Internal Pressure: Its Use and Abuse William J

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解説 Internal Pressure: Its Use and Abuse William J. le Noble*

The internal pressure ( ∂E/ ∂V)T has a range of 0.2-2 GPa for pure liquids. Its effect on the rate and equilibrium constants of chemical reactions can be gauged approximately if the reaction can also be studied in the gas phase at the same temperature. The influence of internal pressure is not different from that of external pressure. A few examples are mentioned. The effect is unfortunately usually overshadowed by other solvent properties such as its ability to engage in hydrogen bonding and solvation of ions and dipoles. [internal pressure, external pressure, volume profile, cohesion, gas phase reactions]

1. Introduction Pi ≈ Tα/β where α and β are the coefficients of thermal expansion The thermodynamic equation of state for any pure liquid: and of compressibility, respectively. It is important,

P + ( ∂E/ ∂V)T = T( ∂P/ ∂T)V however, to be aware of the pitfalls that such indirect differs from that of an ideal gas: methods may pose; for example, if the latter equation is PV = nRT applied to water at 4°C, the result would be zero! only in that the derivative ( ∂E/ ∂V)T equals zero for the Overlooked in that conclusion is the fact that water near its latter. Non-zero values of this term, known as the internal freezing point is not really a pure liquid, but an equilibrium pressure (Pi), are a consequence of the balance between the mixture of ice-like and water-like structures. This is a cohesive and repulsive forces operating between molecules dramatic example of the fact that it is not a good practice to in all fluids. The derivative ( ∂P/ ∂T)V can be measured by assign pure liquid values of Pi to mixtures, or even dilute means of high-pressure pycnometry, and hence the internal solutions; one must be especially careful not to assume that pressure is an experimentally accessible property of pure the solute is subject to the internal pressure of the pure liquids. Such experiments have been carried out for many solvent. The adhesion between solute and solvent is not common solvents, and reviews listing their values have identical to the cohesion between solvent molecules. been published [1]; their values range from 0.2 GPa for simple liquid alkanes to roughly 2 GPa for water. The effect 2. Applications of dipolar interactions, especially of hydrogen bonding, is at once obvious upon inspection of these lists. With these warnings in mind, let us turn to the effect of It should be emphasized that these internal pressure external pressure on rate and equilibrium constants, and the values are not constants of nature; they depend on both the use that these effects have found in mechanistic chemistry. temperature and the external pressure (Pe), which should This topic has been reviewed many times [3]; suffice it here therefore be specified. Indeed, according to Dack [2], at to say that such data permit the construction of the so-called sufficiently high external pressures, repulsive forces may volume profile, which portrays how the volume per mole grow so dominant that internal pressures can actually of reactant changes from the initial state via the transition become negative. state to the product or final state, at the temperature and The values at ambient temperature and pressure can also with the solvent specified. Some examples follow. be estimated indirectly from various other parameters where When a free-radical initiator such as benzoyl peroxide is these are available. For example, the molar heat of allowed to decompose and the rate constant is measured, vaporization is a measure of the energy needed to liberate a one observes that externally applied pressure retards it [4]. mole of molecules in the liquid phase from the cohesion by The conclusion is drawn that the volume increases along the their neighbors. Another method is based on the following reaction coordinate, which is thought to be a consequence equation: of the lengthening of the breaking bonds.

*Department of Chemistry, State University of New York, Stony Brook NY 11794-3400, U.S.A. [email protected]

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toward formation in the transition state. Unfortunately, the Russian journal in which the research was published was not translated at the time, and the work remained unknown Conversely, when cycloadditions such as Diels-Alder in the West for many years. Indeed, the question about the reactions are studied in this manner, one usually observes a concerted or stepwise nature of the Diels-Alder reaction pressure-enhanced rate, and hence a decrease in the volume, was approached again almost a decade later by Walling, and which is attributed to the formation of new bonds [5]. by the same means! However, Walling reported the activation volume in his case to be less than half of the reaction volume, and he drew the conclusion that the reaction was stepwise, via a diradical intermediate [8]. This In solvolyses of substrates such as tert-butyl chloride, the conclusion was criticized by Benson and Berson, on the volume also decreases –even though a bond breaks to form following grounds [9]. ions; the conclusion is that solvation of the ions The experimental dependence of ln k on pressure is not (electrostriction) is responsible, just as it is for the negative linear, and the slope -whether positive or negative- tends to partial volumes of simple inorganic ions in water [6]. level off at increasing pressure. In fact, the steepest The numerical data describing the volume change are curvature occurs at zero pressure, and since the theoretical derived from the initial slope of plots of ln k (or ln K) relation between ln k and P is not known, the value of the versus the external pressure (see Fig. 1), and the question slope there is obviously the most uncertain. Most kineticists we wish to discuss here is: in such plots, should the have evaluated it by means of least squares expressions but pressure axis be represented by Pe, or by Pe, + Pi? It is a Benson and Berson proposed a new way to do it, using an question that occurs sooner or later to every new expression based on the Tait equation, and their investigator in the high-pressure chemistry field. The choice methodology led them to question Walling's conclusion. made is usually to ignore Pi, since the chemistry of interest Their own technique did not gain any substantial following, occurs in solution, and at atmospheric pressure. The author however. Several years later, Eckert [10] and others [11] had his own brush with this question, against the began using much improved laboratory apparatus, which background which follows. conclusively showed that Walling's data should have been The first instance of a mechanistic assignment on the suspected; the more accurate information becoming basis of high-pressure kinetics was published in 1949, when available then left no doubt that pressure did have a very Gonikberg reported the activation volume for a Diels-Alder large accelerating effect on the rates of Diels-Alder cycloaddition to be negative, and almost as large as the reactions, and hence that the mechanism was of a concerted overall reaction volume [7]. He concluded that the reaction nature [12]. But now the author is getting ahead of his story. must be concerted, with both new bonds well on the way I entered the field of high-pressure kinetics at about the time when the Benson-Berson paper appeared. At the outset, several arguments going counter to the Benson-Berson procedure seemed obvious. Thus, the same problem of the slope of the pressure dependence of rate constants applies to that of equilibrium constants, and in that case, the reaction volume can be measured independently, by means of dilatometry as well as by densometry. No discrepancies in reaction volumes determined by these various means have been encountered. Also, one could base mechanistic conclusions upon the slope at 50 or 100 MPa, say; since

there are then further data in both directions, the uncertainty Fig. 1. Some typical ln k versus P plots. of the slope is then much less -if not absent entirely. Reproduced with permission from Fig. 1 of W.J. le Noble, However, I wished to pursue an additional idea to solve the Progr. Phys. Org. Chem., 5, 207 (1967). problem of the uncertain slope at zero pressure, which was

高圧力の科学と技術 Vol.12, No.3 (2002) 226 to obtain data at a negative pressure; if such were possible, measured, and found to be 300 MPa under ambient the problem of the slope at zero pressure would vanish. I conditions. All of the data, both gas phase as well as decided to study a reaction which could be monitored not ambient and high pressure in solution could be only in solution at various pressures, but also in the gas accommodated by a single curve for kα, kγ and K (= kα/ kγ). phase, where it would not be subject to the internal pressure Thus, I concluded that Walling's way of estimating the of the solvent. But which reaction should be chosen? It was activation volumes had been reasonable, although this is of obvious that reactions which were subject to large solvent course not an endorsement of his data. The gas phase results effects would be unsuitable, since these effects were an and our conclusion were not mentioned in the original paper indication of polar interactions that left the value of the [14] because a Referee objected to it; however, they are internal pressure in the neighborhood of the reacting shown in a later survey of high-pressure chemistry [15]. molecule(s) essentially unknowable. A careful study of the It should be noted that this procedure is not entirely literature revealed that the isomerization of allylic azides proper in that it involved the unstated -and, as stated earlier: (later to come known as 3,3-sigmatropic shifts) is very improper- assumption that the solvent pressure upon the suitable in this regard; thus, Winstein had reported [13] that reacting solute molecules is the same as the solvent pressure the rates of isomerization in 70% aqueous acetone were upon itself, and also in that Pi was not measured or included only barely one order of magnitude faster than in pentane. at high pressures (instead, the gas phase results were This acceleration is easily compatible with the size of presented as a negative pressure in the plots). external pressure effects. In other work, we learned in a coincidental way how important the non-polarity requirement was. That finding resulted from a study of β-benzyloxycrotonic acid [16], which decarboxylates completely in a few minutes when it The pressure effects on the reaction shown above are is warmed to its melting point at 125°C. portrayed in Fig. 2. It is obvious from the initial slopes that Me Me COOH H the volume profile has a minimum, indicative of the 125 °C O O + CO2 concerted nature later found to be typical of (3,3)- Ph Ph sigmatropic shifts, with a transition state as represented in the equation. In an effort to obtain a precise value for the yield of this reaction, a sample was entered in a bulb which was then evacuated and placed in a 125°C oven. The reaction was essentially quantitative. However, in a subsequent attempt to duplicate this result, an error occurred: the bulb wound up in an oven set at 250°C by another laboratory worker. When the bulb was removed from the oven the next day, beautiful fine needles began to be deposited on the walls. To my great surprise, these needles turned out to be unreacted acid. Evidently, if the acid was heated rapidly, it vaporized before it had a chance to decarboxylate, and in the gas phase it was stable - at a temperature 125°C higher, and for Fig. 2. The effect of phase and of external pressure upon a duration 100 times longer! This observation showed in α γ the rate and equilibrium constants of - and -methallyl startling fashion that even non-ionic reactions must not be azides. assumed to occur in the gas phase only somewhat less Reproduced with permission from Fig. 11 of W.J. le Noble, Progr. Phys. Org. Chem., 5, 207 (1967). readily than in the liquid phase. If the conclusion were drawn from these data that the reaction must have an We found that the reaction also occurred in the gas phase, extremely large negative activation volume, that inference at a rate a few times smaller than in the methylene chloride would be utterly erroneous: several decarboxylation solutions. The internal pressure of the pure solvent was reactions have been studied at high pressure, and the

高圧力の科学と技術 Vol.12, No.3 (2002) 227 activation volumes were in all cases observed to be small Grieco showed that the reaction could readily be done at and positive [17]. atmosphric pressure in 5 M lithium perchlorate in ether [24]. In later years, there have been a few additional instances He tentatively ascribed this finding to the undoubtedly high of reactions which have comparable rate and/or equilibrium (but unknown) internal pressure of this medium. However, constants in the two phases, so that one can be reasonably that notion was soon overturned. Dailey [25] demonstrated confident in assuming that any solvent effects may be that other Diels-Alder reactions were unaffected by this ascribed to internal pressure variations. A notable example medium, and that Grieco's reaction was accelerated not by was reported by Ouellette [18], who was able to relate internal pressure, but by lithium ion (Lewis acid ) catalysis. trans-gauche conformational equilibrium constants for a That makes his solvent no less spectacular, and at least one few simple non-polar butane derivatives in solution with other application has surfaced [26]: but it also serves as a gas phase data. The variation of the equilibrium constants warning that the invocation of internal pressure as the with solvent was explicable as an effect of Pi, and the reason for solvent effects should be made with reaction volume thus calculated matched that reported in circumspection. Similar conclusions have been reached by the literature for closely related species. Another example other workers [27], who have discussed internal pressure may be furnished by Breslow's report that a substantial and the related concept of cohesive energy density. The increase in the endo/exo product ratio occurs when several most reliable method to predict or understand solvent dienophiles are allowed to react with cyclopentadiene in effects on rate and equilibrium constants at present water as compared to the more traditional organic media continues to be the Taft solvatochromic equation [28]. [19]; this can be attributed to the much higher internal pressure of water and the higher density of the endo product. 3. Conclusion Indeed, the endo isomer is somewhat smaller than the exo product. Still another instance may be the nitrogen The proposition to include internal pressure as extrusion reaction of certain azoalkanes, the rates of which influencing the volume profile is generally not a sound one. were reported by Snyder [20] to be depressed by the use of When transition state theory is applied in the discussion of polar solvents. In inorganic chemistry, Hamann [21] the mechanism of a given reaction in solution, and external successfully used the internal pressures that must exist in pressure is used to fix the volume profile, one is on sound ionic crystals as an argument to support his mechanism of thermodynamic grounds. This pressure is the same the pressure-induced changes observed by Drickamer [22] throughout the solution, in a Pascallian way. However, in the Moessbauer spectra of potassium ferricyanide. when solvent effects and the internal pressures operating in These types of results appear to have been extrapolated mixtures are considered, one makes a subtle shift towards to the proposition that solvent effects and pressure effects the structural scene. The internal pressure of the solvent on chemical rates are basically one and the same upon a reacting solute molecule is not a force uniformly phenomenon. While there is an element of truth in this, it is distributed over an extensive smooth and uniform surface, certainly not correct that the rate in any given solvent can but rather a collection of forces, varying in magnitude, and be calculated from that in another solvent if the Pi values of exerted upon individual atoms and bonds, and there are both are known as well as the activation volume in one of presently no ways to account for them in the simple ways them. that external pressures can. An example qualitatively based on this protocol is the Diels-Alder reaction shown below. It is too slow to allow Acknowledgements the formation of products at ambient pressure, but it had been found to be feasible at 700 MPa [23]. The author gratefully acknowledges support from the

O National Science Foundation for his work in high-pressure chemistry. Drs. T. Asano, S. D. Hamann and F.-J. Klärner O O + are cordially thanked for their comments. Me O O O Me Me

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