycle. Since our introduction of this approach, the basic ideas of our Coordination Model have been further tested and applied to many solvents and solutes by V. Gutmann and-his coworkers (3) in his work on the Donor Number Model providing excellent confirmation of our general approach. Though earlier articles (3a, b) contained differences in the Donor Number Model approach and the Coordination Model ( e x . , the importance of solvating properties of the solvent (3a) and the generality of the donicity scale (36) were in dispute), the moat recent review from this eroun - - ~ - L?c) - ~ ~ - . now utilizes a description which is fully consistent with the Coordination Model. A conclusion of the Coordination Model is that ionic displacement reactions are as much a property of the solvent as of the acids and bases employed. The preceding discussion serves to show the relationship of nonaqueous solvent and acid-base chemistry and provides a guide to the need for and ways of utilizing information about donor-acceptor interactions. This type of cycle is essentially the same basic approach used recently by Arnett, et al. (5). We now focus our attention on the internretation of auantitative data about donor and acceptor strkgths. s u c h a n approach has profound implications for testine the manv qualitative models employed in describing intermolecular inieractions and enabling-us to determine which are unacceptable. ~
~
Design of the Experiment
Ideally, we should base our models for intermolecular interaction on enthalpies' of adduct formation in the gas nhase to he sure that the thermodvnamic data are free of energy contributions from solvation, lattice energies, etc., which invariablv are associated with systems in condensed phases. Gas phase equilibrium measurements based on pressure changes ( I ) can be difficult and time consuming. Alternatively, spectroscopic changes accompanying ad: duct formation in the gas phase can be monitored (61, but most studies to date report large experimental errors, and these are often very optimistic (66) estimates. With limited manpower and the need of extensive, accurate data for generally applicable models to evolve, it was deVolume 51, Number 5. May 1974 /
301
cided to investigate donor-acceptor systems in nonpolar, poorly solvating solvents. Early studies showed that many solvents considered to be inert in fact are quite reactive. This is illustrated by the data inTahle 1. In view of the solvent complications described above, data selection is critical in formulating any model. We have shown that polar oxygen donors cannot be studied in the solvent cyclohexane and must be studied in CClr. On the other hand, nitrogen (7, 8) and sulfur (9) donors interact with CClr and must be studied in cyclohexane as solvent. The literature is filled with examples of studies aimed a t elucidating donor-acceptor interactions which have extensive energy contributions from solvation effects because the experiments were poorly designed. When the solvent is properly selected for the particular system to he studied, one can hope to approach data relatively free of solvation or association energies. For many chemical reactions, it isnot possible to find such solvents. The data collection and analysis aspect of the problem has been discussed in detail (10, 11). In many instances, improper methods have been used to calculate thermodynamic quantities from spectral studies and in most instances unrealistic error limits have heen assigned. Thus, one has to he critical in drawing conclusions from reported work. Some Typical Data and Some Qualitative Rationalizations By examining some typical data on donor-acceptor systems, we can establish some important facts and summarize some of the older qualitative models for rationalizing the results. The data in Table 2 illustrate the very important principal that donors2 (or acceptors) cannot be ordered according to strength unless the acid (or base) is defined. The adducts formed by the acceptors phenol and iodine with oxygen and sulfur donors illustrate the reversals in donor order that can occur as the acid is varied. Toward iodine, the sulfur donor is stronger than the analogous oxygen donor, while toward phenol, the oxygen donor is stronger than the analogous sulfur donor. In both adducts, the nitrogen donor is strongest. In our early approach to these and similar data, a qualitative explanation of the oxygen-sulfur donor reversal was offered based on Mulliken's description of the donor-acceptor hond. The donor-acceptor bonding molecular orbital is described as a linear combination of covalent (charge-transfer) and elecrespectively. trostatic wave functions, ,$ ,, and
In the qualitative use of this model, phenol, which has an appreciable dipole moment and no low energy acceptor orbitals, was predicted to interact best with those donors that have the largest lone pair dipole moment-the oxygen compounds-giving rise to b >> a in eqn. (3). Iodine with no dipole moment is expected to be essentially covalent in its interaction, ie., a >> b in eqn. (3). Iodine should interact best with those donors that have the lowest ionization potential, i.e., the ones whose charge cloud is most easily polarized. Similar considerations have been employed to explain the trends in the donor strengths of primary, secondary, and tertiary amines (12) and in explaining the acid strengths of (13) IC1, Br2. 12, C6HaOH and SOz. These "explanations" are comparable to the earlier descriptions of acid-base chemistry by Chatt and Ahrland (14) in which covalent acids or bases are referred to
It is hmed that the terms donor and acceptor strengths will be
basicity. 302 / Journal of Chemical Education
Table 2. Typical Donor-Acceptor Enthalpies
- AH(kea1 mole-?
Donors
h
IC2HdsO (CsHdnS ICaHdrN
4.2
7.8 12.0
CaHrOH 6.0 4.6 9.1
as Class B, while acids with a dominant electrostatic term are referred to as Class A. At just about this time (15-171, Pearson used the words Hard and Soft to include, along with other effects, the electrostatic (hard) and covalent (soft) contributions to acid-base interactions. Hard-hard and soft-soft interactions reportedly dominate soft-hard combinations. The data in Table 2 can be restated qualitatively in terms of the hard and soft vocabulary. The softer sulfur donors react more strongly with the softer acid iodine and the harder oxygen donors react more strongly with the harder acid phenol. The work of Pearson, et al. (15, 16), called attention to a wide range of systems in which acid-base considerations are relevant and in which at least two different effects are needed to rationalize the results. However, these qualitative explanations, whether they he hard-soft or ionic-covalent or Class A-Class B, all suffer from the arbitrary way in which they are employed. All Lewis acid-base type interactions are composed of some electrostatic and some covalent properties, i.e., ionic-covalent or hardness-softness are not mutually exclusive properties. Usually, in the acid-base or HSAB literature, results are explained after the answer is known. More often than not, -these concepts are used to "explain" data that is not directly related to hond strength. When used in this way, an HSAB explanation will either work or not work. If it does not work, one can blame it on strength. This can't miss approach sweeps a lot of interesting chemistry under the rug and leads one to believe he has understanding when in reality he may not. There is no chance for failure in one's ability to rationalize results and hence no chance to test for reality. What is needed is a quantitative assessment of the essential factors which can contribute to donor strength and acceptor strength. Proper combination of these factors should produce a close approximation to the enthalpy of adduct formation. Until this can he accomplished, it is not even clear that the strength of the donor-acceptor interaction is a function of the individual properties of a donor or acceptor. A Quantitative Scale of Donor-Acceptor Interactions
The organic chemist has been concerned with the correlation of equilibrium constants and rate constants in polar media for some time (18-20). One of the important ways in which our approach differs from earlier studies involves the points made in the section on Design of the Experiment. The earlier correlations invariably considered complex reactions in polar solvents for which there are many energy effects contributing to the thermodynamic data. It is impossible to interpret the resulting parameters in terms of the influence of changes in the electronic structure on bond streneth. One mav auestion what proportion of the total effectohserved in the' data correlateb is due to solvation or entrow effects and what proportion is due to changes in the enthalpy of interaction of the reagents resulting from changes in their electronic structure when substituents are varied. In 1965, Drago and Wayland (22) decided that if the ionic-covalent description of acid-base interactions was to be an acceptable model (for bonding), it should he possible to take quantitative data on the strength of binding and impose such a model on the data by empirically assigning ionic and covalent contributions. Furthermore, it was assumed that the ionic or covalent character in the adduct would be a property of the individual acids and bases involved. These are the usual assumptions in the
aualitative use of the ionic-covalent or other models. Accordingly, the following double scale equation was used to correlate and predict enthalpies of adduct formation in the gas phase and poorly solvating solvents
+
-AH = EAEs CGe (4) The subscripts A and B indicate acceptor and donor, respectively, while E and C are two empirically derived parameters assigned to each donor and acceptor. The set of equations that arises from determining the enthalpies for various combinations of acids and bases (for example, five acids and five bases produce 25 possible enthalpies for the 20 unknown parameters) are nonlinear and have an infinite number of solutions. The ionic-covalent model (or any other model, for that matter) can he imposed by fixing the minimum number of parameters needed to specify a unique solution. This turns out to be four parameters, as described in reference (23). The parameters in the reported fit were selected so that the trend in the E, numbers obtained for the methyl amines roughly paralleled their dipole moments and the CB numbers roughly paralleled their molar refractions. Since the arnines do not undergo a significant change in geometry upon coordination, we hoped to use these properties of the free bases to impose the ionic-covalent model on the system. Our success in doing this can only be gauged by the aereement between the parameters for other molecules in the correlation and the qualitative ideas about covalent and ionic bondine" in these svstems. This approach is nec.. essary, for we have no quantitative, independent way of Table 3. Number of Enthabies'
Acid
breaking up an enthalpy into the two independent effects that we will demonstrate contribute to it. However, our approach can fail if the resulting parameters for the acids and bases are completely out of line with qualitative chemical intuition about the importance of ionic and , and EA covalent bonding in these systems. The C parameters for iodine were set at 1.00 each, the E , number of N,N-dimethylacetamide was set a t 1.32 and the CB number of diethyl sulfide was set at 7.40 in the final fit which employed 280 measured enthalpies in 144 unknowns (23). The program employs the method of nonlinear least-squares (24, 25) analysis to find the values of the parameters which give the best fit between the measured enthalpies and those calculated from eqn. (4). A selected set of the parameters obtained is listed in Tables 3 and 4, along with the marginal and conditional deviations 123). Parameters for more systems are reported in the literature (231, along with the values for the calculated and experimental enthalpies which are seen to he in excellent agreement. Accordingly, by substituting the parameters for an acid from Table 3 and those for a base from Table 4 into eqn. (41, the enthalpies of formation of over 1000 adducts can be predicted with a fair degree of confidence. We can conclude from this fit that there are a t least two independent contributions to bond strengths in this series of acids and bases. The two effects are consistent with our qualitative ideas about covalent and electrostatic contributions to the bonding. This does not prove the ionic-covalent model, for it may be possible to fix our four parameters so that a different unique solution results in which
Some Selected Acid Parameters CA
(Mareinall
E* (Conditional)$
(Marginal) 1.00
Iodine Iodine Mrmoeblotideb p-&rtB"tylphenol p-Methylphenol' Phenol p-fl"ompheno1 ~-chlomphwol rn-fluomphenol rnmiauommethylphenol tert-Butyl Alcoholb Herafluomiaopropyl alcoholi Pymle Bomn niauoride (Gas]l Boron Trimethyl1 Trimethylaluminum" Trimethylgeuium Triethylpdlium niiethylti" Chloride Sulfur dioxide Bis(H~xafluomacety1seetonate) copper (11) Chlomform
.
d ~ a r a m & ris standard. 'The number in narenthese~indicates the number of enthslniea estimated from frequency shift correlations that agree with these parameters. 1 Steric effete co&monly encountered. 9 Marginal and conditional deviations. h The measured enthdpies have been corrected for the enthalpy of dimerization of the acid. i ~ h measured e enthalpies have been corrected for s 1.1 heal mol-2 enthalpy of intramolemlar hydrogen bonding.
Volume 5 1 , Number 5, May 1974
/
303
Table 4. Bas
Number' of Enthalpies
Some Selected Base Parameters En
Ce (Marginal)
(Cditional)
(Conditional)
(Marginal)
DLnethyhmine
(0.02) (0.03) (0.03) (0.03)
Trimethylamine
(0,021)
Triethylamine*
(0.026)
Aeetonihiie
(0.016)
Dimethylaeetamide Ethyl aeetate Acetone Diethyl etherd p-Diorane
(4
Tetrahydrofuran
(0.021)
Dimethyl S"lf0xide
( 0 02)
Diethy1 d 6 d d
(0.015)
Tetramethylenesulfide Pyridine-N-oxide
(0.014)
Pytidine Ammonia
Methylamine
(0.017) (0.013) (0017) ( 0 02)
(0.04)
Benzene
( 0 025)
Mesitglene
( 0 040)
2,2,6,6-Tetramethylpyridine N-oxyld l-Azabieydo[2.2.11 octane 7-Oxabieyelo[2.2.11 heptane
l-Pho~pha-4-ethy1-1.5,7-
triorabicyelo[2.Plloctane
3(H)
(0.73)
.
.
.
.
Number of enthelpies used to determine the parameters. The letter in parentheses indicates the solvent to be employed; H stands for cyclohexane or heran., and C fa* carbon tetrachloride. q e n t a t i v e value obtained from acids with similar C/E ration. These narameters were fired as standards so no deviations are available.
all the parameters are consistent with some other model. Such exercises are futile unless one can come up with an independent way of partitioning the total enthalpy of adduct formation on these systems into two parts corresponding to some model and then check the ability of this empirical approach to reproduce the values. However, there are valuable insights about acid-base chemistry which can he gained by taking other qualitative models and determining whether or not they are capable of passing a quantitative test on those systems for which data is now available. If these models do not, then they must he judged inferior to the ionic-covalent description which also works as well as any other qualitative description on qualitative data. Use of Our Quantitative Approach to Illustrate Some Common Misconceptions about Acid-Base Chemistry It is possible to demonstrate (23) that hoth the HardSoft Acid-Base (HSAB) Model (15-17) and the idea of base Donicity (3) are incomplete models for acid-base in-
teractions. A mathematical analysis based on a matrix formulation of the problem has enabled us to reach this conclusion. Here we shall summarize some of the results. It has been suggested (15, 16) that the E and C model constitutes a quantitative manifestation of the HSAB model. In order to examine this in detail, first consider the possibility that C is directly related to softness and E to hardness. Since hard and soft are opposite quantities for a series of acids and bases, E must decrease as C increases. As can he seen by the data in Table 5, this condition is not satisfied by the present solution, for there 304
/ Journal of Chemical Education
Table 5. A Set of Acids and Bases in whici: i snd C both Increase in the Series Acida
Bases CaHa CHCN (CH4,CO (CHaISO NHs
Cn
E*
CB
EB
1.681
1.34 2.33 2.85 3.46
are many systems in which both E and C increase upon going from one acid to another. A substance can not get both harder and softer at the same time, and examination of the appropriate references for HSAB indicates that no one substance is listed as being hoth very hard and very soft. In the lists (15, 16) of soft acids, for example, one finds substances as widely varying in their strength of interaction as chloranil, 12, BH3, and Pt2+. No further subdivision into varying strengths is made and only rarely (usually when HSAB clearly fails) is strength even mentioned. Due to the weakness of the acid Iz, the soft sulfur donor, tetrahydrothiophene ((CHzCHz)zS), will react more strongly with the hard acid aluminum trimethyl than with the soft acid, 12. This occurs in violation of the principle tenant of HSAB theory that "soft prefers soft and hard prefers hard," but is predicted by the E and C model hecause hoth the E and C numbers for aluminum trimethyl
are larger than those of iodine. Many other breakdowns in the HSAB rule can he predicted by referring to Tables 3 and 4 and finding acids or hases whose E and C numbers are hoth larger than those of another. Other difficulties that one can encounter even in the qualitative use of HSAB have been described (23). As both Klopman (26) and Pearson (156) have pointed out. hardness and softness are related to the CIE ratio. ~ o k e v e r all , predictive value about the magnitude of the interaction is lost in the ratio as can he seen from the fact that 1.49/16.9 for trimethyl aluminum is about the same ratio as 0.50915.56 for hexafluoroisopropyl alcohol. It is probably correct to call this ratio softness in describing the kind of interaction, but it is not softness as Pearson uses the term, for it has no magnitude. It should he pointed out that an assumption other than CA = E A = 1 for IZ would change the magnitude of CIE and the scale for differences in the compounds. It would not change the order. Thus, our use of this ratio is mainly for crude ordering purposes on a scale of relative importance of the covalent to electrostatic term. We have not proved HSAB is incorrect by the ahove discussion, hut just that it is different than E and C. The question now remains, can a mathematical equation he written which states the HSAB concept and can an acceptable solution be found employing quantitative enthalpy data? Since HSAB is generally used in a qualitative way we will be liberal in what we judge to be an acceptable solution. A literal translation of the HSAB rule that soft prefers soft and hard prefers hard can be cast into mathematical form with the equation -AH
=
(K
- Hd(K'
- H,)
+ H,HB
(5)
where HA is the hardness of the acid and K is the same constant for all acids which converts hardness into the opposite quantity softness. K' and Hn are similar quantities for hases. With appropriate numbers for K and K' when hardness is small, the K - H term is large and vice versa. We selected representative enthalpy data from our earlier article and used the nonlinear least-squares program to obtain the parameters K, K', HA and H n which best fit the data. The best fit that could (27) he obtained is summarized in Table 6 under the column headed HSAB. In view of the very poor fit of the data to this model, we decided to try a model involving a nonliteral translation of hard and soft in which the parameters are reciprocal quantities
+
-AH = H a H ~
1 1 -H, H ,
(6)
where HA and H n have the same meaning as ahove. We were also interested in trying to fit the equation k -AH = H A H B + -(7) HAHR where k is a best fit scaling factor determined by the program. The result of all these attempted fits are reported in Table 6 along with the results calculated by taking our E and C Darameters and suhstitutine them into e m . (4). As illistrated by the data in ~ & l e6, we can conclude that in the HSAB concept as it is most commonly employed the misses are large enough to make it incorrect even in a qualitative manner. It works as often as it does hecause of the selection procedure employed in using it. If one looks for systems in which there is a clear dominance by the CnCB or EAEx term, one can find a good deal of chemistry which obeys the simple rule that a covalenttype acid prefers a covalent-type base, and an electrostatic-type acid, an electrostatic-type base. Call these properties soft and hard and we have the HSAB approach. A hardness-softness-strength equation could be written as
Table 6.
Acid
A Comparison of the Data Fit for Equations (4). (51. (61 and (71 - A H Baee
Measured
E and CY
HSAB
Eqn.
Eqn.
(61
(71
1.
CeHsOH
so: AI(CH&
HCCh HFIP
An even better fit of thie data could have been obtained using our E and
where S is the strength of softness and K the strength of and E A = KA(EA/ hardness. However, CA = SA(CA/EA) CA),SO this is a simple rewrite of eqn. (4) with no obvious advantages for this additional complication since "strength of hardness" and "strength of softness" would have to change in a way contrary to the accepted definition of the words. Furthermore, why use three terms (hardness, softness, and strength) for qualitative discussion when two (covalent and electrostatic) do as well. One could counter the ahove conclusion by saying that the hard-soft model is very valuable to the synthetic chemist and should he retained for that reason. In this connection, we should hasten to point out that a miss by 1.4 kcal mole-' in the enthalpy corresponds to about an order of magnitude miss in the equilibrium constant. A product may not be obtained when the K is 90, hut can usually he isolated when the K is 900. Thus, we can see from Table 6 that many incorrect qualitative predictions are also expected from HSAB. We have shown (23) how the qualitative procedures employed by Pearson to order bases as hard or soft gives rise to the wrong assignment to benzene and SO2 and also to the series (CzHs)zS, (CzH&N, and (CZHJ)ZO.We suggest that a qualitative approach employ the terms "large C property" for soft and "large E property" for hard. Suhstances can then be considered to have hoth a large C and a large E relative to some other substance. Large size, low ionization energy, and other properties leading to softness (15, 16) often contribute to a large C, while small size and high charge, etc., contribute to a large E. Listings of acids and bases according to large E's and large C's could very well contain the same substance with a strong ranking in hoth tables. A C ordering for some common bases would > CsH5N > CH3HN2 > NH3 he: (CzHd3N > ( C z H 5 ) ~ S > (C2H5)z0 > (CHdzSO > CH3CN, while an E ordering would he NH3 > CH3NH2, ( C H J ) ~ S O> C5HsN > CH3NHz > (CzH&O > CH3CN. Acids in which the E property dominates prefer bases with a large E, while acids dominated by a C property prefer hases with a large C term and vice versa. This is not a hard and fast rule, for differences in the E terms could he more important than the differences in the C terms even though the CACH product is largest. The exact ,meaning of the term large C or large E as applied to molecular interactions is not established (i.e., the Volume 51, Number 5. May 1974
/
305
Table 7. Systems not Correlated by the E and C Approach Acid
Base
- AH,"wA
-AH-...
B(CHz1. (CHdSnCI (CHalSnCI
Al(CH3z BFa B(CHz1z BFa
'M o m.s , H. L., et sl., Inorg. Chrm., 5, 124 (1966). or ria, H. L., ~ a m r e s M., , and searlea, ~ r . ,s., ~ n o r g .Chm., 5, 2156 (1966). 'See reference (23).
covalent-electrostatic model is not proven), hut even if the HSAB model were correct, the same criticism can be leveled against the words hard and soft. Compromise terminology for those who prefer something more catchy could involve referring to acids and hases as soft and charged, remembering that a substance that is not very soft is not necessarily charged. Clearly, the work of Pearson (15-17) has been very valuable in collecting and illustrating the generality of Lewis acid-base considerations. The reader is strongly urged to read these references to obtain a wealth of information for teaching acid-base chemistry. The reactions "explained" must he qualified by the considerations described in Fiaure 1 of this article-and the ensuing discussion. The descriptive terms hard and soft are quite inappropriate to describe the magnitude of the interaction for we cannot redefine words that have an opposite meaning in commonlv acceoted usaee to suit our . nnrnoses " . even though " their catchiness makes it tempting. This is not simply a auihble about the selection of names for the two oronerties. The either-or character of the theory prevails & (he procedures employed to obtain the hard-soft rankings and are incorrect, for the strength of interaction is often not constant when the softness or hardness orders were inferred. For further details on the two views of this problem, the reader is referred to references (27-29). Interpretation and Uses of the Eand C Parameters As one can see from the previous discussion, a great deal more has been accomplished with the E and C equation than simply empirically obtaining parameters which reproduce known enthalpies. In addition to those accomplishments mentioned above, there are several other significant consequences of this treatment. 1) An important use of E and C numhers is in the calculation of enthalpies of adduct formation for systems which have not been examined experimentally. We are now in a position to predict almost 1000 enthalpies by combining the parameters reported (23) according to eqn. (4). The trimethylaluminum enthalpies are for the monomer (the observed enthalpies are corrected for the enthalpy of dimerization of trimethylaluminum). I t should he remembered that all the parameters in Tables 3 and 4 are not known with equal confidence. The ability of acid parameters to predict accurate enthalpies of interaction when used with accurate base parameters depends upon the number of enthalpies for that acid which were included in the correlation, and upon the range of C / E ratios for the bases involved in those interactions. For example, iodine, trimethylaluminum, and phenol have been studied with a large number of bases including hases with very different C/E ratios. Enthalpies predicted using the parameters for these acids should then he very accurate, as long as the hase parameters are also well known. When it becomes essentiil to draw conclusions on systems not known as well, additional enthalpies must he measured to determine the parameters more precisely. Some bases 306
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have enthalpies reported only with hydrogen bonding acids (with similar C/E ratios). For these, it should be possible to predict gwd enthalpies with other hydrogen honding acids or acids in which the E term dominates. Other systems are not as reliably predicted. As more good data becomes available, the parameters reported on systems for which only limited data is available can change. The change can be large if one of the literature results used in the fit reported here is incorrect. 2 ) The E and C parameters are consistent with chemical intuition and with the earlier qualitative explanations of donor and acceptor strengths in terms of ionic-covalent bonding and consequently provide new insight into this behavior on systems where this insight is absent. For example, compared to the iodine ~ a r a m e t e r s most , ~ hydrogen-bonding acids considered here are found to have a large electrostatic parameter (E,) and a smaller covalent parameter (CA). Phenol, however, has a larger C term than the aliphatic alcohols in keeping with literature reports from dipole moment measurements of hydrogenbonded complexes (30). The data in Tables 3 and 4 provide this information on many more systems. The ionic-covalent model is not proven, so this kind of application should he used with caution. Covalent honding and electmstatic interaction depend on bow far apart the donor and acceptor are in the adduct, so, somehow, this distance function is incorporated into the parameters. Many of the molecules in the E and C correlation undergo drastic changes in their geometry upon adduct formation. Acids like (CH&SnCI, BF3, and SbCls undergo extensive rearrangement from their structure as a free acid when they form an adduct. I t has been shown that the extent of rearrangement is variable depending upon the strength of interaction and that the long expounded concept of a constant promotion energy is not correct (31). The fact that acids with large variable promotion energies fit into the E and C correlation further illustrates the complexity of our E and C numhers and we must understand how this comes about. This is the goal of a substantial amount of our effort a t the moment. 3) The parameten reported in this manuscript come very close to having C numbers for the amines that are proportional to their molar refractions and E numhers for the amines that are proportional to their dipole moments. I t would have been a simple matter to have made an initial selection of the fixed parameters such that the resulting methyl amine parameters paralleled these properties of the free hases almost exactly. A procedure for carrying out transformations of this sort has been described (32). The parameters obtained for many of the other acids and hases in the system do not parallel their dipole moments or molar refractions. In general, the nature of the hond formed is not a property of the free acid or hase. For example, BF3 is planar and has no dipole moment. However, in an adduct, the fluorines occupy positions approaching those on a corner of a tetrahedron. The BF3 fragment in the adduct thus has an appreciable dipole moment, and there are large electrostatic contrihutions to the hond in the adduct. Thus, one should not expect the E and C parameters to parallel properties of the free acids and bases except for limited systems. 4) One of the most important contrihutions of the E and C equation is to quantize the interpretation of intermolecular interactions. This field has a history of wild speculation as imaginative chemists propose a new effect every time they are surprised about the stability or lack $In solving the simultaneous equations leading to the E and C parameten, we arbitrarily set CA = EA = 1for L.Consequently, we cannot compare CA values versus EA values for an acid. The parameter can be interpreted relative to the C, paremeter of iodine or that of some other acid and likewise for EA. Similar limitations apply toE, and CB.
thereof of some species. We have been able to quantitatively treat a large number of systems with just two effects. Tahle 7 contains systems that do not obey eqn. (4), so we now know some new effect is needed for these systems. Some of the discrepancies can be attrihuted to steric effects. When the steric interaction is a function of the geometry of the acid-base pair and not an inherent pmperty of the donor or acceptor, e.g., as in F-strain, (33), one would expect to calculate a larger enthalpy of adduct formation than that measured. Indeed, using the E and C parameters, one calculates an enthalpy of interaction for the boron trimethyl-trimethylamine adduct of -24.7 kcal mole-I compared to a measured value of -17.62 kcal mole-'. The discrepancy, 7.1 kcal mole-l, is attributed to steric strain. The maenitude of this strain enerev was predicted to be 7.8 kcal mole-l by H. C. Brown from heat of combustion data on a hydrocarbon which is structurally analogous to the adduct i33). Other systems which have pronounced steric effects are summarized in Table 7. In the case of (CH&SnCl and BFJ adducts, one would expect the steric interaction to be greater for (CzH&O than for (CH2)rO from examination of Shulman molecular models. Accordingly, the (CHz)rO adduct gives closer agreement hetween AHcaI,. and AH.,, In attempting to obtain meaningful E and C parameters, data in which steric effects are felt to be present must be omitted. Some systems in which steric effects might have been expected, on the basis of a lower than expected enthalpy, are shown not to have these complications. For example, the lower enthalpy for the formation of the ( C Z H ~ ) ~ N - H Cadduct C I ~ than expected (i.e., compared to the pyridine and ether adducts) is not due to steric effects, but due to a small EBterm for (C2Hs)sN and a large relative importance of the E A term in HCC13 compared to other acids. Too often in the past, surprise at the magnitude of some result is met by proposing a steric effect or some other unusual bonding effect. Clearly, this type of insight into intermolecular interactions provided by the E and C correlation which helps eliminate or verifies these surprises is even more valuable than the quantitative prediction of enthalpies. The systems BF3-(CHz)rS and BF3-(CzH&P in Tahle 7 are not clearly understood. In the past, this could have been glihbly dismissed as a hard-soft comhination. Since they do not obey eqn. (4), some new explanation is required (if the data are valid), but more systems which deviate are needed so some pattern can be established before an explanation can be offered. Basically, the E and C equation tells us when to he surprised and gives us some appreciation of the large amount of data that must he obtained before a new bonding concept can be proposed. Data to establish E and C must be obtained and then several exceptions are needed to establish the cause for the exception. Steric effects are but one example of a way to dismiss surprises. The inorganic chemist's favorite one is a hack bondine. " I t mav often be a real effect. but mav . .iust as often be a consequence of a poorly designed experiment for detectine simificant bondine contributions to intermolecular inteiacGons or a poor appreciation of the C and E parameters of a donor or acceptor. Often basicity toward a proton in water is the criterion for donor strengh. Consequently, a backbonding is invoked when an acid with a large C I E ratio is employed because the relative importance of the CC term is not appreciated. It will be very interesting to see if a new term must be added to eqn. (4) t o accommodate systems on which good quantitative, solvation minimized data are available and in which K backbonding is thought to be important. Progress has been slow because of the difficulty in finding a system where most people feel tbis is an important effect and which also satisfies our requirements for a quantitative study. Several
experiments must be carried out to determine the E and C parameters for the donor and acceptor pair which may r backbond on systems where a honding is not important. When tbis acid and base are combined, the E and C equation will predict an enthalpy that is too low if a bonding makes a significant contribution to the enthalpy. A study of the nature of the metal center in methylcobaloxime illustrates several of the ideas contained in this article. Studies related to equilibrium constant or rate constant measurements were reported in the literature on these systems, and they indicated a very large preference for binding to sulfur donors as compared to oxygen donors. This data was used to label the cobalt center as "soft." An investigation of the enthalpy of adduct formation (34% on the other hand, indicated that the bond strength with the oxygen donors (i.e., the enthalpy of adduct formation) is greater than with the sulfur donors and the center is not "soft." In this system, the E and C parameters predicted an enthalpy of adduct formation toward phospbite donors which is lower than the experimental value. Thus, an additional stabilization of the adduct, possibly via * backbonding, is indicated. Applications of this sort constitute a very powerful potential use of the E and C correlation in understanding chemical reactivity. Additional information on this t o ~ i can c be obtained from an audio set of tapes by the ~ m e r i c a nChemical Society on a short course on "Acid-Base Chemistry" by this author. Acknowledgment
The authors gratefully acknowledge the generous support of this work by the National Science Foundation through US NSF GP 31431 X. Literature Cited i l l (sl D r a m R. S., and MafwiyoEZ N. A,, "Acids and Baaps," D. C. Hoafh, Boston. 1968.khapter 1. (b) Orago. R. S.. "Principles of Chemistry with Practical Applications," Allynand Bacon. Boston, 1974. Chapter 7. 121 D r a m R. 8.. and Pureall. K. F.. 'Pmmrs in Inoreanic Chemistrv." (Ediloc Coteneentherein. (31 (a1 Gutman". V.. "New Pathways in i n w a n i e Ch.mist.y." iEdi10r Ehsworth., E. A. V.. Maddock, A. G.. and Shsrpo, A. G.1 Cambridge University Press. 1968. and references thorein. (bl Gutmann. V.. Chsm. in Elit. I, 102 (19711. ic) Msyrc, U.. and Gutmann. V.. Sfrue. and Bond., 1%. 113 I19721 and references therein. (41 Leffler. J . E., end Grunwald. E., in "Rats8 and Equilibria or Organic Raaetiona." John Wilay & Sons. Inc.. New York, 1963. I51 &nett. E.M.,etal., J . Amer Chem. Soc.. 94.4724l19721. I61 la) See, for example. G d e n o w . J. M.. and Tamres. M.. J Chem. P h m . 43, 3393 (19651. lbl Tamres, M.. and Bhat. S. N.. J Amor Chpm Soc. 94.2577 119721. (el Long, F.T.:andStrnng. 8.L.. J A m a r . Chem Soe., 87,2345l19651 (7) Partenheimer. W.. Eplev. T . D., and Dcago, R. S., J. Amer Chem. Sor., 99. 3886 (1968): 91. 2883(19691. (81 N o m i , M.,snd h a p R.S.,submifted. 19) Voge1.G. C.. sndDrago, R.S..J.Amer. C h m . Soc., 92.5347(19701. (101 Guidry,R.M..sndDrago, R.S.,rubmitlad. (11) Slejko, F. C., Drago, 8. S., and Bmwn, 0.. J A m m Cham. Soc., 94. 91W (1972) and reference8 therein. , and Joenen. M. D., IW. chem., 2. 1056 (12) ~ r a g o R. , s., ~ e e kD. , w., ~ o n g h i R., (1963). (131 Drsgo, R. S.. and Wenr, 0. A,. J Amer Cham. Soc.. 84,526 (19621. (i4) Ahrland, S.,Chatt, J., andDaview, N. R.. Quart. R s u . 12.265 119581. (151 (a1 Poaraon, R. G., J Amer. Chcm. Sor., 85, 3533 (19611; ibl Science, 151. I72 (19661: lcl Chem inBritain, 3.103(19671. (16) la1 Peamon, R.G.. J.CHEM. EDUC.. 45,58l19631; (bl 45.643 (19681. (171 Pearson. R.G..andSangstad, J..JAmer. Chem Soe.. 89.1827 (19671. (18) See, for example. Wells, P. R., Chem. R e " , 63, 171 119631; Lefler, J. E.. and Grunwald. "Rates and Equilibria of Organic Reacfionn." John Wiley & Sons. Inc.. Now York, 1963. (191 aft. R. w., "Steric Effect8 in Organic Chemistry: (Editor Nrwman. M. S..l John Wiloy & Sons.Inc.. New York. 1956,Chapfer 13. (20) Swain. C.G., and Scott, C.B..J.Amer Chem Soc., 75.141 (1953). (21) Edwards. J.O..J.Amer. Chem. Sac., 76,1541 (19541; 78, i819i19561. 122) Drago.R.S., and Wsyland, B.B.. J A m o r . Chem Sac., 87,3571 (1965). 1231 Drago. R. S.. Vogd. G. C.. and Needhsm. T.. J . Amer Chem, Soe., 93. €014 (1971) ,... .,.
(24) (251 (26) (n) (28) 129) (30) (311
Hamilton, W.C., "Sfafi~fiesinPhyaiealSeirnee,"RonaldPress. NowYork Lingano.P. J.. andHugus, 2.2.. J~..lnorg.Chem., 9. 757 (19701. Klopman, G J A m e r . Chpm Soe.. 90.223(19681. ~ . s . . s ~ d ~ a b i e r . ~ . ~ . Chem.. , I n o r1~1 . 3 1 ~ ~ 1 9 7 2 1 . Pearson. R.G..horg. Cham., 11,3146(19721. Drago.R.S..lnorg. Chem., lZ.221i 119731. Kimure.K., sndFyishirn. R..Buli. Chem S o c Jopon. 34.301 119611. Bmwn, 0. G., Drsgo. R. S., and Bolles. T. F.. J A m m Chpm S o r , 119681. I321 Sle,ko, F.,..I sndDra$o, R. S..J Amor Chem. Sac., 95,6935 (i9731. (33) Brown, H. C.. J . Chem Soe. 1248 (1956). (34) Cnurtrieht. R.. Drago. R. S.. Nus.. J . A . and Nozari. M.. horg Chem., 12, 3611 (1973).
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