Thermodynamics of proton transfer

Since Gibbs energy is a function of state, Hess s law applies and so the Gibbs energy change for Reaction 2.3 can be expressed as 

The Gibbs energy change is linked to the equilibrium constant, for Reaction 2.3 through the following expressions  

In the above equations T is the absolute temperature, R is the universal gas constant, and the square brackets around the chemical compounds refer to their concentrations in the gas phase. 

3 and the equilibrium position is tilted towards the products. This can be quantified using Equation 2.9. Eor example, if compound M has a basicity some 10 kJ mol above that of compound X, substitution into Equation 2.9 yields Xeq 60 at a temperature of 298 K. Clearly a relatively small difference in basicities will result in a large bias of the reaction towards products or reactants. 

Comprehensive tables of gas-phase basicities for a wide range of compounds have been compiled by Hunter and Lias [3] and a list of basicities for some illustrative classes of compounds is provided in Table 2.2. These gas-phase basicities can be used to ascertain the spontaneity of a particular proton transfer reaction, but it is more common to make use of proton affinity instead. The proton affinity of a compound is defined as the negative of the enthalpy change for the proton acceptance reaction (e.g. Reaction 2.6 or 2.7). Thus if proton acceptance is an exothermic process then the proton affinity is a positive quantity. The gas phase basicity (B) and proton affinity (PA) are related by 

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Studies of the kinetics and thermodynamics of proton transfer and hydride transfer reactions have led to a better fundamental understanding of the range of reactivity available, and how it is influenced by different metals and ligands. This information is also central to the rational development of molecular catalysts for oxidation of H2 and production of H2 described in Chapter 7, and in the broad context of other reactions pertinent to energy production and energy utilization that require control of multi-proton and multi-electron reactivity. 

Now that we have examined various forms of acid-base catalysis, and we have looked at how the thermodynamics of proton transfer are related to the kinetics via the Bronsted catalysis law, let s examine the mechanisms and rates of proton transfer in more detail. The transfer of a proton from an acid to a base is one of the simplest of all chemical reactions, and yet, even this reaction has been found to have several subtle mechanistic twists. The rate of the reaction generally depends upon the driving force (the thermodynamics) of the reaction, but there are cases where intrinsic barriers exist, making even very exothermic reactions slower than one might expect. 

Brouillard, R. and Delaporte, B., Chemistry of anthocyanin pigments. 2. Kinetic and thermodynamic study of proton-transfer, hydration, and tautomeric reactions of mal-vidin-3-glucoside, J. Am. Chem. Soc., 99, 8461, 1977. 

Seminal studies on the dynamics of proton transfer in the triplet manifold have been performed on HBO [109]. It was found that in the triplet states of HBO, the proton transfer between the enol and keto tautomers is reversible because the two (enol and keto) triplet states are accidentally isoenergetic. In addition, the rate constant is as slow as milliseconds at 100 K. The results of much slower proton transfer dynamics in the triplet manifold are consistent with the earlier summarization of ESIPT molecules. Based on the steady-state absorption and emission spectroscopy, the changes of pKa between the ground and excited states, and hence the thermodynamics of ESIPT, can be deduced by a Forster cycle [65]. Accordingly, compared to the pKa in the ground state, the decrease of pKa in the... 

All these reactions are thermodynamically favourable in the direction of proton transfer to hydroxide ion but the rate coefficients are somewhat below the diffusion-limited values. In broad terms, the typical effect of an intramolecular hydrogen bond on the rate coefficient for proton removal is to reduce the rate coefficient by a factor of up to ca 105 below the diffusion limit. Correspondingly the value of the dissociation constant of the acid is usually decreased by a somewhat smaller factor from that of a non-hydrogen-bonded acid. There are exceptions, however. 

In recent years, there have been numerous studies examining the dynamics of proton transfer within the context of recently developed theoretical models. Reactions in the gas phase, in the solution phase, and in matrices have been examined [59-72]. Few of these studies, however, have addressed the issue of how the rate of proton transfer correlates with the thermodynamic driving force, which is an important correlation for discerning the validity of the various theoretical models. However, there have been two series of investigations by Kelley and co-workers [70, 71], and by Pines et al. [65, 66] that have sought to elucidate the role of solvent dynamics on the rate of proton transfer. 

Both kinetic and thermodynamic data on organometallic hydrides should be very useful. The relative rates of proton transfer processes and other reactions determine a good deal of organometallic chemistry. For example, in our synthesis of cis-0s(C0) (CH )H> reactions 2-4, the comparative rates of... 

Directions for Future Work. The measurement of rates of proton transfer from a single acid to more bases differing only in thermodynamic base strength should allow the construction of BrjSnsted plots of kinetic versus thermodynamic acidity. The bases we have used at this early stage of development of the subject have involved different proton acceptor atoms and cannot be so used (although comparison of the Et N transfer rates of... 

Since formation of EGBs from amides, in all cases, is the result of direct reduction and H2 formation (and has to be done ex situ), the monomeric as well as the polymeric EGBs are recovered as the PB. Their reactions as bases have to be driven either by a thermodynamically favored proton transfer reaction or by a fast follow-up reaction of the depro-tonated substrate, which - particularly for (33) -is difficult, since (33) is a good nucleophile. 

Two types of electrogenerated carbon bases have commonly been used (1) dianions derived from activated alkenes, and (2) carbanions formed by reductive cleavage of halogen compounds or by direct reduction of weak carbon acids. In both cases, the efficiency of the proton transfer reaction relies on a thermodynamically favored proton transfer or a fast follow-up reaction of the deproto-nated substrate. 

From the thermodynamics of such dynamical hydrogen bonds , one may actually expect an activation enthalpy of long-range proton diffusion of not more than 0.15 eV, provided that the configuration O—H "0 is linear, for which the proton-transfer barrier vanishes at 0/0 distances of less than 250 pm. However, the mobility of protonic defects in cubic perovskite-type oxides has activation enthalpies on the order of 0.4—0.6 eV. This raises the question as to which interactions control the activation enthalpy of proton transfer. 

The spectroscopic, kinetic, and thermodynamic data discussed are sufficient to describe semiquantitatively the energy profile of proton transfer to a hydride ligand occurring in solution [29, 35, 36]. Figure 10.10 shows the energy as a function of the proton-hydride distance, varying from the initial state to a final product. The average structural parameters of the initial hydrides and intermediates have been taken from earlier chapters. Since proton-hydride contacts of... 

Intermediate 1 could also be stabilised by proton transfer from oxygen to give 3 in Scheme 11.9. The proton acceptor B could be solvent water or a general base catalyst. The reaction will only be catalysed if the rate of breakdown of 1 to regenerate reactants is faster than the rate of proton transfer. In this case, such catalysis would be independent of the base strength of the catalyst B as proton transfer would invariably be thermodynamically favourable and hence occur at the maximum diffusion-controlled rate. If proton transfer to solvent is thermodynamically favourable, such that proton donation to 55.5 M water is faster than to, say, 1 M added base, any observed catalysis by base must represent transition state stabilisation by hydrogen bonding, or a concerted mechanism. 

The dynamics of proton transfer within a variety of substituted benzophenone-iV-methylacridan contact radical ion pairs [e.g. (53)] in benzene have been examined.156 Correlation of the rate constants for proton transfer with the thermodynamic driving force has revealed both normal and inverted regions for proton transfer in benzene. 

The first section, under the heading solute-solvent interactions, considers the origin of the medium effect which is exhibited for reactions on changing from a hydroxylic solvent to a dipolar aprotic medium such as DMSO. This section is subdivided into two parts, the first concentrating on medium effects on rate processes, the second on equilibria of the acid-base variety. The section includes discussion of the methods used in obtaining and analysing kinetic and thermodynamic transfer functions. There follows a discussion of proton transfers. The methods and principles used in such studies have a rather unique character within the context of this work and have been deemed worthy of elaboration. The balance of the article is devoted to consideration of a variety of mechanistic studies featuring DMSO many of the principles developed in earlier sections will be utilized here. 

The rates of proton transfer reactions cover a wide spectrum, from exasperatingly slow to diffusion controlled. Any theory which can rationalize this range has obvious merit. Such a rationalization is in fact accomplished, to a large degree, by Br nsted and Pedersen s (1923) relationship between rate (kinetic acidity) and p/sTa (thermodynamic acidity). The relationship, known as the Br0nsted equation, has the form (8) where B is the catalytic rate constant. The... 

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