The Sign of Entropy

Although the recognition by Clausius and others that the quantity / Dq/T was uniquely important was an all-important step in the development of thermodynamics, it is a pity, in retrospect, that it was used to define a state variable in the sense of equation (5.2). That is, if equation (5.2) were 

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IB (a) The outcome is uncertain in the reaction between ZnS(s) and Ag20(s). We have used A gas to estimate the sign of entropy change. There is no gas involved in this reaction and thus our prediction is uncertain. 

Lin and Yang (1987) also calculated the thermodynamic parameters of diazepam for micellar solubilization in Pluronic surfactant solutions at different temperatures (Table 13.4). For all systems, AG was negative, indicating micellar solubilization was spontaneous. The sign of entropy has been associated with the location of solubilized molecules within the micelles. Positive values have been observed for molecules embedded in the micelle center and negative values for adsorption of the molecules on the micelle surface. The results in this paper indicate that in the F-108 and F-88 Pluronics, diazepam molecules can penetrate into the micelle interior, whereas for F-68 and lower concentrations of F-88, diazepam is adsorbed on the micelle surface without penetration into the micellar core. 

Figure 12.2. Stability at far from equilibrium. Due to the two terms, deSand d,S, the second law does not impose the sign of entropy variation dS= d,S+ deS. Therefore, there is no universal Lyapunov function, which creates ambiguity in the stability of states far...

Always check the signs of entropy values. Standard entropies are almost always positive, while standard entropies of formation are positive and negative. 

Strategy We are asked to predict, not calculate, the sign of entropy change in the reactions. The factors that lead to an increase in entropy are (1) a transition from a condensed phase to the vapor phase and (2) a reaction that produces more product molecules than reactant molecules in the same phase. It is also important to compare the relative complexity of the product and reactant molecules. In general, the more complex the molecular structure, the greater the entropy of the compound. 

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. 

Cycloheptatrienes are in many cases in rapid equilibrium with an isomeric bicy-clo[4.1.0]heptadiene. The thermodynamics of the valence isomerism has been studied in a number of instances, and some of the data are given below. Calculate the equilibrium constant for each case at 25°C. Calculate the temperature at which K= for each system. Are the signs of the enthalpy and entropy as you would expect them to be Can you discern any pattern of substituent effects from the data ... 

Table III presents integral excess entropies of formation for some solid and liquid solutions obtained by means of equilibrium techniques. Except for the alloys marked by a letter b, the excess entropy can be taken as a measure of the effect of the change of the vibrational spectrum in the formation of the solution. The entropy change associated with the electrons, although a real effect as shown by Rayne s54 measurements of the electronic specific heat of a-brasses, is too small to be of importance in these numbers. Attention is directed to the very appreciable magnitude of the vibrational entropy contribution in many of these alloys, and to the fact that whether the alloy is solid or liquid is not of primary importance. It is difficult to relate even the sign of the excess entropy to the properties of the individual constituents.

Self-Test 7.12A Without doing any calculations, estimate the sign of the entropy change for the reaction N2(g) + 3 H2(g) - 2 NH,(g) and explain your answer. 

Show that, if two copper blocks with different temperatures are placed in contact, then the direction of spontaneous change is toward the equalization of temperatures. Do so by considering the transfer of 1 J of energy as heat from one to the other and assessing the sign of the entropy change. Assume that the temperatures of the blocks remain constant. 

Entropy of mixing is usually (though not always) positive, hence the sign of AG is generally determined by the size and magnitude of AH. For nonpolar molecules, AH is found to be positive and closely similar to the enthalpy of mixing of small molecules. In such a case, the enthalpy of mixing per unit volume can be approximated to ... 

When calculating entropy changes, be careful about the sign of q, use the appropriate temperatures, and sum the changes for system and surroundings. 

C14-0064. Without doing calculations or looking up absolute entropy values, determine the sign of A S ° for the following processes ... 

Once the total entropy of a composite system has been formulated as a function of the various extensive parameters of the subsystems, the extrema of this total entropy function may in principle be located by direct differentiation and classified as either maxima, minima or inflection points from the sign of the second derivative. Of these extrema, only the maxima represent stable equilibria. 

We start by introducing the concept of entropy S to explain why some reactions occur spontaneously, without needing additional energy, yet others do not. The sign of A 5 for a thermodynamic universe must be positive for spontaneity. We explore the temperature dependence of A5. 

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