Temperature dependence of enthalpy changes

This is called Kirchhojf s equation AH is the enthalpy change accompanying a reaction and A CP is the sum of the heat capacities of the products less the sum of the heat capacities of the reactants. Integrating from temperature Tt 

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Figure 1.4. Temperature dependence of the change in Gihhs energy, enthalpy and entropy upon transfer of ethane and butane from the gas phase to water. The data refer to transfer from the vapour phase at 0.101 MPa to a hypothetical solution of unit mole fraction and are taken from ref. 125.

Kirchhoffs Law is used to determine the temperature dependence of a change in the specific enthalpy of a chemical process. In most cases, Acp is small at moderate temperature changes, which means that the change in specific enthalpy is relatively independent of the temperature at which the process is carried out. The relationship assumes that no changes occur in the state of aggregation of reactants or reac-... 

If we assume that the temperature dependence of the changes of enthalpy and entropy are small, then... 

Enthalpy changes for biochemical processes can be determined experimentally by measuring the heat absorbed (or given off) by the process in a calorimeter (Figure 3.2). Alternatively, for any process B at equilibrium, the standard-state enthalpy change for the process can be determined from the temperature dependence of the equilibrium constant ... 

The Arrhenius activation energy,3 obtained from the temperature dependence of the three-halves-order rate constant, is Ea = 201 kJ mol-1. This is considerably less than the standard enthalpy change for the homolysis of acetaldehyde, determined by the usual thermodynamic methods. That is, reaction (8-5) has AH = 345 kJ mol-1. At first glance, this disparity makes it seem as if dissociation of acetaldehyde could not be a predecessor step. Actually, however, the agreement is excellent when properly interpreted. 

In addition to chemical reactions, the isokinetic relationship can be applied to various physical processes accompanied by enthalpy change. Correlations of this kind were found between enthalpies and entropies of solution (20, 83-92), vaporization (86, 91), sublimation (93, 94), desorption (95), and diffusion (96, 97) and between the two parameters characterizing the temperature dependence of thermochromic transitions (98). A kind of isokinetic relationship was claimed even for enthalpy and entropy of pure substances when relative values referred to those at 298° K are used (99). Enthalpies and entropies of intermolecular interaction were correlated for solutions, pure liquids, and crystals (6). Quite generally, for any temperature-dependent physical quantity, the activation parameters can be computed in a formal way, and correlations between them have been observed for dielectric absorption (100) and resistance of semiconductors (101-105) or fluidity (40, 106). On the other hand, the isokinetic relationship seems to hold in reactions of widely different kinds, starting from elementary processes in the gas phase (107) and including recombination reactions in the solid phase (108), polymerization reactions (109), and inorganic complex formation (110-112), up to such biochemical reactions as denaturation of proteins (113) and even such biological processes as hemolysis of erythrocytes (114). 

Many workers have offered the opinion that the isokinetic relationship is confined to reactions in condensed phase (6, 122) or, more specially, may be attributed to solvation effects (13, 21, 37, 43, 56, 112, 116, 124, 126-130) which affect both enthalpy and entropy in the same direction. The most developed theories are based on a model of the half-specific quasi-crystalline solvation (129, 130), or of the nonideal conformal solutions (126). Other explanations have been given in terms of vibrational frequencies involving solute and solvent (13, 124), temperature dependence of solvent fluidity in the quasi-crystalline model (40), or changes of enthalpy and entropy to produce a hole in the solvent (87). 

The binding enthalpy change (AH) could be determined either from the plots of the temperature dependence of the binding constant according to the van t Hoff relationship ... 

Marin, J.M., B. Zalba, L.F. Cabeza, and H. Mehling, Determination of enthalpy-temperature curves of phase change materials with the temperature-history method Improvement to temperature dependent properties, Meas. Sci. Technol., 14, 184-189. 

The temperature dependence of reaction enthalpies can be determined from the heat capacity of the reactants and products. When a substance is heated from T to T2 at a particular pressurep, assuming no phase transition is taking place, its molar enthalpy change from AHm (T]) to AHm (T2) is... 

Writing the equation in this way tells us that if we know the enthalpy of the system, we also know the temperature dependence of G -i-T. Separating the variables and defining Gj as the Gibbs function change at Ti and similarly as the value of G2 at T2, yields... 

The equilibrium concentration of the ions A- and B- participating in the equlibrium can be directly observed by mass spectrometry. Thus, the free-energy change can be derived from the equilibrium constant, since the concentrations of the neutral species are known in advance. Similarly, by measuring the temperature dependence of the equilibrium constants, the associated enthalpy and entropy can be obtained from van t Hoff plots. By measuring a series of interconnecting equlibria, an appropriate scale can be established. The primary standard in such work has frequently been SO2 whose electron affinity is well established by electron photodetachment36. 

The Na salts in THF showed an intermediate behavior, and their spectra revealed an interesting temperature dependence. At + 25°C the spectra were very similar to those of the Li salts, but at - 52°C they had changed to the appearance of the spectra of the K salts. The spectra indicate a fast equilibrium 60 (X = Na) 61 with the latter favored by decreasing temperature. Analysis of the temperature dependence of individual chemical shifts allowed the evaluation of AH°, -6.9 kcal/mol, and AS0, -30 e.u., for this equilibrium (i.e., the contact-ion pairs are favored by entropy but disfavored by enthalpy). A similar effect may explain the temperature dependence of the NMR spectrum of 56. 

Since surface pressure is a free energy term, the energies and entropies of first-order phase transitions in the monolayer state may be calculated from the temperature dependence of the ir-A curve using the two-dimensional analog of the Clausius-Clapeyron equation (59), where AH is the molar enthalpy change at temperature T and AA is the net change in molar area ... 

When Equation (10.24) is applied to the temperature dependence of In Kp, where Kp applies to an isothermal transformation, the A// that is used is the enthalpy change at zero pressure for gases and at infinite dilution for substances in solution (see Section 7.3). 

Because of this relationship between (TT — and p-j x.. the former quantity frequently is referred to as the Joule-Thomson enthalpy. The pressure coefficient of this Joule-Thomson enthalpy change can be calculated from the known values of the Joule-Thomson coefficient and the heat capacity of the gas. Similarly, as (H — is a derived function of the fugacity, knowledge of the temperature dependence of the latter can be used to calculate the Joule-Thomson coefficient. As the fugacity and the Joule-Thomson coefficient are both measures of the deviation of a gas from ideahty, it is not surprising that they are related. 

The overall enthalpy and entropy changes for the distribution reaction (i.e., transfer of the metal complex from the aqueous to the organic phase) can be obtained from the temperature dependence of A r according to... 

The temperature dependence of the equilibrium concentration of a product in a thermodynamically controlled process is determined by the heat (enthalpy change) of the catalyzed reaction. For an exothermic process an increase in temperature... 

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