Standard enthalpy and entropy

In a fiormal analogy to the expressions for the thenuodynamical quantities one can now defiine the standard enthalpy // and entropy ofiactivation. This leads to the second Eyring equation. ... 

It is seen from equation (22) that there will, indeed, be a temperature at which the separation ratio of the two solutes will be independent of the solvent composition. The temperature is determined by the relative values of the standard free enthalpies of the two solutes between each solvent and the stationary phase, together with their standard free entropies. If the separation ratio is very large, there will be a considerable difference between the respective standard enthalpies and entropies of the two solutes. As a consequence, the temperature at which the separation ratio becomes independent of solvent composition may well be outside the practical chromatography range. However, if the solutes are similar in nature and are eluted with relatively small separation ratios (for example in the separation of enantiomers) then the standard enthalpies and entropies will be comparable, and the temperature/solvent-composition independence is likely be in a range that can be experimentally observed. 

The solid product, BaO, was apparently amorphous and porous. Decomposition rate measurements were made between the phase transformation at 1422 K and 1550 K (the salt melts at 1620 K). The enthalpy and entropy of activation at 1500 K (575 13 kJ mole-1 and 200 8 J K"1 mole-1) are very similar to the standard enthalpy and entropy of decomposition at the same temperature (588 7 kJ and 257 5 J K-1, respectively, referred to 1 mole of BaS04). The simplest mechanistic explanation of the observations is that all steps in the reaction are in equilibrium except for desorption of the gaseous products, S02 and 02. Desorption occurs over an area equivalent to about 1.4% of the total exposed crystal surface. Other possible models are discussed. 

The equilibrium concentrations of many disubstituted benzenes (containing alkyl and halogen substituents) show that the meta isomer is in nearly all cases the most thermodynamically stable. It is not obvious why this should be so. Shine182 had discussed this problem in terms of the relative sizes of the standard enthalpy and entropy changes between any pair of isomers. 

Standard Gibbs free energies of formation can be determined in various ways. One straightforward way is to combine standard enthalpy and entropy data from tables such as Tables 6.5 and 7.3. A list of values for several common substances is given in Table 7.7, and a more extensive one appears in Appendix 2A. 

At this point we can use AGvap° = AHvap° — TAS °, where AHrap° and ASvap° are the standard enthalpy and entropy of vaporization, respectively, and obtain... 

Solving for In gives an equation relating Tgq to standard enthalpy and entropy changes ... 

The following gives the standard Enthalpy and Entropy of these defect reactions, according to Kroeger (1965) ... 

To begin the problem, we need the standard enthalpy and entropy values for each of the reactants and products. These are the values we ll be using to complete this problem ... 

Equation 2.67 indicates that the standard enthalpy and entropy of reaction 2.64 derived from Kc data may be close to the values obtained with molality equilibrium constants. Because Ar// is calculated from the slope of In AT versus l/T, it will be similar to the value derived with Km data provided that the density of the solution remains approximately constant in the experimental temperature range. On the other hand, the error in ArSj calculated with Kc data can be roughly estimated as R In p (from equations 2.57 and 2.67). In the case of water, this is about zero for most solvents, which have p in the range of 0.7-2 kg dm-3, the corrections are smaller (from —3 to 6 J K-1 mol-1) than the usual experimental uncertainties associated with the statistical analysis of the data. 

A linear relationship between the standard enthalpies and entropies of a series of structurally related molecular entities undergoing the same reaction thus, AH° -I3AS° = constant or AAH° = (3AS°. When P > 0, this relationship is referred to as an isoequilibrium relationship. When the absolute temperature equals the factor P (often referred to as the isoequilibrium temperature), then all substituent effects on the reaction disappear (i e., AAG° = 0). In other words, a reaction studied at T = p will exhibit no substituent effects. This would suggest that, when one studies substituent effects on a reaction rate, the reaction should be studied at more than one temperature. Note also that the p factor in the Hammett equation changes sign at the isoequilibrium temperature. See Isokinetic Relationship... 

AH° and AS° are the standard enthalpy and entropy changes in going from reactants to the transition state (not to products). 

In is species 2, Sb is species 3, and InSb is species 5 in the liquid. AH and AS" are the standard enthalpy and entropy of dissociation of the InSb species into the pure liquid elements. 

Standard Enthalpy and Entropy Changes for the Transition from the Chemisorbed Layer (Assumed to have Composition ITO J to the Three Bulk Oxides... 

As appears from the examination of the equations (giving the best fit to the rate data) in Table 21, no relation between the form of the kinetic equation and the type of catalyst can be found. It seems likely that the equations are really semi-empirical expressions and it is risky to draw any conclusion about the actual reaction mechanism from the kinetic model. In spite of the formalism of the reported studies, two observations should be mentioned. Maatman et al. [410] calculated from the rate coefficients for the esterification of acetic acid with 1-propanol on silica gel, the site density of the catalyst using a method reported previously [418]. They found a relatively high site density, which justifies the identification of active sites of silica gel with the surface silanol groups made by Fricke and Alpeter [411]. The same authors [411] also estimated the values of the standard enthalpy and entropy changes on adsorption of propanol from kinetic data from the relatively low values they presume that propanol is weakly adsorbed on the surface, retaining much of the character of the liquid alcohol. 

The proposed mechanism of the effect of water can be supported by two other findings (i) the calculations of Maatman et al. [410] revealed that the active sites could be identified with surface silanol groups [Sect. 4.1.2.(a)] and(ii) independent studies of other authors [424—426] showed that silica gel could actually adsorb two layers of water the first layer is strongly chemisorbed whereas the second is less strongly adsorbed and retains much of the character of free water. The standard enthalpy and entropy changes on adsorption determined from kinetic adsorption coefficients, Kr and Kr, for the first and second layer, respectively [411], are consistent with this observation. 

The enthalpy of combustion of rhombic sulfur is -70.96 kcal/mole. The enthalpy of combustion of monoclinic sulfur is -70.88 kcal/mole. Calculate the standard enthalpy and entropy of transition from rhombic to monoclinic sulfur. 

Calculate the standard enthalpy and entropy of vaporization for C2H5OH at 25°C. 

The enthalpy of combustion of diamond is -94 50 kcal/mole The enthalpy of combustion of graphite is -94 05 kcal/mole What is the standard enthalpy and entropy of transition from diamond to graphite0... 

Standard Enthalpy and Entropy Changes on Forming Complexes between Cadmium Ion and Methylamine or Ethylenediamine (en)... 

The data required for method II are the measurable quantities AGf°[ij] and, if Kn is not 0, AHmn, Tmn, and Cps[n] and an extrapolated quantity Cp[n], To make use of available data, the standard Gibbs energy of formation can be expressed in terms of the standard enthalpy and entropy of formation. The advantage of this formulation is that thermodynamic information for unstable or metastable systems is required only for the elements (i.e., Cp[n]), for which a better estimate can usually be made. This data base contains no explicit liquid-solution properties. 

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