State University of New York at Stony Brook Stony Brook 11790
I
Reactions in Solutions under Pressure
I
The effect of temperature on reaction rates is well known and readily interpreted in terms of the activation enthalpy and entropy. The transition state by definition differs from the initial state in enthalpy and entropy by the quantities AH* and AS*, and the rate constant is affected by the temperature according to
These activation parameters can be evaluated from the slope and intercept, respectively, of a plot of in k / T versus 1 / T . Typical magnitudes of AH* lie in the range of 10-30 kcal/mole; AS* is usually found to be between -20 and +20 eu. Accordingly, the rate is commonly increased severalfold by a 10°C temperature rise. I t is less well known that pressure can also exert large effects on reaction rates. That this should be so can be shown as follows. Consider the decomposition of tert-butyl peroxide: CH1, ,CHx CH. C-0-0-C-CH~
7 CH3
\
CHs, 2 CH~-C-I~
CHS
This admittedly very crude calculation2 suggests that the rate of this reaction will decrease by a factor of two if a pressure of 3000 atm is applied. This is clearly an easily observable effect. I n general, if the rate constant can be determined with a precision of 5%) AV' can be calculated with a precision of 1 cma/mole. The minus sign in eqn. (2) means that pressure will increase the rate if the transition state is smaller and more dense than the initial state, and that the rate will be decreased by pressure if the initial state must expand as it traverses the free energy profile. This makes intuitive sense: thus, it would be expected that the
"St-
C H ~ products
This molecule iso approximately cylindrical with a radius of about 3 A. The 0-0 bond is normally about 1.5 A long; but in the intermediate radical pair the oxygen atoms will be separated by thesum of their van der Waals radii, which is about 3 A. If we arbitrarily assume that the 0-0 bond length has increased by about 25% when the transition state is reached (see Fig. l ) , the receding radicals will have vacated a cylinder, the volume of which is: = X 3l X (0.25 X 1.5) = 10 Aa/molecule
Figure 1. A sketch suggesting how the activatlonvdvme may be virvdired.
Hence the so-called activation volume will be: AV* = 10 X ( l o * ) * X 6 X XOZa
Since AH - TAS = AF and since 6 F / 6 p ferentiation of equ. (1) gives:
=
V , di-
If we assume for the moment that AV* is constant, then at a pressure of 3000 atm and a t room temperat,ure: log k =
X 6 - 2.3 3000 X 83 X 300
reaction will be retarded if the initial state must do additional work against externally applied pressure. I n most instances, the pressure range covers several thousand atmospheres. This is usually sufficient, although there are some examples of rate constants measured at pressures as high as 50,000 atm (2). 'Paper XIV in the series: "Chemical Reactions under High Pressure." Most of the papers in this series have appeared in the J m m l of fie American Chemical Society and in the J m m 2 of Physical ChnniPly, and several of them have been referred to in the list of references at the end of this paper. The author is pleased to acknowledge the support of the National Science Foundation for his work in thk field. 'The observed value for this reaction in toluene solution is +5.4 cm8/mole (I). Volume 44, Number 12, December 1967
/
729
The pressure effect on rates of reactions occurring in the liquid has a counterpart in reactions in the gas phase. There, even rather small pressure changes cause very large effects on the rate, but not on the rate constants; the pressure effect is one of concentration changes only. In the liquid phase, however, the space available to the transition state is limited, and the pressure effect on the rate constant itself becomes important. Experience has shown that there are some notable differences between activation enereies and activation volumes. For one, whereas the former is usually virtually independent of the temperature over wide ranges, the activation volume is as a rule fairly pressure dependent, and the pressure must therefore be specified when this quantity is reported (Fig. 2 ) . Usually "the
-
i 1 ,
,
Reaction coordinate Figure 3.
Figure 2. Some commonly observed effects of temperature e n d prerrvre on chemicol reaction rater.
activation volume" refers to zero pressure (AVO*). The curvature demonstrates that the initial and transition states have diierent compressibilities, and the volume diierence between them is not necessarily the same at one pressure as a t another. Generally, the activation volume tends to approach zero at extremely high pressures. The compressibility of activation can in principle also be extracted from the data, but this is a more complex problem. The activation volume is also somewhat temperature dependent, but this need not concern us here either. A second major difference is that the activation volume may be either negative or positive; the transition state may be larger or smaller than the initial state. Both situations are frequently encountered. 730
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Journal of Chemical Education
Porribie free energy and volvrns changer during a reaction.
A further difference is that the transition state need n o e a n d very often does not-represent a volume extremum (Fig. 3). In this connection it should be remembered that the pAV* term usually represents but a very small fraction of AF*. In such studies of a mechanism the information thus uncovered is used the same way as any other lead: either it fits with a preconceived notion about the d e tailed pathway, or it does not fit, and one modifies his ideas accordingly. In making a prediction of the activation volume that any given mechanism rould produce, densities of stable compounds as well as analogies with simple reactions of known pressure dependence are uscful. It may occur to the attentive reader that some of the remarks concerning AV* and the factors contributing to it also apply to AS*. There is indeed a broad parallel between the t~vo-they usually seem to have the same sign, for instance (S), and both frequently reflect changes in the surrounding solvent more than in the reacting molecules themselves. One can certainly not make a reliable estimate of the one from the other, however. An advantage of the use of the activation volume is that it is much easier to visualize volume changes than entropy changes. This introduction could, with minor modifications, also serve to describe the influence of pressure on equilibria in the liquid phase. Such data would fit the equation:
In those instances when equilibration is slow enough to measure the densities of the individual components, AVO can of course he measured directly without the use of high pressure data. Methods and Technique
The apparatus, which can he of bench-top size and a variety of which is commercially available, is schematically shown in Figure 4. The transmission fluid is usually methanol or a volatile hydrocarbon such as hexane. The pressure rangea is 1-10 kbar in most of the studies described here. Since most of these studies have the measurement of AVO*as their primary pur-
Figure 4. Schematic high pressure apporatur. In tho flat prnrurirotion stage, volres 1 and 3 are closed, and the piston of the hydraulic prom A mover down; in the second stoge, 2 is dosed and 1 ir opened. The pump B then raises the pressure in the thormortotad pressure vessel C through the hydrovlic press. The reaction mixture is in syringe D.
pose, a very wide range is not necessary; only as many measurements are required as is necessary to fix the shape of the in k versus p curve. The pressure range is furthermore limited by the practical difficulty that many common solvents freeze a t room temperature a t pressures just a little above 1 atm, and above 10 kbar very few are still liquid. It is important to prevent leaks, even the smallest; thus, if a leak of 1 mg/sec develops in a system containing 10 g of water compressed to 10 kbar a t 50°C, the pressure will drop to 5 kbar in 10 min. Since in slow reactions it may be necessary to keep the prassure constant to 1% or less for days a t a time, leak proof connections are obviously essential. This can be achieved with the same principle that seats vacuum stopcocks more firmly the greater the pressure difference. In practice several diierent types are used, but they need not he further discussed here (4). The pressure vessel commonly has a capacity of about 1 in. in diameter and 6-10 in. in height. The reacting solution is contained in a syringe, which is suspended in the transmission fluid. A syringe is used as the reaction vessel because of its self-adjusting capacity; it should he noted, for example, that a sample of 20 ml of hexane will occupy only 12 ml at 10 kbar. Bellows have also been used. These experiments need not be dangerous, in spite of the very high pressures applied. Liquids are relatively incompressible when compared to gases; not very much elastic energy is stored in the system, and if it is well designed this energy cannot he concentrated in a single projectile. In most cases it is necessary to release the pressure and remove the solution from the vessel in order to determine the effect of the pressure on the reaction, but apparatus that allows sampling without pressure release has been described (6). In some instances assay without either sampling or pressure release has been devised; thus, it is possible to measure electronic, ir, and nmr spectra of solutions under pressure, and conductance measurements are also relatively straightforward (6). The pressure measurement can be carried out in a variety of ways. Among the more common, one is based on the effect on heavy-walled, closed spiral tubes (Bourdon gauges), and another takes advantage of the known pressure effect on the resistance of manganin wire. Calibration of such gauges can he carried out with so-called pressure balances; the pressure is determined directly by balancing it against the weight of a known mass resting on a piston of accurately known diameter. A twisting motion imparted to the piston minimizes the effect of friction. Calibration pressures are provided by phase transitions, such as the freezing pressure of mercury at 0°C; freezing can he recognized from a plateau in the pressure versus time curve as the pressure is slowly raised (4). In order to better appreciate the nature of these experiments, one should have some knowledge of the effect of pressure on the various common physical properties (see refs. (4) and (6) for further detail). a The kiiobar, a. suitable unit for these measurements, is deh e d an 109 dynes/m.l In these unite, R = 83.1 kbar cma/mole OK.
Volume 44, Number 12, December 1967
/
731
Since for the large majority of all chemicals the liquid phase is less dense than the solid, the melting point will be raised by increasing pressure. The magnitude of this shift can be calculated by means of the Clapeyron equation:
On the average this effect amounts to about 1°C per 50 bars. Water is one of the few exceptions, and then only in the lower pressure range; a t 2 kbar the melting point reaches a minimum of -20°C. At higher pressures water behaves normally, and a t 6 kbar the freezpoint is back to 0°C. The solubility of solids in liquids decreases similarly as the pressure is raised. These changes, if not anticipated, are sometimes the source of erratic and puzzling changes in the rate constant at high pressures. The effect of pressure on liquid miscibilities is less predictable; one can avoid such problems by not using solutions that are nearly saturated. The solubility of gases in liquids is obviously greatly increased by the application of pressure; it is therefore not desirable to study reactions that d e velop gases unless the concentration of the reactants can be kept low enought to avoid exceeding the solubility of the gas a t 1 bar (since otherwise the excess gas will evolve when the pressure is relieved). The density of liquids increases in a manner well described by the Tait equation:
In eqn. (5) B is a pressure, usually several hundred bars, characterizing the substance and C is a constant (about 0.2) more or less independent of the substance. Water at 10 kbar has a density of about 1.2 g/cma; most organic liquids are considerably more compressible. It is believed that the compression of liquids is due to the disappearance of holes between the mole cules, and that bond lengths are affected very little; thus, the compressibility of diamond is very much smaller (7). The viscosity of liquids is affected more than any other property; in most cases it approximately doubles every kbar. The dielectric constant resembles the density in its pressure dependence. For the purpose of measurements of rate constants, it is obviously important that both pressure and temperature be maintained constant. The pressure will change if the density of the reacting solution changes as the reaction progresses; for this reason dilute solutions are once again desirable. The temperature presents a problem since the initial pressurization will bring about a temperature rise, perhaps of 10°C or more. A correction for this initial period is therefore necessary; it can be kept to a minimum by using p r e cooled solutions. About 10-20 min may elapse from the time that the solutions are mixed until the time that the pressure and temperature have become constant; the rate of the reaction should therefore be reasonably slow. Generally this presents no serious problem, as one may select the temperature, solvent, concentrations, catalyst, substituents, eta, in order to adjust the rate. After the rate constants have been determined a t several pressures, AVO*must be calculated axcording to eqn. (2). This requires that the slope b In k/bp be 732
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lournol o f Chemical Educafion
evaluated, and since the theoretical relation between
In k and p is not known, some empirical calculation is required. Most authors have found it convenient to fitthe data to the least squares expression Ink=ap*+bp+c
(6)
and then to use b as the value of the slope at zero pressure (8). Since the primary aim of the measurement of AV* is to learn something about the mechanism of the reaction, it is pertiment to ask whether the pressure may bring a change in pathway. The answer to this question is confirmatory; it can indeed happen, but only under certain circumstances. Thus, the reaction must first of all be subject to more than one pathway at all pressures, and among these pathways, the one contributing most to the overall reaction at atmospheric pressure must have a much larger activation volume (more positive or less negative) than the secondary path. Conceivably the side reaction may then b e come the dominant reaction under hieh nressure: however, if this happens one can hardly fail to recognize it (Fig. 5).
Figure 5.
Competing mechanirmr under prenure.
Pressure Effects on Equilibria
Pressure effects on equilibria in solution may give us insights that are useful in a consideration of activation volumes and we will therefore discuss them first. If the densities (or, better yet, the partial molal volumes) of the individual equilibrating species are known, the pressure effect can be predicted. AT' has in many instances been determined both from density measurements and from the pressure effect on the equilibrium constant, and satisfactory agreement has been found in each case. Thus, pressure favors the 7-isomer in the equilibrium:
The data show that its molar volume is 1.8 ~ m . ~ / m o l e
less than that of the a-isomer. Direct density measurements show that the difference is 1.5 cm3/mole (9). However, if the equilibration is relatively rapid, direct density measurements cannot he made, and one hecomes dependent on the pressure coefficient of the equilibrium constant to calculate the difference in molar volume. An example is the ketc-en01 equilibrium of ethyl acetoacetate (pure liquid) (10):
At 4 khar the en01 percentage is only about half of what it is at atmospheric pressure (7.7%); the detailed data show that its molar volume is about 4 cma greater than that of the keto-form. This is information which cannot he obtained directly. I n some instances density measurements may suffice to determine the volume change in an equilihrium even though equilibration is very rapid. Thus, the volume of ionization of acetic acid can he deduced from the densities of solutions of acetic acid, hydrochloric acid, sodium acetate, and sodium chloride: Values of AV, so obtained are in satisfactory agreement with the results deduced from the pressure dependence of the equilibrium constant. For instance, by these two methods, the ionization volume of acetic acid is -12.5 and -12.2 cms/mole, respectively; numerous other examples of such agreement are known (11). Turning now to the most important features that seem to influence the molar volume, one observes first of all that bond formation tends to be favored by preesure. The dimerization of nitrogen dioxide for instance is increased by pressure; AV equals -20 cm5/mole(1.9). Is- is similarly favored by pressure over I2 I- (IS). Infrared spectra of alcohol solutions under pressure have shown that H-bond formation is also characterized by a volume decrease, which amounts to about 5 ema/ mole (14). Unfortunately, data for this type of equilibrium change are scarce. Much more information is available on the ioniza tion equilibria of weak acids and bases. Some representative data are shown in Table 1. Inspection of these data (see refs. (11) and (14) for more extensive compilations) shows first of all that the volume of ionization is invariably negative, in spite of the fact that no new bonds are formed:
+
HA+H.OaA-+&O+ B
+ H n O F t B H + + OH-
This volume decrease must therefore he due to solvsr tion of the ions, and hence it is now usually referred to as electrostn'ctim; in a sense one could consider this phenomenon bond formation of a special type. The magnitude of the volume decrease does not seem to vary in a very drastic manner with the nature of the electrolyte. Most carhoxylic acids have ioniza tion volumes of about -10 to -12 cm3/mole, and most simple amines have ionization volumes of about
Table 1.
Ionization Volumes of Some W e a k Acids and Bases in Woter ( 1 1 , 14, 15)
Electrolyte
AVi (cm'lmole)
Formic acid Acetic acid Propionic acid Benzoic acid Phenylacetic acid Carbonic mfd (I) (11) PhospPoric a:jd (I) (11) Citric ay;d ( I ) (11) " ,' (111) Hsdroaen sulfide WiterPhenol p-Nitrophenol Aniline Ammonia Trimethylamhe n-Nitronhenol*
-25 to -30 cma/mole. The volume change that accompanies the second ionization of a dibasic acid is invariably greater than that characteristic of the first; it is furthermore noteworthy that the ionization volumes of phenol, water, and carbonic acid are larger than average. Many of these observations can he qualitatively correlated by means of the Drude-Nernst equation, usually written:
In this expression, V , is the volume change resulting from the immersion of an ion of charge q and radius r from a vacuum into a dielectric. Inspection of eqn. (7) shows that V , will he negative, the more so the smaller the ion and the greater its charge, and that it is independent of the sign of the charge. In some of the more complex ions the charge is subdivided among two or more atoms, and to the extent that these atoms interact with the solvent independently, eqn. (7) requires that the volume decrease he less pronounced the more subdivided the charge. This expression thus provides a rationale for the fact that amines cause larger volume decreases upon ionization than carboxylic acids; in carhoxylate anions the charge is evenly divided hetween two oxygen atoms. I n phenoxide ion, the charge is probably largely concentrated on the oxygen atom, and the volume decrease is correspondingly larger; for water itself, V , is larger still. The fact that first ionization volumes tend to he less negative than the changes in the second step has a similar interpretation. The anomalously large first ionization volume of carbonic acid is considered to he the sum of two terms: hydration and ionization (16). COS HzCOI
+ H 2 0 Ft HsCOs + H1O H,O+ + HCOa$
The last entry in Table 1 is an interesting result ohtained by Hamann (15); it shows that p-nitrophenol in the excited electronic state, in which the structure can be approximately represented as
Volume 44, Number 12, December 1967
/
733
Table 2.
HxO CHsOH CH3(OCHa)2
Pressure Effect on Product Distribution
1 atm 5 kbsr 1 atm
5 kbar 1 atm
R khar
62% 42 99.5 92 100
inn
17% 18 0.4
5 0
n
21% 40 0.1
3 0
n
the ionization volume becomes positive. Evidently the resulting ions are solvated less than the unionized species. Another interesting datum resulted from a measurement of the effect of pressure on the dissoci* tion of magnesium sulfate ion pairs in water (17). The corresponding volume decrease of 7 cma/mole shows that the electrostriction process continues through the ion pair stage to the completely separated ions. Attention should be called to the dependence of V . on the dielectric constant and its pressure coefficient. Eqn. (7) suggests that V , will have much larger negative values in nonpolar solvents than in water; nonpolar solvents are more compressible and allow iondipole interactions over a wider range. No data on any solvent effects on AVI are known, hut we shall see below that the activation volumes of ionic reactions often show a pronounced solvent dependence. In equilibria involving no change in either the number of molecules or the number of charges, the pressure effects tend to be small, and we therefore need not consider them here. Pressure Effects on Reaction Roles
For the purpose of this discussion it is convenient to categorize reactions into groups according to whether bonds are being broken or formed, and according to whether charges are being formed or neutralized. I n most cases the transition state is formed with a combination of these factors operating; however, if the pressure effect on equilibria is any guide, we may expect that pressure will accelerate those reactions in which additional bonds form and those in which new charges appear, and that it will retard those that are characterized by covalent bond cleavage and/or neutralization. Covalent Bond Cleavage in Neutral Molecules. A number of examples have been studied, among them the decomposition of benzoyl peroxide (IS), tertbutylperoxide ( I ) , pentaphenylethane (18), azo-bis-isobutyronitrile (Id), etc. I n every case the reaction is pressure retarded and the volume of activation is positive. On the average the results for AV* is +5 to +15 cmg/ mole, depending on the case and on the conditions. Bond Deformation in Neutral A4olecules. In reae tious of this type, typefied by the racemization of optically active biphenyls, no large volume changes would be expected, and none are found. I n several examples, AV* has been observed to range from +2 to - 1 cm3/mole (19). Bond Formation in Neutral Molecules. The most clear-cut examples of bond formation of this sort are the DielsAlder reaction, and the propagation step of free radical polymerization reactions. The first of these is a reaction in which two bonds are formed simultaneously, if present understanding is correct (80, 81). Relatively large, negative values of AV* (about -25 cmJ/mole) have been found for this reaction (88, 23) 734
/
Journal o f Chemical Education
as might reasonably be expected. Free radical propagation in styrene is characterized by a AV* value of about -10 cm3/mole (18, 84). A n apparently clearcut case of bond formation is the termination step in free radical polymerizations; yet the activation volume for this reaction has been deduced to he positive in some instances (18). It is now believed that bond formation is not the rate controlling feature of this reaction, and that the pressure induced retardation demonstrates this reaction to be diffusion controlled. The rate is a reflection not of the free energy required to form a covalent bond with two radicals, but of the numerous.diffusion steps required to bring the radicals together. In view of the very large effect of pressure on viscosity referred to earlier, this picture is a reasonable interpretation of the sign of the activation volume. It may be noted in passing that in a typical free radical polymerization under pressure the retarded initiation, accelerated propagation, and inhibited termination all contribute to greatly increased molecular weights of the polymer. A similar argument can he invoked to explain why the yield of iodohenzene in the thermal decomposition of phenylazotriphenylmethane in the presence of iodine decreases from 97% at atmospheric pressure to 31% a t 2.5 kbar (M) ; when the pressure is high, recombination and abstraction reactions compete favorably with the diffusion process required to produce the reaction with iodine. Neutral Displacamts. Reactions of this type, which include abstractions, chain transfer reactions, Claisen rearrangements, etc., involve bond cleavage and bond formation. A consideration of the bond energies and of the activation energy would lead us to expect that the new bond proceeds further toward' formation than the breaking bond does toward cleavage, hut there is little direct evidence on this score. It is therefore perhaps reassuring that the activation volumes for these processes are negative, and that therefore the transition states are apparently smaller than the separate reactant molecules in these reactions. Thus, chlorine abstraction from carbon tetrachloride by the polystyryl radical has an activation volume of about -20 cm3/mole (86). Hydrogen abstractions from aldehydes (86) and from mercaptans (87) show a number of interesting variations thought to reflect steric effects:
In these equations, R,is a polystyryl radical and R% denotes the stable radical 2,2-diphenylpicrylhydrazyl; the numbers following them are the activation volumes. This sort of correspondence between the magnitude of the activation volume and steric hindrance has been observed in several series of reactions. It appears that the more crowded the transition state is, the higher is its density. It is not clear whether this compactness should he ascribed to interpenetration of the interfer-
ing groups or the restriction of their motion. There is much current interest in this phenomenon, since the possibility of unusually large pressure-induced accelerations of sterically retarded reactions has an obvious and important synthetic implication. Chain transfer reactions also belong in this category; they are accelerated by pressure, but not as much as chain propagation (Z8). Many examples are known of pressure effects on Claisen rearrangements: C.H60CHGH=CH2
-
o-C6H+(OH)CH2CH=CHz
In this reaction bond formation and cleavage occur in concerted fashion. The activation volume is in the range of -7 to -15 cm3/mole (?29,30). Similar values are found in the related Cope rearrangement (SO), and in the rearrangement of allylic azides (9). The presence of the cyclic feature is an item that has been much discussed; its effect on the activation volume is probably small, and we need not review the arguments here (6). Ionization Reactions. As might be expected from our earlier discussion of the effect of pressure on ionization equilibria, pressure accelerates S Nreactions. ~ The activation volume is usually about - 15 cma/mole, hut its exact value depends on the nature of the incipient carbonium ion, the leaving group, the solvent, etc. Some of these variations may be observed in the following examples: (31, 32) CIHsCl CIH,Br CIHJ (CH,),CClC=CH
+ CHIOH + CH,OH + CH,OH
+ H?O
+
---
+ HC1 + C2HsOCHa+ 131 CIHsOCHs
-40
CsHbOCH3 HBr
-30
(CH&C(OH)C=CH
CaHaCHzCl HzO CsHiCHIOH 110 mole % C2H60H above 20 mole % CZHGOH reaction 30 mole % CnHsOH cat,alysed by
I
[ 40 mole % CIH~OH
+ IICl
+ HCI
-25
-16 -8 -17
-18
Evidently the volume decrease that occurs as these molecules approach the transition state is most severe for the smallest leaving anion, as is predicted by eqn. (7). An interesting solvent effect is observed if the hydrolysis of benzyl chloride is studied in highly aqueous ethanol; AV* exhibits a minimum at about 70 mole % water. The partial molal volumes of many salts in aqueous ethanol show similar minimum behavior, so that this observation further confirms the highly dipolar character of the transition state. Equation (7) can again be invoked to interpret the rather small value of AV* for benzyl chloride in pure water; charge delocaliza tion into the phenyl ring, usually assumed to account for the fast rate of this reaction, would diminish the electrostriction of the carbonium ion. A recent proposal has been made to use the same phenomenon to t,est more controversial types of charge delocalization, such as that proposed for exo-norbornyl brosylate:
The expected difference is indeed found in some eases ($4); however, additional supporting information will be required before this method can definitely be regarded as a reliable tool to investigate this problem. Ionization with Bond Fomaation. The foregoing discussion should serve to suggest that large and negative activation volumes may be expected: an additional bond and a pair of charges both adding t o the effect. This combination of circumstances occurs in nucleophilic aromatic substitutions by amines. Thus, the reaction of 2,4-dinitrochlorobenzenewith n-butylamine in ethanol has an activation volume of -25 cm3/mole, and that with tertbutylamine has an activation volume of -35 cm3/mole (the difference can probably be ascribed to the steric factor) (35). The reaction of various halonaphthalenes and haloquinolines with piperidine (36) is characterized by AV* values as low as -70 cm3/ mole at rather high temperatures (up to 190°C); the solvent would be expected to be quite tenuous then. It has been shown in these reactions that AV* has much larger negative volumes when the solvent is pure piperidine than when water is admixed; this is presumably the solvent effect on V , predicted by eqn. (7). Ionization with Displacement. The polar halogenation of olefins and the Menshutkin reaction are examples of this type. The iodination of ally1 alcohol in nitromethane has an activation volume of about -40 cm3/mole (31). Some examples of the Menshutkin reaction follow: (37-38)
Q
+
RBr
-0 + Y aq. CsH.OH
Br--26
+
Volume 44, Number 12, December 1967
/
735
1-
+ CsllsN~(Cllr)iCrlls-C211d+ CsllsN(CIIa)l
--
+ CNO+ BrOr- + 6HC NIT,+
5Br-
These examples demonstrate again that nonpolar solvents undergo more electrostriction than polar media, and that small ions have a more drastic effect than large ones. The steric factor also once again comes into play. An extreme example of this latter effect has been encountered by Okamoto (40): 2,6ditert-butylpyridine, which normally does not react with methyl iodide, readily forms a salt at 5 kbar. Reactions Dependent a Prior Ionization. This category includes uncatalyzed ester formation and related reactions, and electrophilic aromatic substitution. Some examples follow (41-46) (RIR,CO is a cortisone derivative) :
The activation volume in these cases reflects both the pre-equilibrium and the subsequent rate-coutrolliug step; both AVt and AV* are undoubtedly negative. The large, negative value in the formation of di-tert butylketoxime (45) is another indication of the steric factor. The rather small value of AV* in the nitration of toluene in acetic acid is in agreement with the fact that the reaction is zeroth order under those conditions; the rate limiting step is the formation of nitronium ion, :~ndthe toluene is not involved. By contrast, benzene under these conditions exhibits first order kinetics as well as a much larger negative activation volume. Reactias Involving Charge Neutralization. It follows from the foregoing discussions that charge neutralization should lead to solvent relaxation and therefore to expansion. Positive activation volumes are indeed Ionnd in thcsc reactions, as can be scen in thc following exa~nplcs(47-50) : 736
/
Journal of Chemical Education
NH.CONH, 3Br2
+33
f 7 f 3
+ 3Hx0
In each case, some charge neutralization clearly must have occurred by the time the transition state is reached. In the acid promoted oxidation of bromidc by bromate the activation volume is surprisingly small, which suggests that most of the neutralization occurs past the transition state. The rate limiting step in the Orton rearrangement is probably the formation of chlorine from chloride and protouated substrate (51). B a d Formation Involving ions. Base catalyzed hydrolysis of esters and amides and nucleophilic aromatic substitution by anions are examples of rate determining bond formation between a substrate and an anion whose presence is not dependent on preequilibria. Negative values of AV* are found in these reactions. Thus, base catalyzed hydrolysis of ethyl acetate (52) is characterized by an activation volume of about -10 cm3/mole, and that of acetamide (52) by -15 cm3/mole; similar results are obtained in the reaction of methoxide with a-haloquinolines (53). Bond formation between pairs of ions of like charge has also been studied; thus the addition of hydroxide ion to phenolphthalein has been found to have avolume of activation of -20 cm3/mole (54). Ionic Displacement Reactions. I n 8 ~ 2displacement reactions a new bond is formed and another is broken simultaneously; and in the process, a charge is transferred to another atom so that partial desolvation must occur. I n most cases AV* for these reactions is between - 5 and -10 cm3/mole, apparently slightly less negative on the average than neutral displacements. Some examples follow (48, 55-59) : CHaBr
+ OH-
NHGI
+ OH-
CH,BrCOO-
+ S20s
CHnBrCOOC2Hs
+ SIO?
+
C0(N&)~Br2+ OH-
--
CH80H
+ Br-
-8
NH,OH
+ CI-
- 3
+ Br- - 5 CHnSIOs-COOCIHs + Br- + 3 CH,S20s-COO-
Co(NH&OIIs+
+ Br-
+
9
The last three of these are particularly instructive. Displacement of bnmide by t.hiosulfate from an anion has a value of AV* = -5 cm3/mole; displacement id bromide by thiosulfate from a neutral compound, whicb involves charge dispersal, has a value of +3 em3/ mole; and finally, displacement of bromide by hydroxide from a cation, which involves charge neutralization inthe transition state, has an activation volume 9 cm3/mole. of Bond Fission in I a i c Species. Decarhoxylations arc especially prominent among t,he examples involving anions. Tllc formation ol c;lrbon dioxide from lri-
+
haloacetate, acetoacetate, and malonate anions have h e n studied by Brower and found to have activation volumes between +5 and +10 cm3/mole (GO). Thc h : ~ catalyzed hydndysis of chloroform, usually considered to pass through CC13- and CClz intermcdiates (see below), has a volume of activation of +16 cma/mole. (33) Similar results have been obtained with cations under.going hond cleavage. Examples of this description include inner-sphere electron transfer reactions (61), the decomposition of aryldiazonium salts (M), the decomposition of alkylmercury cations (60), and the hydrolysis of certain protonated ethers such as sucrose (60) and certain esters such as 8-propiolactone (63).
Problems, Applications and Prospects
Several hundred activation volumes are now known (6), and the results are invariably in agreement with other mechanistic features known about these reactions. I t may therefore be asserted that the factors influencing AV* are reasonably well understood, and that this ur~rlerst,andingpermits us to make reliable guesses about l.hr sign and approximate magnitude to be expect,ed iu :my given case. The understanding is not so good that :~ccuratepredictions can be made, however, and in those cmes in which mechanistic assignments hinge on small differences between alternatives, studies of closely related reactions of known mechanism are absolutely essential. There are very few known measurements of pressure cffects that cannot be interpreted in the terms described here. The clearest example of such a situat,ionin thereaction of hydroxide ion wit,h ma lac hit,^ green, which has an activat.ion volume of -12 cmx/m~~lc (64).
The Question of A1 versus A8 Mechanisms. I t is notoriously difficult to learn whether a solvent molcrnle has become involved when the transition state is reached in those reactions in which solvent is iriclnded in the stoichiometry. This is especially true if the molecule that the solvent may or may not react with in that manner is a reactive intermediate present in low concentration. This situation occurs in the acidcatalyzed hydrolysis of ethers, esters, and certain amines; the reaction is labelled A2 or A1 depending on whether or not a solvent molecule has become hound in the transition state.
The two principal criteria that had been used were the solvent isotope effect and the correlation between the rate constant with either the pH or the H , function (64). However, some dubious assignments had been made on the basis of these criteria. Thus, trimethylene oxide (65) and epichlorohydrin (66) were considered to go by the A1 mechanism and thus to involve primary carboninm ions in aqueous medium. Whalley developed the activation volume in these reactions as a new criterion (67). He assumed that pressure would have little effect on the pre-equilibrium, that the A1 mechanism, which involves hond cleavage, would have a positive activation volume, and that the A2 mechansim, like all other displacements, would be characterized by a negative volume of activation. The conclusious on that basis correlate very nicely with what would he predicted on the basis of the stability of the incipient carbonium ions. Thus, diethyl ether (68) has an activation volume of hydrolysis of -8.5 cm3/ mole; methyl orthoformate has a value of AV* = +2.4 cm3/mole; acetals (6) have values close to 0, etc. Trimethylene oxide and epichlorohydrin on this basis clearly hydrolyze by A2 mechanisms (-5.5 and -8.5 cm3/mole, respectively) (69). A closely related question has been encountered in inorganic chemistry. Two extreme cases may be mentioned here, which involve prior dissociation (70) and expansion of the coordination sphere (71), respectively: Ca(NHz),H,Oa+ PtCl2-
Neutralization in this instance should have given rise t o a rate decrease under pressure, rather than a rate increase. Whether this fact reveals inadequate understanding of the mechanism of the reaction or of the effect of pressure on it is a t present a matter of conjecture. The majority of all reports on pressure effects to date have been carried out with the objective of understanding such effects on reactions of well-known mechanism; however, there are also some outstanding examples of such studies conducted with the aim of elucidating the mechanism. A few of these are described below.
+ H90 + H,O
--
+
Co(NHi)dHZOh" NHa PtCla(H,O)- Cl-
+
+ 1.2 -20
The Questia of BI versus B8 Mechanisms. The problem just described has a counterpart in base catalyzed hydrolysis reactions. Chloroform is shown as an example: CHCL
+
OH-=
HIO CI-
+
+
CCls-
CCL
products
Volume 44, Number 12, December 1967
(B1)
/
737
The early criteria here included the use of the H- fnnction, which led t,o a B2 assignment for t,he hydrolysis of chloramine-at variance with other evidence (72). I n the case of chlorofornl t,here was likewise very little to support the B1 mechanism. The predict,ed pressure effects in both types of reaction are similar to those in the acid catalyzed reactions. The results to date have shown that chloramines exhibit small, negative activation volumes (57) and are therefore of the B2 or SN2 type; chloroform has a value of +IF cma/mole and therefore does indeed hydrolyze via free CClz (32). A recent application of this method to difluoramine (73) has shown that its hydrolysis involves fluoronitrene (NF), a new and promising intermediate. Othev Applications. Walling ($2) has studied the cffect of pressure on the reaction:
which might conceivahly proceed t,hrough eit,her a Cope-rearrangement :
The activation volume (> +6 cma/mole) clearly rules out a Cope mechanism in this case. A further interesting application has been contributed by Hamann (74). Since pressure generally increases the viscosity of liquids very greatly, he investigated some simple SN~-displacementreactions a t very high pressures (to 40 kbar) in order to learn whether diffusion control would eventually limit their rates. It was indeed found that the reaction of isopropoxide ion with ethyl bromide, which is pressure accelerated in the normal manner in isopropyl alcohol at atmospheric pressure, undergoes a reversal of sign of the activation volume at about 30 kbar and is retarded at higher pressure. In mixtures of isopropyl alcohol and the viscous liquid eugenol such reactions are retarded even at about 10 kbar. As a final example, we may consider the effect of pressure on the product distribution in a group of simultaneous and competing reactions. Kornblum (76) had studied the reaction: 738
/
Journal of Chemical Education
and found that the product distribution was dependent on the solvent in a remarkable way. Whereas ally1 phenyl ether is the only product in ethereal solvents such as monoglyme, significant amounts of the ringalkylated products are observed in weakly acidic solvents such as water, phenol, and fluorinated alcohols. I n still more weakly acidic solvents such as methanol only trace amounts of the allylphenols can be found. Kornblum attributed these observations to strong salvation of the oxygen atom in certain solvents, which would promote ring alkylation. The pressure effect on the product distribution provides an excellent test for this idea. Since solvation may be expected to be reinforced under pressure, the yield of product I1 should be further diminished under such conditions, and, to the extent that solvation may also interfere with the formation of 111, pressure should favor IV more than 111. The same effect should begin to be visible in methanol under pressure, but not in monoglyme. The results shown in Table 2 clearly verify all of these predictions. These examples should serve to suggest that. the uses of this tool have by no means been exhausted. It seems indeed possible that the activation volume will soon become as accessible to measurement and as indispensable in the dissection of reaction mechanisms as the thermal activation parameters are now. Future applications are especially likely to include further studies of reactions involving reactive neutral intermediates; since AV* tends to be negative in most reactions, the positive activation volumes characterizing the formation of such species as carbenes, nitrenes, benzynes, and free radicals tend to he revealing bits of information when the question of the freeness of these species is considered. Since furthermore AV* so often reflects changes in the solvent shell, the activation volume is likely to find increasing use as a probe to investigate the solvent surrounding the activated complex. Nor are small scale synthetic applications ruled out; the demonstrated effects of pressure on the product distribution in competing reactions and on the rates of sterically retarded reactions clearly foreshadow such uses. Literature Cited (1) (2)
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E. G., PERRIN,bf. W., A N D Glnsoa, K. O., (42) WILLIAMS, Proc. Roy. Soe., ,4154, 684 (1936). (43) KOSKIKALLIO, J., PODLI,D., A N D WHALLEY, E., Cnn. .I. Chem., 37, 1360 (1959). (44) KosaraALL~o,.T., AND WRILLEY, E., Cam. J. Chem., 37, 7x3 - (19.59). ~, (45) JONES, W. IT., TRISTBAM, E. W., AND BENNING, W. F., J. Am. Chem. Soe., 81, 2151 (19.593. (46) COILLET, D. W., A N D HAMANN, S. D., Trans. Famday Soc., 57, 2231 (1961). (47) STEWART, J. M., AND WEALE,K. E., J. Chem. Soc., 2854 1196.51. (48) DAVID, H. G., AND HAMANN, S. D., Trans. Faraday Soc., 50, 1188 (1954). (49) MOESVELD, A. L. T., 2. physik. Chem. (Leipzig), 103, 486 (1923). (50) HARRIS,R. T., AND WEALE,K. E., J . Chem. Sac., !J53 (1956). (51) INGOLD, C. K., "Strwture and Mechanism in Organic Chemistry," Carnell Univemity Press, Ithaca, N. Y.
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. .
.
in press.
Erratum The ilbseisua. of the graph entitled Figwe 3 which appears i n the article "A ha.Temneratrire Fused Salt Exneriment" on D. 534 of the September, 1
