Relation between AH and

The relation between AH° and enthalpies of formation is perhaps used more often than any other in thermochemistry. Its validity depends on the fact that enthalpy is a state property. For any reaction, AH° can be obtained by imagining that the reaction takes place in two steps. First, the reactants (compounds or ions) are converted to the elements ... 

We can obtain a relation between AH and AE for a chemical reaction at constant temperature by starting with the defining equation relating enthalpy, H, to energy, E ... 

To calculate the relation between AH and A U, we suppose that the amount of ideal gas reactant molecules is initjai. Because for an ideal gas TV = nRT, the initial enthalpy is... 

From the relation between AH and AS, the relation between AG and AS follows immediately. Of course, log k can be plotted directly instead of AG ... 

The last method for illustrating an isokinetic relationship is based on the dependence on a parameter. If both AH and AS are related to the parameter then by its elimination from the two equations, the relation between AH and... 

Another simple approach assumes temperature-dependent AH and AS and a nonlinear dependence of log k on T (123, 124, 130). When this dependence is assumed in a particular form, a linear relation between AH and AS can arise for a given temperature interval. This condition is met, for example, when ACp = aT" (124, 213). Further theoretical derivatives of general validity have also been attempted besides the early work (20, 29-32), particularly the treatment of Riietschi (96) in the framework of statistical mechanics and of Thorn (125) in thermodynamics are to be mentioned. All of the too general derivations in their utmost consequences predict isokinetic behavior for any reaction series, and this prediction is clearly at variance with the facts. Only Riietschi s theory makes allowance for nonisokinetic behavior (96), and Thorn first attempted to define the reaction series in terms of monotonicity of AS and AH (125, 209). It follows further from pure thermodynamics that a qualitative compensation effect (not exactly a linear dependence) is to be expected either for constant volume or for constant pressure parameters in all cases, when the free energy changes only slightly (214). The reaction series would thus be defined by small differences in reactivity. However, any more definite prediction, whether the isokinetic relationship will hold or not, seems not to be feasible at present. 

In this equation, 6AH must equal the first and 6AS the second term on the right-hand side so that there is no simple relationship between them. However, the imaginary isokinetic temperatures Pi and P2, corresponding to the two interaction mechanisms, can be defined as J3i=-A/B and P2 -C/D. The resulting relation between AH and AS is scattered (2) as shown in Figure 19. 

Figure 19. Relation between AH and AS for two interaction mechanisms characterized by the values p, and Pj (schematic example).

The data reported in Table 13 do show a relation between AH and ALFSE which is in general agreement with the above assumption. For Mn(III) the AH values are slightly high which may result from the observed tetragonal distortion in the solid state which places these complexes slightly off the D3d-D3h reaction pathway. Since ALFSE is in units of Dq the complexes from the second row of the periodic table should enantiomerse dower than their first row counterparts. Hence the trends in AH ... 

Many other relations between -AH and Av (many of which are valid for separate classes of organic acids and bases) and a relation between -AH and the Vxh band intensity enhancement (AA 2) ave been proposed [34]. A more detailed and thorough analysis of the experimental spectral characteristics and enthalpies for various organic acid ase H-complexes was provided by logansen on the basis of several methods (chromatography, calorimetry and so on). The author suggested an universal proportionality relationship which was named the intensity rule [34] (equation 7), where AA / =... 

Assuming ideal behavior and constant temperature, the relation between AH and AE can be derived from the equation (page 14)... 

The relation between Ah° and temperature is sketched in Figure 12.6. From this figure we see that the enthalpy change of the reaction at Ti is... 

Equilibrium constants and Gibbs energies of complexation are given in Table 2.3. These data can be used to study the existence of a linear relation between AH° and AG° for the complexation of SbCls. A plot of AH° versus AG° values for 28 Lewis bases (mostly carbonyl compounds) is shown in Figure 2.2. Only 84% of the variance of AH° is explained by AG°. The lack of a linear AH—AG relationship has been attributed to pronounced... 

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