More on Entropy

In Example 3.2, we calculated the entropy change for an isothermal process. What if the process were not isothermal For a given mass 

For n moles, this equation becomes AS = uCln(Tf/Ti) and C will have units of J/mol K. If C has units of J/g K, then the mass of the system is necessary. If the heat capacity is not constant over the specified temperature range, then the temperature-dependent expression for C must be included explicitly inside the integral and the function must be evaluated on a term-by-term basis. 

Fortunately, most expressions for heat capacity are simple power series in T, whose integrals are easy to evaluate on a term-by-term basis. 

There is no V or p subscript on the symbol for the heat capacity in equation 3.20. That s because it depends on the conditions of the process. If it occurs under conditions of constant volume, use Cy If it occurs under conditions of constant pressure, use Cp. Usually the particular process involved dictates the choice. 

Now consider gas-phase processes. What if the temperature were constant but the pressure or the volume changed reversibly If the gas is ideal, AU for the process is exactly zero, so dq y = —dw = +p dV. Substituting again for dq, then  

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On the basis of the values of AS° derived in this way it appears that the chelate effect is usually due to more favourable entropy changes associated with ring formation. However, the objection can be made that and /3l-l as just defined have different dimensions and so are not directly comparable. It has been suggested that to surmount this objection concentrations should be expressed in the dimensionless unit mole fraction instead of the more usual mol dm. Since the concentration of pure water at 25°C is approximately 55.5 moldm , the value of concentration expressed in mole fractions = cone in moldm /55.5 Thus, while is thereby increased by the factor (55.5), /3l-l is increased by the factor (55.5) so that the derived values of AG° and AS° will be quite different. The effect of this change in units is shown in Table 19.1 for the Cd complexes of L = methylamine and L-L = ethylenediamine. It appears that the entropy advantage of the chelate, and with it the chelate effect itself, virtually disappears when mole fractions replace moldm . ... 

However, solubility, depending as it does on the rather small difference between solvation energy and lattice energy (both large quantities which themselves increase as cation size decreases) and on entropy effects, cannot be simply related to cation radius. No consistent trends are apparent in aqueous, or for that matter nonaqueous, solutions but an empirical distinction can often be made between the lighter cerium lanthanides and the heavier yttrium lanthanides. Thus oxalates, double sulfates and double nitrates of the former are rather less soluble and basic nitrates more soluble than those of the latter. The differences are by no means sharp, but classical separation procedures depended on them. 

Check out the video clip giving more information on entropy at www. brightredbooks.net... 

Students often state the laws of thermodynamics this way. You cant win because you cant get any more energy out of a system than you put into it. You can t break even because no matter what you do, some of your energy will be lost as ambient heat. Lastly, you cant get out of the game because you depend on entropy-increasing processes, such as solar nuclear fusion or cellular respiration, to remain alive. 

Destabilizing. /3-substitution reduces conformational freedom. His and Tyr may also form hydrogen bonds with polypeptide backbone in unfolded state. Very destabilizing. Buries less hydrophobic surface area, makes less van der Waals contacts, and loses more conformational entropy on folding. 

At this point the need arises to become more explicit about the nature of entropy generation. In the case of the heat exchanger, entropy generation appears to be equal to the product of the heat flow and a factor that can be identified as the thermodynamic driving force, A(l/T). In the next chapter we turn to a branch of thermodynamics, better known as irreversible thermodynamics or nonequilibrium thermodynamics, to convey a much more universal message on entropy generation, flows, and driving forces. 

Gaggioli, R. A., "More on Generalizing the Definitions of Heat and Entropy," Int. J. of Heat and Mass Transfer, 12,... 

The free energy of micelle formation has been found to be more dependent on entropy than on enthalpy factors (Kavanau, 1965 Elworthy, 1968). Micelle formation has been treated theoretically either... 

The activation parameters for the exchange reactions of 17 and 18 were determined by a combination of variable-temperature ll NMR lineshape analysis16 and spin saturation transfer experiments.17 Rate data for 17 were measured over a temperature range of 100 "C. Rates for compound 18 were measured over a 65 °C range. The enthalpy of activation was found to be considerably smaller in the case of 17 (12.2(2) kcal/mol) relative to 18 (17.6(3) kcal/mol). Ion pair dissociation is therefore facilitated by the presence of a lone pair of electrons on the boron substituent. The entropy of activation for 17 is -2.3(6) eu, while that of 18 is 8(1) eu. The more positive entropy of activation measured for 18 may be interpreted as the creation of two independent particles from a closely associated ion pair. 

Some solvent effects on entropy and enthalpy contributions to the free energy of activation of Sif2 reactions are expressed in dimensionless units in Table 23. As already noted, much more could be said about these data if appropriate enthalpies of transfer for ions and molecules were known. However it is significant that in Sn2 reactions of anions at a saturated carbon atom, the large increase in rate, on transfer from water or methanol to DMF, is due to a decreased enthalpy of activation, which is only partially compensated for by a small increase in entropy of activation. For 8 2 reactions of anions at aromatic carbon, the change in both the enthalpy and entropy of activation, upon solvent transfer, favours reaction in DMF. As at saturated carbon, the solvent effect on AH is considerably larger than that on J-S, with the exception of one reaction of SON". 

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