Entropy relationship with standard

The formation of ReFg IrFg as an intermediate in (5) means that AG (8) 0. An estimate of the entropy change for equation (8) has been made. It has been found that the standard entropies 8293 of closely packed solids are in approximately linear relationship with their formula unit volumes. The empirical relationship is... 

This relationship between entropy and enthalpy has been reported many times in the literature. An example of a graph relating (AH°) to (AS°), produced by Martire and his group [8], is shown in Figure 9. From a theoretical point of view, this relationship between standard enthalpy and standard entropy is to be expected. An increase in enthalpy indicates that more energy is used up in the association of the solute molecule with the molecules of the stationary phase. This means that the... 

The result indicates that the standard entropy value, S°, at 298.15 K is proportional to the heat absorbed by that solid to get it from 0 to 298.15 K with the proportionality constant 0.00671 K . The heat that is absorbed by the solid in this process is dispersed through the various energy levels of the solid. The simple relationship clearly shows that the greater the amount of heat (energy) that is absorbed when one mole of the solid is heated from 0 to 298.15 K, the greater its standard molar entropy. Thus, the standard molar entropy of a solid is a direct measure of the amount of energy stored in the solid. 

Finally, it is perfectly possible to choose a standard state for the surface phase. De Boer [14] makes a plea for taking that value of such that the average distance apart of the molecules is the same as in the gas phase at STP. This is a hypothetical standard state in that for an ideal two-dimensional gas with this molecular separation would be 0.338 dyn/cm at 0°C. The standard molecular area is then 4.08 x 10 T. The main advantage of this choice is that it simplifies the relationship between translational entropies of the two- and the three-dimensional standard states. 

The amount of heat released during a reaction is proportional to the amount of substance involved but the relationship is complicated in enzyme studies by secondary reactions. Although the use of entropy constants means that calorimetry theoretically does not require standardization, in many instances this will be necessary. The initial energy change can often be enhanced, giving an increase in the sensitivity of the method. Hydrogen ions released during a reaction, for instance, will protonate a buffer with an evolution of more heat. 

Boyer et al. [20] have measured the heat capacity of crystalline adenine, a compound of biologic importance, with high precision, from about 7 K to over 300 K, and calculated the standard entropy of adenine. Table 11.8 contains a sampling of their data over the range from 7.404 K to 298.15 K. Use those data to calculate the standard entropy of adenine at 298.15 K, which assume the Debye relationship for Cp. The value for 298.15 K is calculated by the authors from a function fitted to the original data. 

Electromotive force measurements of the cell Pt, H2 HBr(m), X% alcohol, Y% water AgBr-Ag were made at 25°, 35°, and 45°C in the following solvent systems (1) water, (2) water-ethanol (30%, 60%, 90%, 99% ethanol), (3) anhydrous ethanol, (4) water-tert-butanol (30%, 60%, 91% and 99% tert-butanol), and (5) anhydrous tert-butanol. Calculations of standard cell potential were made using the Debye-Huckel theory as extended by Gronwall, LaMer, and Sandved. Gibbs free energy, enthalpy, entropy changes, and mean ionic activity coefficients were calculated for each solvent mixture and temperature. Relationships of the stand-ard potentials and thermodynamic functons with respect to solvent compositions in the two mixed-solvent systems and the pure solvents were discussed. 

Bakeeva, Pashinkin, Bakeev, and Buketov [73BAK/PAS] measured the selenium dioxide pressure over gold selenite in the interval 489 to 599 K by the dew point method. The pressure was calculated from the dew point temperature by the relationship for the saturated vapour pressure in [69SON/NOV]. The data in the deposited VlNITl document (No. 4959-72) have been recalculated with the relationship selected by the review. The enthalpy and entropy changes obtained from the temperature variation of the equilibrium constant are A //° ((V.123), 544 K) = (576.8 13.0) kJ-mol and A,S° ((V.123), 544 K) = (899.4 + 24.0) J-K -mor. The uncertainties are entered here as twice the standard deviations from the least-squares calculation. 

Berman6 has summarized the procedure that is followed in making the calculations to obtain the equilibrium transition line, starting with equation (15.15). The effects of temperature on the standard enthalpy (AH°) and entropy (AS0) are obtained from the relationships -... 

Linear enthalpy-entropy compensation is well known to physical organic chemists and has been the subject of controversy since the relationship was first discovered experimentally. We have discussed the complications elsewhere and will only note here that the linearity found by Beetlestone et al. is statistically reliable for most of their examples. The most extensively studied set of small-solute compensation processes in water are the ionizations of weak acids. When acids such as acetic acid or benzoic acid are substituted in their nonpolar parts to form homologous series, the standard enthalpies and entropies of ionization are found to demonstrate compensation behavior with 7], values in the 280-290°K range but only after extraction of all the contributions to these quantities from the electronic rearrangements using methods developed by Hepler and Ives and their coworkers. The obvious conclusion is that this behavior in small-solute processes is due to solvation effects and thus a manifestation of some property of water. As a result of the comparison of their data with these small-solute examples, Beetlestone et al. suggested that bulk water also plays an important role in the protein processes they studied. 

In these equations, the referenee states of H tq) are, by convention, equal to zero as are the functions AHf e[g ) and AG ( ( ,). The absolute entropies for the gaseous ions are calculated from statistical mechanics (Bratsch and Lagowski 1985a) and agree fairly well with the experimental values reported by Bertha and Choppin (1969), who interpreted the S-shaped dependence of standard state entropies on ionic radius in terms of a change in the overall hydration of the cation across the lanthanide series. Hinchey and Cobble (1970) proposed that this S-shaped relationship was an artifact of the method of data treatment and calculated a set of entropies from lanthanide... 

SECTIONS 19.6 AND 19.7 The values of AH and AS generally do not vary much with temperature. Therefore, the dependence of AG with temperature is governed mainly by the value of T in the expression AG = AH — TAS. The entropy term —TAS has the greater effect on the temperature dependence of AG and, hence, on the spontaneity of the process. For example, a process for which AH > 0 and As > 0, such as the melting of ice, can be nonspontaneous (AG > 0) at low temperatures and spontaneous (AG < 0) at higher temperatures. Under nonstandard conditions AG is related to AG° and the value of the reaction quotient, Q AG = AG" + RT In Q. At equilibrium (AG = 0, Q = K), AG = —RT InkT. Thus, the standard free-energy change is directly related to the equilibrium constant for the reaction. This relationship expresses the temperature dependence of equilibrium constants. 

The equation AG" = AfP - TAS° provides a relationship between free energy, enthalpy, and entropy. If we can obtain values for any two of these variables (in this case the entropy and free energy changes) for a given reaction, we can calculate the third. So if we calculate AS" for the formation reaction of the substance in question, we can use that value along with the known value of AG° to find AH°. (We would use the standard temperature of 298 K)... 

Because it applies mostly to electrolytes, it is discussed in Chapter 15. Briefly, Helgeson models the behavior of solutes by developing equations for the standard state partial molar volume (Helgeson and Kirkham 1976) and standard state partial molar heat capacity (Helgeson et al. 1981) as a function of P and T, with adjustable constants such that they can be applied to a wide variety of solutes. If you know these quantities (V°, C°p), you can calculate the variation of the standard state Gibbs energy, and that leads through fundamental relationships to equilibrium constants, enthalpies, and entropies. 

---