Reactions entropy change

It is difficult to discuss the accuracy of the thermochemical results reported by Oldani and Bor, because they rely on some estimated data of unknown reliability. Based on a simple model that is used to predict reaction entropy changes, we anticipate that the entropy of reaction 14.21 would be considerably larger than 300 J K-1 mol-1, possibly even higher than 400 J K-1 mol-1 [226]. 

Here AH is the standard enthalpy change of reaction AS the standard reaction entropy change R the gas constant T the temperature /(eq the equilibrium constant for the reaction, given simply by the product of concentrations (activities in reality) of all the products to the power of their stoichiometric coefficients over the same product for reactants m the number of products / / the forward rate constant kr the reverse rate constant n, the stoichiometric coefficient of species i and 1 the number of reactants. A AG value below zero indicates a reaction with an equilibrium point where there is an excess of products over reactants, a... 

Based on careful work on Fe(III)(C204)3 reduction, Sluyters considers that the potential dependence of a, observed with certain electrode processes, really arises from kinetic complications and that the transfer coefficient for the elementary step of charge transfer is constant at —0.5. However, the work of Hupp and Weaver on the Cr(OH2)6 system demonstrated a relation between the temperature and potential dependence of the rates, and showed that at overpotentials of ca. 0.7 — 0.9 V the potential dependence of rate arises extensively from the entropic factor (p. 133). It was also shown that the Marcus theory was able to predict a potential dependence of A5" " comparable to or > that of A// when the system has a large entropic asymmetry, i.e., a large net reaction entropy change. 

In any practical electrochemical experiment the absolute, but unknown, metal/solution p.d. at the reference electrode must normally vary with temperature on account of the single interface reaction entropy change. This leads to the now well-known situation that measurements of or io as a function of temperature can never give the true or real heat of activation for the electrode process. This was first pointed out by Temkin who showed that... 

It is curious that the striking deviations of electrochemical kinetic behavior from that expected conventionally, which are the subject of this review, have not been recognized or treated in the recent quantum-mechanical approaches, e.g., of Levich et al (e.g., see Refs. 66 and 105) to the interpretation of electrode reaction rates. The reasons for this may be traced to the emphasis which is placed in such treatments on (1) quantal effects in the energy of the system and (2) continuum modeling of the solution with consequent neglect of the specific solvational- and solvent-structure aspects that can lead, in aqueous media, to the important entropic factor in the kinetics and in other interactions in water solutions. However, the work of Hupp and Weaver, referred to on p. 153, showed that the results could be interpreted in terms of Marcus theory, with regard to potential dependence of AS, when there was a substantial net reaction entropy change in the process. 

The Standard Entropy of Reaction Entropy Changes in the Surroundings Entropy Change and the Equilbrium State Spontaneous Exothermic and Endothermic Reactbns... 

Chemical Reactions Entropy Changes and Free Energy... 

For most substances, the values of standard entropies are not available for a wide range of temperatures. Most commonly, tables present only data at 25°C. For most purposes, it is sufQcient to use the standard entropies at 25°C to calculate reaction entropy changes at other temperatures because A5 rxr does not generally depend highly on temperature. If accurate work is needed, however, or if the temperature of interest is well removed from the temperature for which data are available, it is necessary to correct the tabulated values for the change in temperature. To do this, we can use a procedure analogous to that outlined in Section 7.7 for the calculation of AT/j n at alternate temperatures. 

Equation 8.24 describes the temperature dependence of the reaction entropy change and is analogous to Kirchhoff s law for the temperature dependence of the reaction enthalpy change (Equation 7.49). 

Whatever the cause of the anomalous behavior in the C- B- A transformation as temperature is increased, the A (B or C) H- X appears to obey all the rules. In this case there is an overall symmetry increase and the density decreases. The structural details of the H and X phases are not fully elucidated. It has been observed (Traverse, 1971) that the da ratio decreases sharply as does the density as the A-form transforms to H. There is a sharp increase in both a and c but a increases more rapidly, reducing the ratio. Since the space group of H is unknown, one cannot say what changes in symmetry occur when it is formed from A but there is clearly an increase when the hexagonal H decomposes to cubic X. As with other high temperature reactions entropy changes are likely to be of utmost importance. One final observation on fig. 27.2-the region of stability of each polymorph narrows at some point as the radius of the rare earth atom decreases until finally lutecium (and scandium) transforms directly from C-type to the melt. 

B2.4.2). The slope of the line gives AH, and the intercept at 1/J= 0 is related to A imimolecular reaction, such as many cases of exchange, might be expected to have a very small entropy change on gomg to the transition state. However, several systems have shown significant entropy contributions—entropy can make up more than 10% of the barrier. It is therefore important to measure the rates over as wide a range of temperatures as possible to obtain reliable thennodynamic data on the transition state. 

Steinberg, I. Z., Scheraga, H. A. Entropy changes accompanying association reactions of proteins. J. Biol. Chem. 238 (1963)172-181. 

Here we have the formation of the activated complex from five molecules of nitric acid, previously free, with a high negative entropy change. The concentration of molecular aggregates needed might increase with a fall in temperature in agreement with the characteristics of the reaction already described. It should be noticed that nitration in nitromethane shows the more common type of temperature-dependence (fig. 3.1). 

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. 

The thermodynamic properties of the solid silicates show the expected entropy change of formation from the constituent oxides of nearly zero, which is typical of the reaction type... 

The small value of the entropy change reflects the fact that only liquids are involved in tlris reaction. The heat balance in canying out tlris reaction may be calculted, according to Hess s law, by calculating tire heat change at room temperarnre, and subtracting tire heat required to raise the products to the hnal teirrperamre. The data for tlris reaction are as follows ... 

It can be shown - p- that if an LFER is observed over a range of temperatures, and if the enthalpy and entropy changes are temperature independent, then the enthalpy changes must be directly proportional to the entropy changes for the reaction series. Let us start with the proposition that a real effect of this type has been demonstrated for a reaction series we write this as... 

An important question for chemists, and particularly for biochemists, is, Will the reaction proceed in the direction written J. Willard Gibbs, one of the founders of thermodynamics, realized that the answer to this question lay in a comparison of the enthalpy change and the entropy change for a reaction at a given temperature. The Gibbs free energy, G, is defined as... 

Alberty, R. A., 1969. Standard Gibb.s free energy, enthalpy, and entropy change.s a.s a function of pH and pMg for reaction.s involving adeno.sine pho.sphate.s. of Biological Chemistry 244 3290-3302. 

The ease of dissociation of the X2 molecules follows closely the values of the enthalpy of dissociation since the entropy change for the reaction is almost independent of X. Thus F2 at 1 atm pressure is 1% dissociated into atoms at 765°C but a temperature of 975°C is required to achieve the same degree of dissociation for CI2 thereafter, the required temperature drops to 775°C for Br2 and 575°C for I2 (see also next section for atomic halogens). 

Hammett originally demonstrated that the sigma-rho relation might be expected to hold if entropies of activation (or entropy changes) were constant in a series. It has since been shown that a sufficient condition is a linear relation between enthalpies and entropies of activation (or reaction), and such hnear relations are frequently encountered. Although the existence of such linear relations has always appeared somewhat mysterious, some rationale for this relationship has recently been given. 

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