Dissecting the Enthalpies

We are neglecting any enthalpy changes resulting from mixing so that the partial molal enthalpies are equal to the molal enthalpies of the pure components. The molal enthalpy of species i at a particular temperature and pressure, is usually expressed in terms of an enthalpy of formation of species i at some reference temperature Tr, plus the change in enthalpy that 

The reference temperature at which // (Tr) is given is usually 25°C. For any substance that is being heated from T, to T2 in the absence of phase change, 

A large number of chemical reactions carried out in industry do not involve phase change. Consequently, we shall further refine our enei y balance to apply to single-phase chemical reactions. Under these conditions, the enthalpy of species i at temperature T is related to the enthalpy of formation at the reference temperature Tr by 

The heat capacity at temperature T is frequently expressed as a quadratic function of temperature, that is, 

However, while the text will consider only constant heat capacities, the PRS RH.3 on the DVD-ROM has examples with variable heat capacities. 

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Abstract - This work is concerned with the origin of effects on rate equilibrium processes when reactions are performed in dipolar aprotic media such as dimethyl sulfoxide and dimethyl-formamide compared to typical hydroxylic media. An example of processes studied in our laboratory is the competition between proton abstraction and a-complex (Meisenheimer adduct) formation in the interaction of nitroaromatic compounds with basic systems (e.g. 1,3-dinitrobenzene in DMF-D20-Na0D). Other reactions studied are the base catalyzed isotopic exchange of D2 in aqueous DMSO mixtures, and also isotopic exchange of fluoroform. It has been found possible in certain cases to dissect the initial state and transition state contributions to the reaction rates from the kinetically measured enthalpies of activation and the thermodynamically evaluated enthalpies of transfer of the reactants. This procedure affords insight into transition state properties and behaviour. 

Kinetic studies of the reaction between the a-nucleophile, butane-2-3-dione oximate (Ox ), and p-nitrophenyl thionobenzoate (18) in DMSO-H2O mixtures of varying compositions at 298,308, and 318 K revealed that, based on a comparison of rates of reaction with a normal nucleophile, p-chlorophenoxide, the a-effect showed a bell-shaped profile, the maximum value occurring at 50% DMSO at all temperatures, but decreasing as the temperature increased. Dissection of the activation parameters, A7/ and revealed that the bell-shaped a-effect behaviour is due to entropy of activation differences rather than enthalpy terms, although the enthalpy term controls almost entirely the solvent-dependent dramatic increase in reaction rate (about 2000-fold greater in 80% DMSO than in H2O). Differences in the TS structures for the reactions with Ox ... 

If a Ceo or C70 fullerene were dissected, corannulene (71) would be the smallest segment with a curvature similar to that of the spheroids. Gas-phase electron diffraction analysis, aided by B3LYP/6—31(d) calculations, shows the corannulene carbon skeleton is unlike the Ceo one in that the hexagonal rings are not planar but bent out so as to flatten the molecule. In two dimensions, corannulene resembles a contracted coronene but the nonplanarity of the corannulene would be expected to mitigate its aromaticity compared to the larger, planar coronene. In fact, not only is corannulene not 5/6 of coronene (252 kJ/mol), its gaseous enthalpy of formation, 463.7 7.3 kJ/mol, is more endothermic than that of coronene (302.0 kJ/mol). Of the many semiempirical and ab initio calculations of the enthalpy of formation quoted for corrannulene, only two are close to the reported experimental value. Those two values are even closer (460.7 from MM2 and 459.6 kJ/mol from additivity ) if a recommended value of 118.6 4.7 kJ/mol for the enthalpy of sublimation is accepted. 

We will now dissect the molar flow rates and enthalpy terms in Equation (11-9) to arrive at a set of equations we can readily apply to a number of reactor situations. 

Since AG and AG are combinations of enthalpy and entropy terms, a linear free-energy relationship between two reaction series can result from one of three circumstances (1) AH is constant and the AS terms are proportional for the series, (2) AS is constant and the AH terms are proportional, or (3) AH and AS are linearly related. Dissection of the free-energy changes into enthalpy and entropy components has often shown the third case to be true. °... 

For soft cations, such as Ag+ and Pb2+, covalent contributions are much more important, and consequently the observed order of complex stabilities is quite different from that for alkali cations NH > O > S for Pb2+ and NH, S > O for Ag+. Dissection of the overall effect into enthalpy and entropy contributions (Table 15) reveals the complicated nature of the heteroatom effect. For K+ and Ba2+, the more favourable entropy contribution for N and S ligands is more than offset by the unfavourable change in enthalpy of binding. 

Very recently, a dissection of 6AH and 5A values for reaction 15 has been completed(52). Unfortunately, since values of AH and AS° for the product ion-pair are not available, it is not possible to obtain the equivalent of Z values from any enthalpy or entropy plots. However, dissections in terms of enthalpy or entropy can be used to test for specific solvation of the transition state in particular solvents. In Table XIII are details of the values of AG°, AH, and AS for the Et N/Etl transition state the "normal" solvent acetone has been taken as the reference solvent. 

The dissection of solvent influences on rate constants into initial-state and transition-state contributions, especially when combined with a knowledge of solvent effects on the thermodynamic properties of suitable model solutes, is a powerful method for the examination of transition states. In favorable cases with electrically neutral transition states, it is possible to estimate the degree of charge separation in the transition state and its position along the reaction coordinate. Dissections in terms of enthalpy and entropy are useful also in probing specific transition-state/solvent interactions. 

Thus, if both transfer free energies and enthalpies are available it should be possible to achieve complete dissection of the effect of solvent on the various thermodynamic parameters. 

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