Erwin Buncel Queen's University Kingston. Ontario K7L 3N6 Canada Harold Wilson John Abboti College Ste. Anne de Bellevue, Quebec Canada
II (
Solvent Effects 0t1 Rates and Equilibria A practical approach
I
The Qualitative Approach
Standard free energy-reaction coordinate diagrams are used routinely in a qualitative manner by teachers of organic chemistry to rationalize solvent and structural effects on rates and equilibria. The normal procedure is to compare two related reactions on a 2-D diagram (Fig. l a ) and t o discuss equilibrium variations by comparing AGIO and AG$, while rate variations are discussed by comparing AGlt and AG2t. Used in this manner the diagrams are extremely useful, but they can lead to incorrect explanations of observed phenomena. This problem can he illustrated by considering two specific cases: (i) In aqueous media the pK. of p-nitrophenol is less than that of m-nitrophenol. (ii) The rate constant for reaction of azide ion with p-nitrofluorobenzene is much higher in dimethyl sulfoxide (DMSO) than in methanol. In discussing the acidities of the phenols (eqns. 1and 2),
I R e a c t i o n Co-ordinates
N R+ x-
0I
R-X
Bond Order
the standard free energies of reactants and products of one of the isomers, say meta, are arbitrarily placed on the diagram (solid line in Fig. 2a), with the phenolate ion given the greater standard free energy. One then makes an educated guess concerning the corresponding energy levels of the other isomer. A common assumption is to make the standard free energies of the uncharged reactants approximately equal, see Figure 2a. In comparing the products, however, the p-nitrohen oxide anion is considered t o be lower in standard free energy because of superlor inherent resonance stahilizntim. tor thepuru isomer From the dingram it is apparent that Mn is 1owt.r than AC;,'for the mptn, which would explain the relative order of acidity. Discussion of kinetic behavior of the SNAr reaction (eqn. 3)
in two different solvents involves comparison of the standard free energies of the reactants and of the transition state in the two media Again, arbitrarily, the standard free energies in one of the two solvents, say methanol, are placed on the diagram, (Fig. 2b). In DMSO, i t is normal to assume an increased free
N R-x
N-R
Bond Order
+N-R--X
Figure 1. Free energyqeaction&inate diagams W in qualitative discussiar of SOIYB~Iand structural effects on rates end equilibria. (a) Two-dimensional representalonof a unitery process. (b) Three dimensional represemion of W e nucleaphilic substiMion remion N f R - X +NR + T,showing Gw reactim caardinate (- - - -) and "anti-Hamrnond"motion (-).
-
energy for a small negative ion, because of desolvation (I).The transition state for this reaction is a large polarizable charged entity, which should he reasonably well solvated in the aprotic solvent as well as in methanol; hence the transition states are assigned similar free energies in the two solvents. Again, from H the diagram, it is apparent that AG$x,mo < A G ~ M ~ oand thus the increased rate is effectively rationalized. Unfortunately, these rationalizat,ions are incorrect, as we will see subsequently. Another difficultv that arises in aualitative re diction of the effecr ot solvent or .;tructural changes on the transition state of a reaction ( 2 )is the limitrttim of the two dimensional energy diagram. ~ & n tstudies ( 3 , 4 )have demonstrated the utility of 3-D energy diagrams (5) in this regard. Figure l b is an example of such a diagram for a nucleophilic substitution in a particular solvent. How should the effect of solvent change on the transition state he represented? Simple 2-D treatments only consider the effect of solvent on NIR-X and Nf-R /X-, i.e. the species along the reaction coordinate. If the solVolume 57, Number 9, September 1980 1 629
ls.."toY. , .....-.
I
TRANSITION
Figure 3. illustration of relationship between the free energies of reactants and of the banslion stant,and the hee energies of solvation, tor a reaction occuning in two solvent systems.
b
eqn. 3.
vent destabilized N, then according to the Hammond postulate, the effect would be to move the transition state toward B, which would give rise to an earlier transition state. The advantage of the 3-D diagram is that it enables alternate pathways to be considered. For instance, in the substitution reaction there is the ~ossihilitvof formation of ion air intermediates. Stal~ilizatimnt surh species h y sdvent change would result in movement oithe SN2 transition stace to ~ o i n t C. This motion perpendicular to the reaction coordinate has been termed an "anti-Hammond" effect and would not be considered in terms of the 2-D approach. At this time the use of 3-D diagrams is restricted to very few reaction types. Fortunately knowledge of these surfaces is not requisite for the analysis of solvent effects outlined in this article. The above qualitative treatments of solvent effects appear to be theoretically sound, but when it is emphasized that the arguments given for both earlier examples are now believed to have incorrect foundation, the problems with the method should be obvious. In fact.. the DK, . - difference has been shown to be o consequence of differential solwtion of the un-ionized Dhenols (61.while the increased rate in 1)MSO in the second kxamplehai been found in large part to he due to increased stabilization of the transition state (7).I t is apparent, therefore, that qualitative discussion of solvent effects on rates and equilibria can be misleading without quantitative evaluation of solvent effects on free energies of stable species and of transition states. Relevant thermodynamic as well as kinetic measurements are required in turn. The Quantitative Approach
Initial efforts to quantify solvent effects on rates and equilibria attempted to correlate the effects with a single solvent parameter. Some success was achieved after the development of absolute rate theory by the application of Kirkwood's electrostatic model (8)to the reaction between two dipolar molecules A and B in a continuous medium with dielectric constant r. This application led to the LaidlerEyring (9) eqn. (4) 630 I Journal of Chemical Education
-
which accommodated reasonably well the rate data fur the R?N'H' X - I in cerMennchutkin reaction ( R ? N H'X tain binary solvent systems. It has been fbund, however, that such correlations with the solvent Darameter c do not have general applicability (10). The limited success of this earlv a t t e m ~to t correlate reaction rates with a single solvent property & been paralleled in recent years by the apparent limitations of usine other solvent parameteis as a measure of solvent influence G l , 12). The major difficulty is that a correlation is being attempted with a quantity ( A G t or AGO) which represents the difference of two states and these may be affected differentially by the solvent change. In order to obtain direct information about the nature of the solvent involvement it is necessary to dissect solvent effects into initial state and transition state (or final state) contributions (13). This dissection is possible using theoretical models ( 1 4 ) , but i t is far more practical to use thermodynamic transfer functions. Figure 3 shows the 2-D standard free energy reaction coordinate diagram for a reaction carried out in a standard solvent 0 and in a solvent S. The standard free enerev ... of the reactant R in the standard solvent is designated GoR and in the solvent S as GqH.The differenre in free enerries hetween the two solvents (GSR- GoR) is termed the transfer free energy 6Gt,R. 6GtrR= G,R - GoR (5) Similarly for the transition state T o n e obtains
+
Figure 2. illustration of use of free energy diagrams in qualitative discussion of rater andequiiibria. (a) Acidities of nitrophenois: - mnitrophenol: - - - - p nitrophenol. (b) Solvent effects on substitution rates for the SNAr reaction in
I... 8 . 0 . g , O f reactants i n a o l v s n t 0
+
6GtrT = G.T - GOT (6) The difference in free energies of activation for the two processes is designated 6 A G t and from Figure 3 i t is apparent that GAG* = AG., - AGO' = (GST- G,o) which simplifies to
- (GOT- GOO)
(7)
SAG1 = 6GtrT - 6Gt.R (8) Thus 6GtrT can be evaluated from the measurable transfer free energies of stable solute species and kinetic activation parameters. The required transfer-free energies can be obtained from activity coefficient measurements (15) using eqn. 9 in which y refers to solute activity coefficients in the different solvents. 6Gt: = -RTln rJy0 (9) The y values are evaluated using the standard methods of vapor pressure, solubility and distribution coefficient measurements and are referred t o the same standard state in solvents S, 0 or any other medium. For the equilibrium situation, 6 A G h is the difference in the
standard free energies of reaction between the two solvents (eqn. 10) and, in a like manner, the relationships 11 and 12 follow, where P refers t o the products.
Table 1. Free Energies of Transfer of Ions from Water to Nonaqueous Solvents Given in kcal per mole at 2S°C on the Molar Scale (20). Values Based on the Assumptlon GG,.(~P,AS+)= ~G..I*~B-I. Methanol 1.0 2.0 2.4 2.4 2.3 0.2
Transfer functions can also be defined for other state functions and the ease of calorimetric men~urementshas made the transfer enthalpy dH,,' readily available (16. 17). When 6H,,' is cornlined u,ith A(;,' it is possible to achirve complece dissection of the effect of sulvent on the vnriuus thermodvnamic parameters (vide infra) (18). Applications to Equilibria A simnle hut instructive case of the use of thermodvnamic trnnsier functions amcerns the dissociation constants of acids and bases in different advents. For the case of the reneral acid HA, the pK. variation due to solvent change is g&en by eqn. 13 which follows readily from eqn. 12.
- pKa0 = [6Gb(Ht) + GGdA-) - 6GdHA)IlZ. 303 R T (13) The applicability of eqn. 13 can be demonstrated in certain systems where the required thermodynamic data are available. Thus for henzoic acid in acetonitrile (S) and water (0) we have pKaH20 = 4.2, 6Gt,(Hf) = +11, 6Gt,(@C02-) = +9.7 and GG+.(+COPH)= -2.0 kcallmole (19). This develo~mentleads to a pred~rtadvalue ior p#,cH1"N = 29.9 which compare well with an ~ x u h n e n t a vulue l of 20.:. Verv few calculat~onsof this type a;e possible because of the paucity of thermodynamic data relatine to the transfer function GG+.(H+).However. this .;ituntim is impruviny and recently new electrochemiral(20) and s~ectro~hotometric (21, techni(~ueshave heen devised to measure the value of 6Gt,(H+) from water to aqueous alcohols, and from water to aaueous dioxan, res~ectivelv. Abnormally large ratios are often observed for the first to the second dissociation constants of many dicarboxvlic acids. One cause of these ratios is undoubtedly electrostatic in origin, hut there is also the possihi&ty of intramolecular hydrogen bonding in the monoanion, HA-. However, for aqueous media i t was shown by Westheimer and Benfey (22) that such hydrogen bonding was absent for the homologous series heginning with oxalic acid. In aqueous solution, hydrogen bonding with the solvent leads to greater stabilization of the anion, relative to intramolecular hydrogen bonding. On the other hand, in a dipolar protophohic solvent-like acetonitrile intermolecular bonding should be negligible, which might allow for the existence of the HA- species. In principle this phenomenon can he detected using transfer free energies. Consider the case of succinic acid dissociation, in eqn. 14:
pK.8
If there were no intramolecular hydrogen bonding in acetonitrile, then usina additivity of transfer functions, to a first nppnAnation, the rrlationship i,t'ecln. 15 would he npplicable. When the activity n~effirientsfor these solute species GGtJbisuccinate ion) = BG&cetate ion) + GGt,(acetic acid) (15) were measured (23), it was found that 6Gt.(bisuccinate ion) is much smaller than that calculated from eqn. 15. This finding supports the postulate of intramolecular hydrogen bonding in acetonitrile solvent. Solvent effects on a variety of equilibrium processes can in principle be predicted from a knowledge of the appropriate transfer functions. In this regard it is noteworthy that data
-5.6 3.0
are available for both charged and neutral species (1,18,24). 6Gt,' values for single ions are presented in Table 1. I t must be pointed out that for sinale ions the evaluation of transfer free energies requires the use of an extrathermodynamic assumption. The values obtained using two different assumptions, 6Gtr(@4N+)= GG*(@&) and 6Ge(Me4N+) = 0, show similar trends. Kim (25) recently carried out a critical examination of the first oi these aasumptinns and found it quite saticfactory in amphiprotic and dipolar-aprotic sol\~enrs (Table 1). Application to Rate Processes The large rate accelerations which are often observed for reactions involving an anionic reagent, on changing the solvent from protic to dipolar aprotic, are well-known (1, 12, 26). These find ready explanation in the data of Table 1, noting that there are large salvation differences between small anions in which charge is localized on an electronegative atom and those of large charge-diffused anions. Considerable solvation differences also exist in the case of neutral molecules. Availability of this data allows each case to be treated individually in a quantitative manner and thus avoids the generalizations which sometimes lead to incorrect predictions (vide supra). Other solvent changes on reaction rates may he less dramatic but can nevertheless embody interesting relationships. Transfer free enerav data are available for the alkaline hvdrolysis of ethyl Getate in aqueous dioxan (27). For the transfer from water to 50:50 mole % aqueous dioxan the following results were obtained: 6Gt,(ester) = -0.36 kcallmole, 6GtdOH-) = +1.3 kcallmole. Considering the initial state interactions alone, an increase in rate should be expected. In fact the opposite was found, as seen from the increase in the free enerw of activation. 6AGt = +0.045 kcallmole. Thus destabili;itionoithe transition stateon transfer (JG,, = +1.0 kcal mde, has more than balanced the destabilizarion of the reactants.'It is noteworthy also that of the two reactants one becomes stabilized and the other destabilized on transfer between the two solvents. Obviously, the free energy of transfer terms, 6Gei, can he positive (destabilization of species i in solvent S relative to solvent O),negative (stabilization), or zero (no effect). When 6GtrTand 6Gt,R have the same sign it is termed a balancing situation and when they have opposite sign a reinforcing situation. These terms lead quite&urallyio a system ofclassifyina solvent effects on reaction rates (28). In Table 2 the various possibilities are listed and solvent effects classified according to: (i) (rate increase), - (rate decrease), 0 (no effect); (ii) balancing or reinforcing situation; (iii) transition state controlled (6GtrR 0) or reactant controlled (GGt,T0). Use of this designation can be demonstrated by reference to the reactions in Fig. 4. Considering reaction A, 6GeR is and 6GtrTis -,assuming transfer from the solvent 0 to solvent S; this is a reinforcing situation resulting in a rate acceleration and can he classified as a positive reinforced solvent
+
-
+
Volume 57, Number 9, September 1980 1 631
effect. In contrast B (6GeR = 0, 6GtrT is -) is a positive transition state controlled effect. The classification of Table 2 is, of course, equally applicable to transfer enthalpies; for some pertinent examples, see ref. (30). Several of these solvent effects result in increased reaction rates and may be considered the source of solvent catalysis. It has been DroDosed, however, that the term solvent catalysis be limited 6 a-process by which a solvent induces a rate acceleration without input of thermodynamic work or coupling with other irreversible processes (30). This limitation immediately excludes all cases where the free energy of reactant is raised on solvent transfer (input of thermodynamic work) and thus the only cases of solvent catalysis in Table 2 are those in which the transition state is stabilized by change in solvent. The effect responsible for a solvent rate acceleration can be determined by alternative methods. Thus Kemp et al. (30) investigated the nature of the solvent rate acceleration for the decarboxylation of 3-carboxybenzisoxazole (eqn. 16) using extraction techniques. This reaction proceeds much faster in
-
)
Transfer Functions and Transition S t a t e s
Earlier i t was shown that the effect of solvent on transition state can he qualitatively discussed in terms of a 3-D energy contour diagram. What information can be obtained about the transition state from transfer function data? This question can heanswered appropriately hy referring t o ~ h r a h & m 'res sults for the reaction of tetraethyltin with mercuric chloride
The activation parameters for this reaction are known in methanol and in the less oolar solvent. t-hutanol. There is a large difference in the kntropies of activation (6ASf = AS,,.,,,nn mol-I). Conventionallv. - - - - - - A S h w = 22 cal K-' the decrease in entropy of activation.on transfer to the less polar solvent would be discussed in terms of differential solvation of the polar transition state. The use of transfer functions prevents such a pitfall; a cursory glance a t the data in Table 3 reveals that this decrease is largely an initial state effect, since the transfer effects on the transition state are, in fact, quite small (6StrT = -2.8 cal K-' mole-', 6HhT = 1.59 kcal molecl). In the derivation of transition state transfer functions no assumption was made concerning the transition state. Thus, in rcneral. values of dS,,'"and 6HtWT. .. . t ~" vthemselves. eive no information about its diture. In order to deduce tr&ition state properties the values of these transfer functions must be compared to those of stable solutes. Abraham has devised several procedures for this comparison and these have been reviewed elsewhere (15,28). The transition state for reaction (17) is believed to he quite polar, in fact similar to that for t-hutyl chloride solvolysis. This polarity is borne out by the fact that similar transition state transfer functions are obtained for the two processes. The values of the functions are quite different from those obtained for dissociated s ~ e c i esuch s as MeaN+ CI-. . which suggests they are poor models for these particular transition states. At~raham'smore so~histicatedmethods t 15.32)sueeest that ion pairs are better transition state models i n thG"in~
~
+ CO*
06)
0-
d i ~ o l a ra ~ r o t i csolvents than in oolar solvents. Thev conelided that the factors which influence the rates of decarboxvlation are carboxvlate ion-hvdroeen bond formation in protic solvents, which inhihits the reaction, and transition state stabilization in dipolar aprotic solvents, which accelerates the reaction. This reaction is an example of a positively reinforced situation and can he considered a case of solvent catalysis. Clearly these conclusions could be corroborated using thermodynamic transfer function methods.
+
~
~~
~~
Table 2. Transfer Free Energies of Reactants (6GtrR),of Transition States (~G,,T)and Solvent Effects on Reaction Rates. Classification of Reaction Types. -
Effen
case 1 2 3 4 5 6 7
6Q -
6GT
on Ratea
-
0
-
+, 0, or +
+
0 0 0
0
+ 0
-
8
+
9
0
+ + +
Reaction Type Balancedb Positively reinforced Positive Vansition state control Negative initial state control
++
-
Positive initial state control Solvent independent Negatively reinforced
-
Balanceda Negative transition state control
t.0. or -
-me plus sign refers to rate acceleration, me minus sign to rate relardation, and zem m no effect. a in nw h!mdsnmtian, a rate acceleration wlli rewn if 6&R
it a+*
< aGT.
> dCfl snd a rate rstardstim
-
Table 3. Thermodynamic Transfer Functlon Data (Methanol tButanot at 25%) tor the Reaction of Tetraethyltin with Mercuric Chloride (32).
6H,, (kcal Et&n k l a 2
Transition State
moi-') -0.39 6.03 1.59
6AHt = -4.05
6 3 2 1 Journal of Chemical Eduqtion
(cal K-' mo1-') 3.9 15.3 -2.8 6ASt = -22
I R e a c t i o n Co-ordbnatsa Figure 4. Reaction prof les ill~stratng the clas%t~cation ol solvent effectsaccording to Table 2. la) Pasitove remforcement.(bl Posotwe Vansltm state controlled
