Entropy positional

Any change taking place which results in an increase in entropy has a positive entropy change (AS). Most spontaneous thermodynamic processes are accompanied by an increase in entropy. Entropy has units of Joules per degree K per mole. For representative values see table on p. 393. 

If the entropy of each element in some crystalline state be taken as zero at the absolute zero of temperature, every substance has a finite positive entropy, but at the absolute zero of temperature the entropy may become zero, and does so become in the case of perfect crystalline substances. 

STRATEGY We expect a positive entropy change because the thermal disorder in a system increases as the temperature is raised. We use Eq. 2, with the heat capacity at constant volume, Cv = nCV m. Find the amount (in moles) of gas molecules by using the ideal gas law, PV = nRT, and the initial conditions remember to express temperature in kelvins. Because the data are liters and kilopascals, use R expressed in those units. As always, avoid rounding errors by delaying the numerical calculation to the last possible stage. 

The third law of thermodynamics establishes a starting point for entropies. At 0 K, any pure perfect crystal is completely constrained and has S = 0 J / K. At any higher temperature, the substance has a positive entropy that depends on the conditions. The molar entropies of many pure substances have been measured at standard thermodynamic conditions, P ° = 1 bar. The same thermodynamic tables that list standard enthalpies of formation usually also list standard molar entropies, designated S °, fbr T — 298 K. Table 14-2 lists representative values of S to give you an idea of the magnitudes of absolute entropies. Appendix D contains a more extensive list. 

The decomposition of N2 O4 requires a bond to break. This is the reason why the decomposition has a positive A 77 °. At the same time, the number of molecules doubles during decomposition, which is the reason AS° has a positive value. The positive enthalpy change means that energy Is removed from the surroundings and constrained, whereas the positive entropy change means that matter is dispersed. At temperatures below 315 K, the enthalpy term dominates and decomposition is not spontaneous, but at temperatures above 315 K, the entropy term dominates and decomposition is spontaneous. 

More recently, a number of reports dealing with 1,3-sulfonyl shifts which proceed by other mechanisms have been published. For example, Baechler and coworkers suggested that the higher activation enthalpy observed for the isomerization of the deuterium labeled methallyl sulfone 72 in nitrobenzene at 150°C as compared to the corresponding sulfide, together with the positive entropy of activation may be taken as evidence for a homolytic dissociation mechanism (equation 44). A similar mechanism has also been suggested by Little and coworkers for the gas-phase thermal rearrangement of deuterium labelled allyl sec-butyl sulfone, which precedes its pyrolysis to alkene and sulfur dioxide. 

Solid ammonium nitrate is an orderly, crystalline substance, a state considerably less random than a solution of ions in water. In this case, the positive entropy change outweighs the enthalpy change. That is TAS > AH. The Gibbs free energy change is negative, so the process will proceed spontaneously. 

The Gibbs energy of mixing of an ideal solution is negative due to the positive entropy of mixing obtained by differentiation of Ald.xGm with respect to temperature ... 

Thermodynamic analysis of the binding constants of BSA and procyanidin dimer and trimer from the Van t Hoff equation (29) indicates a reaction with a positive entropy change, a positive... 

Note that Eq. (6) includes thermodynamic equilibrium (v° = 0) as a special case. However, usually the steady-state condition refers to a stationary nonequilibrium state, with nonzero net flux and positive entropy production. We emphasize the distinction between network stoichiometry and reaction kinetics that is implicit in Eqs. (5) and (6). While kinetic rate functions and the associated parameter values are often not accessible, the stoichiometric matrix is usually (and excluding evolutionary time scales) an invariant property of metabolic reaction networks, that is, its entries are independent of temperature, pH values, and other physiological conditions. 

Free energy variations with temperature can also be used to estimate reaction enthalpies. However, few studies devoted to the temperature dependence of adsorption phenomena have been published. In one such study of potassium octyl hydroxamate adsorption on barite, calcite and bastnaesite, it was observed that adsorption increased markedly with temperature, which suggested the enthalpies were endothermic (26). The resulting large positive entropies were attributed to loosening of ordered water structure, both at the mineral surface and in the solvent surrounding octyl hydroxamate ions during the adsorption process, as well as hydrophobic chain association effects. 

As noted in table 11.1, the ability of THFTCA to separate LJO from trivalent lanthanide ions is mainly of enthalpic origin. Reaction 11.33 has a considerably more unfavorable enthalpic contribution than reaction 11.32. The complexation is, however, predominantly entropy driven because the T ArS° term dominates the ArH° contribution for all systems. The large positive entropy changes observed for reactions 11.32 and 11.33 result from the release of water molecules coordinated to the metal on complexation with the tridentate THFTCA2- ligand. Note that a negative entropy contribution would be expected if these reactions were truly 2 particle = 1 particle reactions [226]. 

A change in mechanism between two semiclassical pathways, one with a larger enthalpy of activation and more positive entropy of activation that dominates at higher temperatures and the other with a smaller enthalpy of activation and more negative entropy of activation that dominates at low temperatures. 

In order to account for the large positive entropy of activation for the reaction, it is necessary to assume that there is virtually free rotation of the incipient ethylene molecules in the complex. The second possible transition complex involves the complete rupture of one carbon-carbon bond to give the tetramethylene biradical, and the reaction path may be envisaged as shown below ... 

A reversible adiabatic expansion of an ideal gas has a zero entropy change, and an irreversible adiabatic expansion of the same gas from the same initial state to the same final volume has a positive entropy change. This statement may seem to be inconsistent with the statement that 5 is a thermodynamic property. The resolution of the discrepancy is that the two changes do not constitute the same change of state the final temperature of the reversible adiabatic expansion is lower than the final temperature of the irreversible adiabatic expansion (as in path 2 in Fig. 6.7). 

Equation (11.4) provides a convenient value for that constant. Planck s statement asserts that 5qk is zero only for pure solids and pure liquids, whereas Nernst assumed that his theorem was applicable to all condensed phases, including solutions. According to Planck, solutions at 0 K have a positive entropy equal to the entropy of mixing. (The entropy of mixing is discussed in Chapters 10 and 14). 

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