Affinity and heat of reaction

Example 8.4 Affinity and heat of reaction Describe the relationship between the affinity and heat of a chemical reaction. The affinity is defined as a partial derivative of the Gibbs free energy 

The condition in Eq. (8.86) may not be easily satisfied. For simultaneous reactions, we have 

In particular we notice the two last formulae which may be written cf. 3.26, 3.28)  

These formulae link the affinity with the heats of reaction and dUjd )T y, They show that at sufficiently low temperatures the heat of reaction becomes equal to the affinity this will be so when  

In this case the affinity and the heats of reaction have the same sign, and exothermal reactions dUjd C. )) are spontaneous. 

The importance of (4.8) lies in the fact that it enables the affinity to be calculated at a temperature T, if its value at some given temperature Tq is known. Thus if we integrate (4.8) between Tq and T, at constant p and I we have 

It has already been seen (chap. II, 5) that specific heats may usually be expressed as a power series in T, so that with the aid of KirchhofiTs equation (2.32), dHjdi)T,p can be expressed in the form  

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Relationship between affinity and heat of reaction according to the two laws of thermodynamics. 

In Chapter IX. it was shown that the affinity of a chemical reaction can be calculated for any temperature, provided its value is known (from experiment) for any one temperature, and provided the heat of reaction and the variation of the heat of reaction with the temperature are known for the range of temperature in which we wish to calculate the affinity. The heat of reaction and its temperature coefficient, which is determined by the specific heats of the reacting substances, can both be determined calorimetrically without difficulty. On the other hand, it is not possible to calculate the affinity or the position of a chemical equilibrium by means of the two laws of thermodynamics and these thermal quantities alone. It is always necessary to know in addition the value of the affinity for some one temperature. The experimental determination of the affinity is often attended with considerable difficulty. It was thereforie eminently desirable to discover a new method which would avoid even this single determination and enable us to calculate the affinity from thermal quantities alone. The valuable researches of Nernst which resulted in the discovery of his heat theorem have placed at our disposal a means of solving this important problem. ... 

We now wish to see how the activity coefficients enter into the affinity, the heat of reaction and the expansion accompanying the reaction. From (7.65) and (6.22) we see that... 

As an example, Equation 1 gives the results for the proton affinities (PA) of ethers and alcohols. The proton affinities, the heats of reaction released on protonation of alcohols and ethers, can be calculated from the electronegativity parameters, X12, being a measure of the inductive effect, and aa, representing the polarisability effect. ... 

Describe the relationship between the affinity and heat of a chemical reaction. Solution ... 

Other measures of nucleophilicity have been proposed. Brauman et al. studied Sn2 reactions in the gas phase and applied Marcus theory to obtain the intrinsic barriers of identity reactions. These quantities were interpreted as intrinsic nucleo-philicities. Streitwieser has shown that the reactivity of anionic nucleophiles toward methyl iodide in dimethylformamide (DMF) is correlated with the overall heat of reaction in the gas phase he concludes that bond strength and electron affinity are the important factors controlling nucleophilicity. The dominant role of the solvent in controlling nucleophilicity was shown by Parker, who found solvent effects on nucleophilic reactivity of many orders of magnitude. For example, most anions are more nucleophilic in DMF than in methanol by factors as large as 10, because they are less effectively shielded by solvation in the aprotic solvent. Liotta et al. have measured rates of substitution by anionic nucleophiles in acetonitrile solution containing a crown ether, which forms an inclusion complex with the cation (K ) of the nucleophile. These rates correlate with gas phase rates of the same nucleophiles, which, in this crown ether-acetonitrile system, are considered to be naked anions. The solvation of anionic nucleophiles is treated in Section 8.3. 

Let us discuss now the conditions required for the electron transfer process. This reaction requires, of course, a suitable electron donor (a species characterized by a low ionization potential) and a proper electron acceptor, e.g., a monomer characterized by a high electron affinity. Furthermore, the nature of the solvent is often critical for such a reaction. The solvation energy of ions contributes substantially to the heat of reaction, hence the reaction might occur in a strong solvating solvent, but its course may be reversed in a poorly solvating medium. A good example of this behavior is provided by the reaction Na -f- naphthalene -> Na+ + naphthalene". This reaction proceeds rapidly in tetrahydrofuran or in dimethoxy... 

Nernst, in his Theoretische Chemie, devoted a whole chapter to a critical examination of the rule of Thomsen and Berthelot, and he concluded that in many cases the heat of reaction certainly does correspond very closely with the maximum work, AT, which latter magnitude he took from van t Hoff as a measure of the chemical affinity. Whilst pointing out that it very often gives results wholly incompatible with experience, and cannot therefore be indiscriminately applied, Nernst showed that the rule nevertheless holds good in too many cases to be wholly false in an appropriate metaphor he claimed that it contains a genuine kernel of truth which has not yet been shelled from its enclosing hull. This labour of emancipation was partially effected in the newer work of the same author, Applications of Thermodynamics to Chemistry, 1907, which is an attempt to place the rule of Berthelot on a scientific basis, and to determine under what conditions its use is legitimate. He points out that the equation ... 

T. W. Richards, The Significance of Changing Atomic Volume 111. The Relation of Changing Heat Capacity to Change of Free Energy. Heat of Reaction. Change of Volume, and Chemical Affinity". Z. Physik. Chem. 42. 129-154 (1902). 

The heats and rates of reaction of carbenes with substituted pyridines to form ylides have been measured and used to calculate the ylides heats of formation.54 The heats of reaction of methylchloro- and phenylchlorocarbene with were found to correlate well with the pXa s and proton affinities of the pyridines. However, the correlation is not good for sterically demanding... 

In writing the Etudes de dynamique chimique (1884), van t Hoff drew on Helmholtz s 1882 paper but especially on the work of August Horstmann, a student of Bunsen, Clausius, and H. Landolt.59 As has often been discussed, van t Hoffs was an ambitious and original synthesis of disconnected ideas and theories about opposing forces, equilibrium, active masses, work and affinity, electromotive force, and osmotic pressure. He demonstrated that the heat of reaction is not a direct measure of affinity but that the so-called work of affinity may be calculated from vapor pressures (the affinity of a salt for its water of crystallization), osmotic pressure (affinity of a solute for a solution), or electrical work in a reversible galvanic cell (which he showed to be proportional to the electromotive force). 

Computational methods have also been used frequently to estimate the thermodynamic stabilities of superelectrophiles. These calculations have often involved the estimation of barriers to gas phase dissociation or deprotonation, and the proton affinities of conventional electrophilic intermediates. Other useful studies have calculated the heats of reactions for isodesmic processes. An interesting example of these calculations comes from a study of the protoacetyl dication (Cf COH2"1- ).42 In calculations at the 6-31G //4-31G level of theoiy, the protoacetyl dication (83) is estimated to react with methane by hydride abstraction with a very favorable... 

Additional knowledge is available from computational investigations. Geometries for Nj were determined at many levels of theory from RHF/6-31G over B3LYP/6-311+G(3df) to CCSD(T)-fc/cc-pVQZ [3,12-20], Vibrational frequencies [3,5,8,12-14], NMR-shifts [3], and heats of formation [3,8,13,18] were published, too. The nature of bonding in N5 was investigated in detail [8,18-21]. Other publications explore reactions that N5 may undergo [5,7,8,14-17], Nj has been the object of computational studies, too. Its heat of formation [5,7,18,22] and the barrier towards dissociation into Nj and N2 have been determined [5,7,14,23,24], Proton affinities in the gas-phase and in water have been studied [25-28]. Salts of Nj have been studied elsewhere [23,29-33]. 

Equation 3.39 holds valid for the system in which only a single process or reaction is occurring. In a system in which multiple chemical reactions are simultaneously occurring, Eq. 3.27 for the uncompensated heat can be expressed by the sum of the products of all independent affinities and their conjugated reaction rates as given in Eq. 3.40 ... 

Equations 3.28 and 3.29 have shown the relationship between the affinity A and the heats of reaction dU/d% at constant volume and dH/d at constant pressure as shown in Eq. 4.7 ... 

The physical quantity that we usually call the affinity of a reaction corresponds to the average affinity of the reaction. Generally, the affinity of a reaction at constant T and V differs numerically from that at constant 2"and p, as compared to the heat of reaction whose... 

This is the direct relation connecting the average affinity and the average heat of reaction. 

We see that the average affinity A of a reaction at a temperature T can be calculated, if we know (a) the average affinity A 11 at one specified temperature T0 at the pressure p (b) the heat of reaction (AH)T(j p at T0 and (c) the partial molar heat capacities of the constituent substances as a function of temperature throughout the whole range from roto T. 

The development of primary antibodies reacting with fixation-resistant epitopes has somewhat improved this situation. However, the introduction of enzymatic pre-treatments for tissue sections — and particularly the introduction of methods for the heat retrieval of tissue antigenicity—were aimed at restoring the affinity and avidity of the immune reaction and have become very important pre-treatment tools in immunohistochemistry (IHC) (3). 

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