Entropy Changes at

Once again, we need to correct a state variable for temperatures other than the standard state  

We know from the previous chapter that we may have to integrate over the various terms of a polynomial heat capacity, but there is a slight difference in the first term in this case. Once again, we can calculate the difference in the Cp polynomial coefficients according to the , coefficients in the balanced reaction. 

Aa = X l riiOi — rijOj and similar expressions for Ab, Ac, Ad, and Ae are obtained using Cp polynomials from Table 4.3. Thus, we need to integrate a slightly different formula for AS (T). 

The main difference in the entropy integration is in the first natural logarithm term. 

One curiosity of entropy is a relationship between boiling points and heats of vaporization. At an early age, F.T. Trouton (1863-1922) observed a pattern in boiling points and published two papers on a trend now known as Trouton s rule. This rule falls within the realm of familiar rules in organic chemistry, which often have exceptions but are still usefid. Basically Trouton s mle states that 

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This is die entropy change for a complete conversion to NH3 where 1 kmol of N2 is converted. The entropy change at 428 K is ... 

C14-0087. Calculate the standard entropy change at 298 K of each of the following reactions, which are important in the chemistry of coal. Assume that coal has the same thermodynamic properties as graphite. 

The addition reaction has a substantial negative entropy change => At low temperatures, the TAS° term in AG° = AH° - TAS°, is not large enough to offset the favorable AH° term. 

The reaction favours the formation of ozone with a significant equilibrium constant. Appendix C also lists the enthalpies of formation and the standard enthalpy of the reaction ArH° can be calculated. The answer for the enthalpy calculation is ArH° = —106.47 kJ mol, showing this to be an exothermic reaction, liberating heat. The entropy change at 298 K can also be calculated because ArG° = ArH° — T ArS°, so ArS° = 25.4 Jmol-1 K-1, indicating an increase in the entropy of the reaction as it proceeds by creating one molecule from two. 

If we consider an entropy change at constant pressure, then from Equations (6.49) and (4.53),... 

In a reaction such as that represented by Equation (12.23), the standard entropy change at the temperature T is given by the expression... 

Several evidences, reported in the literature and briefly reviewed in the present article, demonstrate that the carbohydrate recognition at the surface of organized systems is somewhat different from that observed in isotropic media. These differences lie in (1) the conformation of carbohydrate which is affected by hydrophobization and by the nature of the surrounding lipids, (2) cluster effects from which can result in high energies of binding and which are affected by the fluidity of the lipid system, (3) entropy changes at the surface of a supra-molecular structure. 

Figure 15 displays specific heat data for itinerant antiferromagnetic Nplr2 ° (Tn = 7 K) while results for NpSn3 ° are presented in Fig. 2, showing the BCS-like specific heat anomaly the entropy change at the transition is almost 0. In the case of Np Ir2, the saturation is less clear bad fitting below Tn is attributed to second phase contamination. 

The last results we shall discuss concern antiferromagnetic UO2 (Tn = 30.5 K) which is a semiconductor, and for which precise data exist as well as for Th02 The spin wave low temperature predictions fit the experiment data at low temperature with reasonable agreement and an excess found in the temperature range 30 K - 120 K is attributed to the Jahn-Teller effect. The entropy change at the transition is within 9% of the Rln 3 value expected for the F5 triplet ground state. 

All the plastic phases listed in the table possess FCC structure crystal-plastic crystal transition temperature AS, entropy change at T, AS , entropy change at T , activation energy for molecular reorientation obtained from NMR spectroscopy. 

At higher temperatures the observed entropy change at the transition (AS=2.6 eu) at 1 atm is nearly equal to y Tc (Tc =150 K). Although the value of S should be somewhat less than that given by S=y T, because the specific heat is not necessarily linear, there can be no doubt that a major part of the entropy is electronic. 

Values of enthalpy and entropy change at isotropic-nematic transitions... 

Calcd. quantities <.r2>0lnl2 = 1.60 or 4.22a Entropy change at constant volume, (ASu)y... 

An important motivation for studying entropy changes at low temperature is to obtain reaction entropies AS (5.76) that could be combined with thermochemically measured reaction enthalpies A7/rxn to give the Gibbs free energy changes for chemical reactions. Starting from the observation that... 

Later in this text (Frame 13) we shall encounter the Gibbs energy of a reaction, A XG° which combines the effects of both enthalpy change, AXH° and the entropy change, ATS° (equation (13.10), Frame 13, see also section 13.2). 

Calculate the entropy change at the standard condition for the formation of 1 mole of water from H2 and 02 gases ... 

The entropy change at polymerization has the tendency to increase with growing complexity of monomer structure [19], The values of the heats of polymerization and of the entropy changes of some common monomers are summarized in Table 1. 

State the reaction occurring in the cell for the passage of one faraday, and evaluate the heat content, free energy and entropy changes at 25 . 

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