Reaction entropi

The reversible reaction heat of the cell is defined as the reaction entropy multiplied by the temperature [Eq. (15)]. For an electrochemical cell it is also called the Peltier effect and can be described as the difference between the reaction enthalpy AH and the reaction free energy AG. If the difference between the reaction free energy AG and the reaction enthalpy AH is below zero, the cell becomes warmer. On the other hand, for a difference larger than zero, it cools down. The reversible heat W of the electrochemical cell is therefore ... 

The calculation of the reaction free energy is possible with Eq. (34) and the determination of the reaction entropy AS follows from Eq. (33). 

Of course, even in the case of acyclic alkenes reaction enthalpy is not exactly zero, and therefore the product distribution is never completely statistically determined. Table V gives equilibrium data for the metathesis of some lower alkenes, where deviations of the reaction enthalpy from zero are relatively large. In this table the ratio of the contributions of the reaction enthalpy and the reaction entropy to the free enthalpy of the reaction, expressed as AHr/TASr, is given together with the equilibrium distribution. It can be seen that for the metathesis of the lower linear alkenes the equilibrium distribution is determined predominantly by the reaction entropy, whereas in the case of the lower branched alkenes the reaction enthalpy dominates. If the reaction enthalpy deviates substantially from zero, the influence of the temperature on the equilibrium distribution will be considerable, since the high temperature limit will always be a 2 1 1 distribution. Typical examples of the influence of the temperature are given in Tables VI and VII. 

If it is assumed that penultimate unit effects on the reaction entropy are insignificant, the terms in eqs. 18 and 19 corresponding to the stabilization energy of the reactant propagating radical will cancel and rVli=ryly There should be no explicit penultimate unit effect on copolymer composition. On the other hand, the radical reactivity ratio j (eq. 20) compares two different propagating radicals so... 

The reaction enthalpy and reaction entropy were derived from the curves comparing with data for the all-or-none model140 using the computer program of Rosenbrock139 (Table 6). 

To calculate the change in entropy that accompanies a reaction, we need to know the molar entropies of all the substances taking part then we calculate the difference between the entropies of the products and those of the reactants. More specifically, the standard reaction entropy, AS°, is the difference between the standard molar entropies of the products and those of the reactants, taking into account their stoichiometric coefficients ... 

The standard reaction entropy is the difference between the standard molar entropy of the products and that of the reactants weighted by the amounts of each species taking part in the reaction. It is positive (an increase in entropy) if there is a net production of gas in a reaction it is negative (a decrease) if there is a net consumption of gas. 

STRATEGY We write the chemical equation for the formation of HI(g) and calculate the standard Gibbs free energy of reaction from AG° = AH° — TAS°. It is best to write the equation with a stoichiometric coefficient of 1 for the compound of interest, because then AG° = AGf°. The standard enthalpy of formation is found in Appendix 2A. The standard reaction entropy is found as shown in Example 7.9, by using the data from Table 7.3 or Appendix 2A. 

For an exothermic reaction (AH0 < 0) with a negative reaction entropy (AS° < 0), — TAS° contributes a positive term to AG°. For such a reaction, AG° is negative (and the pure reactants are poised to form products spontaneously) at low temperatures because AH° dominates — TAS°, but it may become positive (and the reverse reaction, the decomposition of pure products, spontaneous) at higher temperatures when —TAS° dominates AH° (Fig. 7.28a). 

For an endothermic reaction (AH° > 0) with a positive reaction entropy (AS° > 0 ), the reverse is true (Fig. 7.28b). In this case, AG° is positive at low temperatures but may become negative when the temperature is raised to the point that TAS° becomes larger than AH°. The formation of products from pure reactants becomes spontaneous when the temperature is high enough. 

FIGURE 7.28 The effect of an increase in temperature on the spontaneity of a reaction under standard conditions. In each case, "spontaneous" is taken to mean AC0 < 0 and "nonspontaneous" is taken to mean AC° > 0. (a) An exothermic reaction with negative reaction entropy becomes spontaneous below the temperature marked by the dotted line, (b) An endothermic reaction with a positive reaction entropy becomes spontaneous above the temperature marked by the dotted line, (c) An endothermic reaction with negative reaction entropy is not spontaneous at any temperature, (d) An exothermic reaction with positive reaction entropy is spontaneous at all temperatures. 

Calculate the standard reaction entropy from standard molar entropies (Example 7.9). 

Use data in Table 7.3 or Appendix 2A to calculate the standard reaction entropy for each of the following reactions at 25°C. For each reaction, interpret the sign and magnitude of the reaction entropy, (a) The formation of... 

Calculate the standard reaction entropy, enthalpy, and Gibbs free energy for each of the following reactions from data found in Appendix 2A ... 

It is usually reasonable to assume that AHr° and A.S r° are both approximately independent of temperature over the range of temperatures of interest. When we make that approximation, the reaction entropies cancel, and we are left with... 

For many reactions entropy effects are small and it is the enthalpy that mainly determines whether the reaction can take place spontaneously. However, in certain... 

In equilibrium measurements, there is the possibility of determining the reaction enthalpy AH directly from calorimetry and of combining it with logK (i.e., AG°) to get the reaction entropy, AS . This case, advantageous and simple from the statistical point of view, was only mentioned in a previous paper (149). Since that time, this experimental approach has been widely used (59, 62-65, 74-78, 134, 137, 138, 210, 211) hence, a somewhat more detailed mathematical treatment seems appropriate. 

The use of direct electrochemical methods (cyclic voltammetry Pig. 17) has enabled us to measure the thermodynamic parameters of isolated water-soluble fragments of the Rieske proteins of various bci complexes (Table XII)). (55, 92). The values determined for the standard reaction entropy, AS°, for both the mitochondrial and the bacterial Rieske fragments are similar to values obtained for water-soluble cytochromes they are more negative than values measured for other electron transfer proteins (93). Large negative values of AS° have been correlated with a less exposed metal site (93). However, this is opposite to what is observed in Rieske proteins, since the cluster appears to be less exposed in Rieske-type ferredoxins that show less negative values of AS° (see Section V,B). 

The evaporation of B is causing a significant increase in the reaction entropy. As we stated before is this necessary to reach a high energy density within the storage. 

A high reaction entropy increase influences the reaction temperature of the thermochemical dissociation equilibrium. Assuming that the reaction enthalpy and the reaction entropy have no significant temperature dependence, this simplified equation can be derived. 

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