Relative standard entropies

Since we are concerned with the Arrenhius activation energy under equilibrium conditions, a further correction should be made for the TAS change with the system in equilibrium under standard conditions, i.e., considering the relative standard entropies for for Fe2+, Fe3+ equal to -137.7 and -315.9 J/mole-K,190 a difference of -178.2 J/mole-K. The... 

Entropy Absolute or third-law entropies (relative to a perfectly ordered crystal at 0 K) of a compound in its standard state S or of an... 

To obtain the entropy relative to the standard state, we substitute Equation (4.252) into Equation... 

Standard value of entropy at temperature T Standard deviation Relative standard deviation Initial surface area... 

To achieve a separation between two substances, thermodynamics has shown that their standard free energy of distribution must differ. As the difference between enantiomers are solely spatial and not structural, any separation must be achieved by primarily changing the relative standard free entropy contribution to the standard free energy of each isomer. It will be seen later that this does not exclude a significant contribution from a change in free enthalpy as well, but the primary effect must be entropic in order to realize the corresponding change in free enthalpy. This will be better understood when actual separations are discussed. Thus, in order to obtain some selectivity between enantiomers, the structure of the stationary phase must be such that one isomer will fit... 

Calculate the standard Gibbs energy and enthalpy of formation of CT(aq) and its entropy (relative to H ) at 298 K... 

The entropy relative to its standard value at fixed temperature Pis specified by invoking the appropriate Maxwell relation ... 

Relative Standard Entropies Gases, Liquids, and Solids As we saw in Section 17.3, the entropy... 

Relative Standard Entropies Molar Mass Consider the standard entropies of the noble... 

Relative Standard Entropies Allotropes As mentioned previously, some elements can exist in two or more forms—called allotropes— in the same state of matter. For example, the allotropes of carbon include diamond and graphite— both solid forms of carbon. Since the arrangement of atoms within these forms is different, their standard molar entropies are different ... 

Relative Standard Entropies Molecular Complexity For a given state of matter, entropy generally increases with increasing molecular complexity. For example, consider the standard entropies of the argon and nitrogen monoxide gas ... 

The standard entropy change for the atom-molecule reactions is in the range 5-20 mole and the halogen molecule dissociation has an eiiU opy change of about 105 e.u. The halogen molecule dissociation energy decreases from chlorine to iodine, but the atom-molecule reactions become more endothermic from chlorine to iodine, and this latter effect probably influences the relative contributions to the mechanism from chain reaction and biinolecular reaction. 

Equation (1) can be viewed in an over-simplistic manner and it might be assumed that it would be relatively easy to calculate the retention volume of a solute from the distribution coefficient, which, in turn, could be calculated from a knowledge of the standard enthalpy and standard entropy of distribution. Unfortunately, these properties of a distribution system are bulk properties. They represent, in a single measurement, the net effect of a large number of different types of molecular interactions which, individually, are almost impossible to separately identify and assess quantitatively. 

Different portions of the standard free energy of distribution can he allotted to different parts of a molecule and, thus, their contribution to solute retention can be disclosed. In addition, from the relative values of the standard enthalpy and standard entropy of each portion or group, the nianner in which the different groups interact with the stationary phase may also be revealed. 

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 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. 

As to the computation of reaction enthalpies and entropies, AH and AS , the same arguments apply if they have been obtained from the temperature dependence of the equilibrium constant. A different situation arises vdien AH is determined directly from calorimetry, say with a constant relative error 6. The standard entropy AS then has the standard error... 

However, the rate of substitution of pyrrole is too high and that of benzene too low to be followed by standard techniques, and consequently a kinetic study was limited to furan, thiophene, selenophene, and tellurophene. Activation entropies are constant for all four members of the series, indicating that the arrangement of the atoms around the reaction center is similar, i.e., the transition states of all four rings occur at similar positions along the reaction coordinate. The relative rates for the formylation are thus controlled by the activation enthalpies. At 30UC relative rates are furan (107), thiophene (1), selenophene (3.64), and tellurophene (36.8).68... 

Figure 1.5 Standard entropy of aluminium relative to 0 K. The standard entropy of fusion (AfuS S m) is significantly smaller than the standard entropy of boiling (A pS, ).

Interestingly, the standard entropies (and in turn heat capacities) of both phases were found to be rather similar [69,70]. Considering the difference in standard entropy between F2(gas) and the mixture 02(gas) + H2(gas) taken in their standard states (which can be extracted from general thermodynamic tables), the difference between the entropy terms of the Gibbs function relative to HA and FA, around room temperature, is about 6.5 times lower than the difference between enthalpy terms (close to 125 kJ/mol as estimated from Tacker and Stormer [69]). This indicates that FA higher stability is mostly due to the lower enthalpy of formation of FA (more exothermic than for HA), and that it is not greatly affected by entropic factors. Jemal et al. [71] have studied some of the thermodynamic properties of FA and HA with varying cationic substitutions, and these authors linked the lower enthalpy of formation of FA compared to HA to the decrease in lattice volume in FA. 

Entropy changes were estimated with Eq. 4 assuming that V, is equal to the total stationary phase volume existing in the column. Therefore, these values reflect more properly the relative differences in entreaties of transfer instead of the standard molar entropies that would require to use the volume of the active stationary phase. 

Fig.1 Calculated free energy diagram for hydrogen evolution at a potential U = 0 V relative to the standard hydrogen electrode at pH = 0. The free energy of H+ + e is by definition the same as that of j - i at standard conditions. The free energy of H atoms bound to different catalysts is then found by calculating the free energy with respect to molecular hydrogen including zero-point energies and entropy terms (reprinted from Ref 83 with permission).

A model has been considered for Sn2 reactions, based on two interacting states. Relevant bond energies, standard electrode potentials, solvent contribntions (nonequi-librinm polarization), and steric effects are included. Applications of the theory are made to the cross-relation between rate constants of cross- and identity reactions, experimental entropies and energies of activation, the relative rates of Sn2 and ET reactions, and the possible expediting of an outer sphere ET reaction by an incipient SN2-type interaction (Marcus, 1997). 

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