Michael R. J. Dack Australian Notionol University Canberra, Australio
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The Influence of Solvent on Chemical Reactivity An alfernafive approach
Reactant solubility should no longer he the sole criterion of solvent selection. The choice of one solvent over another can result in millionfold rate changes for a particular reaction, and because ways of accelerating or retarding reaction rates are constantly being sought in industry and in medicine, an understanding of solvent effects becomes essential to the practicing chemist. Early workers regarded a reaction solvent as a homogeneous dielectric medium in which a reaction was conducted. Specific solute-solvent interactions were neglected, and solvent structure ignored. Weak electrostatic interactions simply created a loose solvation shell around a solute molecule. It was in this climate of opinion that Hughes and Ingold (I) resented the first satisfactory qualitative account of solvent effects on reactivity. Their approach to the subject, based on the transition state theory, has formed the backbone of later theories. Hughes and Ingold realized that the transition state of a reaction contains either more or less charge than the ground state, or a greater dispersal of charge than the ground state. The extent of solvation in the two states therefore differs, since a polar solvent solvates the more polar species with greater efficiency. Moreover, a polar solvent solvates a given solute molecule more efficiently than a less polar solvent. Solvation lowers the free energy of a state (see the figure) so that solvent transfer invariably alters the free energy of activation of a reaction. We now know that specific solute-solvent interactions of the donor-acceptor type (including hydrogen bonding) also affect the free energy of the reactants and the activated complex. In fact the enormous rate changes mentioned above stem from the ability of one class of solvent (protic solvents) to form hydrogen bonds with anionic solutes, and another class (dipolar apmtic solvents) being unable to donate hydrogen bonds to the anions. The dipolar aprotic solvents enable anionic solutes to react from a much higher free energy level (2). Thus, the Hughes-Ingold theory, or various modifications of it which account for specific solvent effects (3), has remained unquestioned for 40 years. There are, however, a number of disquieting features to the theory which make an alternative approach worth considering.
must be admitted that predictions of solvent effects on entropy controlled reactions, using the Hughes-Ingold theory, agree with experimental results. Nevertheless a theory which holds for the wrong reason must be suspect. A second limitation to the theory concerns its inability to deal in detail with electroneutral reactions (e.g., DielsAlder reactions, radical reactions). Since no movement of charee occurs on passinp from the mound state to the tran&ion states or these reactions, their rates might be expected to he solvent independent. The observed rate constants do vary with solvent, although the variations rarely exceed an order of magnitude. The final failing of the Hughes-Ingold theory concerns its neglect of changing solvent structure. Solvent-solvent interactions are usually very small compared to solute-solvent interactions, but~considerationm i s t he given to solvent association when reactions are conducted in a highly structured solvent like water, Cohesive Forces and Internal Pressure Before the advent of the transition state theory, and the resulting nreoecu~ationwith the enereetics of solutes in u solution, a large number of solution phenomena were explained in terms of the cohesive forces of a solvent acting bn a solute.
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Criticisms of the Hughes-lngold Theory The first of these features involves the assumption made by Hughes and Ingold (5) that the contribution of entropy changes (AS) to changes in free energy of activation are negligible. In other words, enthalpy changes (AH) dominate the free energy (AG) expression AG-AH - T M The assumption is necessary because an increase in solvation usually decreases the entropy of a given state as well as its enthalpy. Changes in the two components of the free energy counteract each other. Fortunately solvent effects on most chemical reactions are cont~olled by enthalpy changes; some are not (e.g., Menschutkin reactions). I t
Reaction
Coordinate
The effect of a change to a more polar solvent on the free energy of activation of a reaction. 1 Free energy of activation of a reaction in a given solvent; 2 Effect of a change to a more paiar solvent-reactants more polar than activatad complex; and 3 Effect of a change to a more polar solvent-activated complex more paiar than reactants.
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The cohesive forces holding a liquid together create a pressure within the liquid which has been termed the internal pressure, Pi. In addition to experiencing this pressure due to solvent structure, dissolved solute molecules are also subjected to pressures from solute-solvent interactions. These "chemical pressures" around a solute cause the solvent cavities to contract. The system as a whole contracts in the Drocess known as electrostriction. is defined as (AE/AV)-the change Internal in internal enerev of a system durine small isothermal volume change. Early workers found difficulty in measuring this property. Hildehrand (6) therefore adopted the cohesive energy density (c.e.d.) of a liquid as an appmximation of its internal pressure. Cohesive energy densities are obtained from
where AH is the latent heat of vaporization of a liquid at a temperature T,and V, is its rnolnr volume. The property is a measure of the energy ( A E ) required to remove one mole of liauid from a milliliter of the liuuid. and it renresents thetotal molecular cohesion per ml of thk liquid. . Pi and c.e.d. only agree for nonpolar liquids. Polar liquids, in which appreciable association of the molecules occurs, possess values of c.e.d. far in excess of Pi. Ethanol, for example, has a c.e.d. of 168 cal cm+ and a Pi of 69.5 cal cm-3 (7). Thus the difference can be ascribed to the structure-making effect of hydrogen bonding. Table 1 contains values of c.e.d. and Pi for a selection of solvents in units of cal cm-3. The conversion to atmospheres is also included to give an indication of the magnitude of the internal pressures being discussed. The square root of Pi appears in working expressions of solubility problems. Hildebrand (6) defined 6, the soluhility parameter, to be the square mot of c.e.d., and 6 is known for a host of solvents, polymers and synthetic materials. It must he remembered that 6 is based on c.e.d. and not on Pr, a fact that sometimes detracts from its usefulness. Rates of Chemical Reactions Since we intend to show the effect of "chemical" and "structural" solvent pressures on the rates of reaction, we must also consider volumes. Like entropies and enthalpies, pressures and volumes go hand in hand. Reactant molecules have a certain volume I F ) in a given solvent. The volumes depend on the structure of the molecules and also on the ability of the solvent to compress this volume by electrostriction. The volume of the activated complex (Vf) of a reaction is governed by the same two factors. The difference (Vf - VR) is the volume of activation (AVI) which accompanies a reaction process. Volumes of activation are usually obtained by conducting Table 1. Cohesive Energy Densities (e.e.d.) and Internal Pressures (Pi) for a Selection of Organic Solvents ( 7 ) Solvent Ethylene glycol Dioxane Acetophenone Methyl iodide Toluene Ethyl acetate Carbon tetrachloride Acetone Ethanol Methanol Diethyl ether Pentane Water 232
Pi c.e.d. (cal cm-a) (cal em-?
120 119.3 109.3 89.5 84.8 84.5 82.4 80.5 69.5 68.1 63.0 54.8 41.0
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212 96 109 99 80.6 83.0 74.6 95 168 212 59.9 50.2 547.6
c.e.d.
(atm) 8681 3909 4466 4047 3278 3374 3040 3853 6871 8621 2474 2038 22608
a reaction a t varying external pressures (P) and ohsenring (a In k l a P ) ~where , k is the rate constant. If pressure variations of a few thousand atmospheres can produce substantial changes in k, one can imagine the effects of a solvent change from hexane (c.e.d. = 2164 atm) to water (c.e.d. =22,608 atm) on a reaction. Richardson and Soper (8) were the first to notice the connection between solvent cohesion and reactivity. They found that reactions in which the products had greater cohesion than the reactants proceeded faster in solvents of highest cohesion. The converse also applied. Reactions which underwent little change in the cohesion of the species responded pwrly to solvent change. Glasstone (9) later came to the same conclusions from theoretical considerations. The following important relationship can be derived (10) for a reaction between A and B in solvent S
The constant refers to the rate of the reaction in some standard state. This expression was derived for reactions devoid of specific solvent effects, in solvents free from self-association. Values of 6 obtained from c.e.d. could therefore he used in it. Thus the rate of a reaction depends on the difference in molar volume between reactants and activated complex (AVf), and the relative internal pressures of reactants, activated complex and solvent. One assumption is necessary before we can proceed with an analysis of solvent effects on reactivity. We must distinguish between reactions with positive values of AVf (eqn. (2)) and those with negative values (eqn. (3)). Since a net lwsenine of bonds occurs in ean. (2). . . it is assumed that 6~ > Mi,, where R denotes the reactants. In case eqn. (3). 6. < 6+ because a comnression of intermolecular bonds
Effectof Solvent Polarity and Internal Pressure on Reactivity Consider first of all the nonpolar reactions-i.e., those with nonionic mechanisms and involving molecules of low nolaritv. Solute-solvent interactions (el&trostriction) are almost absent, so that the volume of the reactants, VR, and activated complex, Vf, remain insensitive to solvent transfer. The relative reaction rates will depend on (6R as)* - (6t - 6#. When the reaction is of type eqn. (11, In k decreases as 6~ increases, while In k increases as 6s increases in reactions of type eqn. (2). Equation (1)therefore predicts that the internal pressure of solvents influences reaction rates for nonpolar reactions in the same direction as external pressures. Changes in VR and Vf for polar reactions cannot be ignored. In fact, electrostriction effects are so great that the internal pressure terms in eqn. (I),( 6 ~ 6 d 2 - (6i ; 6s)', are relegated to a minor contribution to i n k. Accordingly, solvents which produce a more negative volume of activation (i.e., increase F / V f ) in a polar reaction will accelerate that reaction. An exception would be polar reactions in nonpolar solvents, where solvent internal pressure might still he expected to govern the rates The above account of solvent effects, therefore, embraces both nonpolar and polar reactions. Once the sign of AVf for a particular reaction has been established, the effect of solvent transfer on the rate is determined by the influence of solvent internal pressure and polarity on AVf. We now demonstrate how the theory can he applied to reactions of different charge type.
Table 2. Scheme~forthe Pressure/Volume Approach to Solvent Effects on Chemical Reactivitv
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Effect of increased solvent polarity on Reactants AV* Activated comnlex
Effect of increased polarity/intemal pressure on rate of reaction
Application of the ~ressure/VolumeApproach to Solvent Effects Polar reactions have been divided according to the Hughes-Ingold classification (5), and they form reaction types 3-8 in Tahle 2. Types 1 and 2 are unimolecular and bimolecular nonpolar reactions, respectively. Predicted volumes of activation also appear in Table 2, along with an estimation of the effect of solvent polarity/internal pressure on the reaction rates. Nonpolar Reactions Ouellette and Williams (11) have pointed out that variations in rates caused by the changing internal pressure of solvents should be small in most solvents and should not exceed an order of magnitude. Radical reactions are notoriously reluctant to alter their rates on solvent transfer, and the variation of k for Diels-Alder reactions over a large range of solvents is also quite small. These ohsewations appear to indicate the involvement of solvent internal pressure in the reactions. Unimolecular decomposition reactions must have a positive value of AVX. No matter what the detailed mechanisms of the reactions mav " be.. bond hreakine must occur to some extent in the transition state. On theother hand, reactants in a bimolecular reaction come within each other's van der Waals radii in the transition state, so that a volume contraction occurs (12). We would therefore expect a change to a solvent of higher internal pressure to retard nonpolar decomposition reactions of such compounds as nitrogen pentoxide (13) and phenylazotriphenylamine (14). The rates of Diels-Alder reactions (AVt e -20 em3 mole-l) should increase (1.5) on transfer to a sol-
vent of higher Pi. Both predictions are home out by experiment, as are other predictions made below. A word of caution is required when dealing with radical reactions. Species are sometimes created which behave uniquely towards certain solvents. "Cage effects" in these reactions, for example, can discredit any prediction of solvent effects. However, nonadherence to the theory may provide useful information about the reaction mechanisms. Polar Reactions Reactions which proceed by ionic pathways involve charge formation, destruction, or dispersal a t some stage. Specific and electrostatic solute-solvent interactions tend to be strong, and it follows that solvent electrostriction exerts a powerful effect on the volumes of the dissolved species. Experimental data show that the dissociation of a neutral molecule into two free ions produces a contraction as great as 45 cm3 mole-' in methanol (12). Volumes of electrostricactivation range between *40 cm%ole-'; tion clearly dominates changes in AVX. Reaction types 3 and 5 in Tahle 2 illustrate reactions where neutral reactants undergo charge-separation in the transition state. By analogy with the nonpolar decompositions, the volume of the activated complex of the unimolecular reaction (type 3) should be larger than that of the reactant because of hond stretching. The creation of charge, however, causes such electrostriction of the solvent that a volume contraction actually occurs. Thus the hydrolysis of t-hutyl chloride in 80/20 ethanol/water at 25°C is accompanied by AVf = -17 em3 mole-' (16). Electrostriction has the same effect on bimolecular reactions of type 5. Volumes of activation for Menschutkin reactions lie in the range -20--45 cm3 mole-' (12, 17). while the SN2 solvolysis of allyl bromide in methanol a t 23°C gives a value of about -27 cm3 mole-' a t atmospheric pressure (18). A change to a solvent of higher polarity reduces Vt further. Values of AVt become more negative, and the rates of reaction increase. I t is as if the changed internal pressure of the solvent is now acting on a "new" volume of activation. Reactions of types 4 and 6 lose some of their reactant charge in the transition state. Electrostriction therefore acts more stronelv - " on the reactants to give hoth the unimolecular reaction and the bimolecular reaction positive volumes of activation. Decomuosition of dimethvl-t-butvl sulfonium ion in water a t atmospheric pressure yields A V ~ = +9 cm3 mole-' (19). The following charge-neutralization reaction (12) has a volume of activation of +8 cm3 mole-' a t 25°C and 1atm
-
NHCICOCH,
NHWCH,
+ cr
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and the iodide catalyzed hydrolysis of protonated diethyl ether (20) a t 1 atm and 200°C has AVt = +1.0 cm3 mole-1. An increase in solvent polarity increases solvent electrostriction around the reactants relative to the activated complex, thereby causing the rates of reaction to fall. The remaining polar reactions (types 7 and 8) are of the charge-dispersal type. Charge carried by one of the reactants is spread over hoth reactant molecules in the transition state. In the absence of electrostriction, a volume contraction should accompany a bimolecular reaction though its transition state. Electrostriction favors the more concentrated charge and so it will act to reduce the volume of the reactants in relation to the activated complex. I t is found that this is a small effect--one that does not overcome the ."natural" volume contraction of the reactants. Experimentally determined volumes of activation for reactions such as the isotopic exchange of iodide Volume 51. Number 4, April 1974
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ion in propyl iodide (21), and the attack of NO=+ on benzene in the nitration reaction (22) are negative. Values of k, therefore, decrease with increasing solvent polarity. Estimation of Solvent Polarity In the absence of experimental values of AVt, a measure of the relative electrostriction effect of solvents around a particular solute is required. The use of the electrostatic factor4efined as the product of dielectric constant and dipole moment-has been proposed (23) as a measure of electrostatic solute-solvent interactions. Neither property on its own appears adequate. A number of solvent basicity scales are available to represent the ability of solvents to accept hydrogen bonds from solutes (24-26). In addition empirically derived solvent "polarity" scales give an account of the effects of solvents towards a model system (27-29). The use of such scales has been discussed recently (30). Thus, it should be possible to obtain an estimate of the relative effect of solvents on volumes of activation from these measures of solute-solvent interactions. Observed Relationships Between Solvent Internal Pressure and Rate Data Stefani (31) believes that many polar reactions may he dependent on the internal pressure of solvents. This arises when solvation of the reactants and the transition state occurs to a similar extent. Even though the "chemical pressure" of the solvent may he dominant in a particular system, a cancelling out between the ground state and the transition state may promote the "structural pressure" to a new importance. In support of his suggestion Stefani has linearlv correlated the soluhilitv " ~ . a r a m e t e.r .6.. with rate constants for a few polar reactions: the esterification of ethanol with acetic anhydride. two Menschutkin reactions, and the reaction of: meth;l acrylate with cyclopentadiene-all in a variety of polar and nonpolar solvents. Herbrandson and Neufeld (32) proposed 6 as a "new solvent parameter" for reactions. They found that although 6 should not really he applied to polar reactions, fair correlations are obtained with measures of solvent polarity such as ET (29), Z (28). and Y (27). These authors are also of the opinion that solvation effects may largely cancel out between the ground state and the transition state in many reactions. Gordon (33) has similarly stressed the importance of internal pressure to reactivity and has found good, separate, linear correlations for protic and aprotic solvents with a spectroscopic polarity parameter, XR. Other workers have expressed reservations about the importance of solvent internal pressure to chemical reactions (34). Clemens and Colter (351, for example, observed an increase in rate constant with increasing 6 for the racemization of 1,l'-hinaphthyl in 13 solvents, hut the scatter of the points was so large as to make a prediction of additional rate constants impossible. These observations were in direct contrast to the linear relationship found by Wmkler and coworkers (361 between 6 and rate data for the isomerization of cis-azobenzene to trans-azohenzene. Both reactions had ~reviouslybeen considered to be nonpolar reactions. e he results o f Clemens and Colter may indicate that a greater redistribution of charge than expected occurs during the racemization reaction. A lack of
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Journal of Chemical Education
correlation between 6 and rate data for other nonpolar reactions may also he explained in this way. Summary The pressure/volume approach to solvent effects on chemical reactivitv can be summarized as follows Solvents which lower the value of the volume of activation of a reaction by electrostriction accelerate the rate of that reaction. 2) Those solvents able to raise the value for the volume of aetivation of a reaction cause the rates to fall. 3 1 S u l v e n l ~ntcrnalprersulr nrrs on the r a t e r 01' nunpolar rcacrinns, and on polar reacrimi in nonpolar sol\.mta, in the ram* direction a i cxwrnal pressures. 1)
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It should be noted that the pressure/volume theory has been referred to as an alternatiue approach throughout this article. The theory can deal with electroneutral reactions, and i t does not reauire a distinction between enthalpy and entropy. By considering solvent internal pressures i t also accounts for solvent structure. However. the Hughes-Ingold theory is perfectly adequate for most purposes. Our aim has been to demonstrate that it is possihle to approach the subject of solvent effects from more than one direction. An increased effort in this area may well add to our knowledge of the influence of solvents on chemical reactions and on other phenomena in solution. Acknowledgment Thanks are due to Professor A. J. Parker for encouragement and helpful criticisms. Lilerature Cited
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11) Hughes, E.D., andingold. C.K J Chem Soe.. 24411935). 12) Parke?.A. J.. QuanL. R s u , 16.16311962). 131 Arnett. E. M.. Be,ntrude. W. G.. Burke. J. J.. and Dupgleby. P. McC.. J Amer Cham. Sor.. 87. l 541 (1965). I41 Robmtmn. R. E.. IHeppolefte. R. L.. and Scott. J. M. W.. Con. J. Chem.. 37.803
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