Negative entropy

Conversely, it s also possible for a process to be favored by enthalpy (exothermic, negative AH) yet be nonspontaneous, because it is strongly disfavored by entropy (negative AS). The conversion of liquid water to ice is nonspontaneous above 0°C, for example, because the process is disfavored by entropy [AS° = -22.0 J/(K mol)] even though it is favored by enthalpy (AH° = -6.01 kj/mol). 

One remarkable feature shown in this figure is that not only is the excess entropy negative, but also... 

The thermodynamic parameter AS for a chemical reaction is not easily measured. Even if it were easily determined, its value depends on changes that occur not only in the system under study but also in the surroundings (see Chapter 1, Section 1.3.3). Intrinsically unfavorable reactions (AG° > 0) can take place if a change in the surroundings compensates for a decrease in the entropy (negative AS) of the reaction. 

The standard reaction enthalpies are positive, the standard reaction entropies negative the amount of monochloride increases with increasing temperature and decreasing pressure. For a given temperature and pressure the equilibrium shifts to the right as the group is descended from boron to indium. 

The maximum entropy method appfoach to resolution enhancement treats the signal and the noise as separate entities [101]. This method sets out to minimize random errors and noise on the basis of two criteria. First, an assumption is made about the shapes of the peaks present. Secondly, the best fit with respect to noise is obtained by maximizing the configurational entropy (negative information content), 5, by using the equation... 

A general prerequisite for the existence of a stable interface between two phases is that the free energy of formation of the interface be positive were it negative or zero, fluctuations would lead to complete dispersion of one phase in another. As implied, thermodynamics constitutes an important discipline within the general subject. It is one in which surface area joins the usual extensive quantities of mass and volume and in which surface tension and surface composition join the usual intensive quantities of pressure, temperature, and bulk composition. The thermodynamic functions of free energy, enthalpy and entropy can be defined for an interface as well as for a bulk portion of matter. Chapters II and ni are based on a rich history of thermodynamic studies of the liquid interface. The phase behavior of liquid films enters in Chapter IV, and the electrical potential and charge are added as thermodynamic variables in Chapter V. 

Wlien H has reached its minimum value this is the well known Maxwell-Boltzmaim distribution for a gas in themial equilibrium with a unifomi motion u. So, argues Boltzmaim, solutions of his equation for an isolated system approach an equilibrium state, just as real gases seem to do. Up to a negative factor (-/fg, in fact), differences in H are the same as differences in the themiodynamic entropy between initial and final equilibrium states. Boltzmaim thought that his //-tiieorem gave a foundation of the increase in entropy as a result of the collision integral, whose derivation was based on the Stosszahlansatz. 

Lewis acid and the ligand. By contrast, soft-soft interactions are mainly enthalpic in origin and are characterised by a negative change in entropy" ... 

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). 

In Fig. 5.21, from Dawson s paper, the uptake at X for the 250°C-outgassed sample is dose to the calculated value for a monolayer of water with a (H20) = 101 A. Point X has therefore been ascribed to a close-packed monolayer of water on a hydroxylated surface of rutile. The fact that the differential entropy of adsorption relative to the liquid state (calculated from the isosteric heat of adsorption) changes sharply from negative to positive values in this region with A s 0 at X was regarded as supporting evidence. ... 

The sign of AG can be used to predict the direction in which a reaction moves to reach its equilibrium position. A reaction is always thermodynamically favored when enthalpy decreases and entropy increases. Substituting the inequalities AH < 0 and AS > 0 into equation 6.2 shows that AG is negative when a reaction is thermodynamically favored. When AG is positive, the reaction is unfavorable as written (although the reverse reaction is favorable). Systems at equilibrium have a AG of zero. 

Since the 0 s are fractions, the logarithms in Eq. (8.38) are less than unity and AGj is negative for all concentrations. In the case of athermal mixtures entropy considerations alone are sufficient to account for polymer-solvent miscibility at all concentrations. Exactly the same is true for ideal solutions. As a matter of fact, it is possible to regard the expressions for AS and AGj for ideal solutions as special cases of Eqs. (8.37) and (8.38) for the situation where n happens to equal unity. The following example compares values for ASj for ideal and Flory-Huggins solutions to examine quantitatively the effect of variations in n on the entropy of mixing. 

Obviously, B can never be negative in these cases to the extent that equation 5 is vaUd, miscibility can only be driven by combinatorial entropy, and this possibihty is maximized by matching the values of 5 and 5g as nearly as possible. In general, high molecular weight, nonpolar polymers are rarely miscible with each other. 

The chemical potential, plays a vital role in both phase and chemical reaction equiUbria. However, the chemical potential exhibits certain unfortunate characteristics which discourage its use in the solution of practical problems. The Gibbs energy, and hence is defined in relation to the internal energy and entropy, both primitive quantities for which absolute values are unknown. Moreover, p approaches negative infinity when either P or x approaches 2ero. While these characteristics do not preclude the use of chemical potentials, the appHcation of equiUbrium criteria is faciUtated by the introduction of a new quantity to take the place of p but which does not exhibit its less desirable characteristics. 

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