Solids positional entropy

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. 

Negative A liquid (moderate entropy) combines with a solid to form another solid. Positive One mole of high entropy gas forms where no gas was present before. Positive One mole of high entropy gas forms where no gas was present before. Uncertain Same number of moles of gaseous products as of gaseous reactants. Negative Two moles of gas (and a solid) combine to form just one mole of gas. 

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). 

The positional entropy has been calculated (Hirschfelder et al., 1937 Lennard-Jones and Devonshire, 1939) to be approximately 8-12 J / K mol for most organic molecules. This number results from a mathematical expression of the probability of finding the centers of a particular number of liquid molecules arranged as they are in the solid. 

Some of these categories of ions show distinctive structural and thermodynamic properties. The nonacidic metal cations and nonbasic anions are distinct from aU of the other categories, in that there is a positive entropy change accompanying their hydration as they dissolve from the solid state (Figure 2) they are known to physical chemists as electrostatic structure breakers because these large ions... 

At low temperatures, the intrinsic Arrhenius curves of the H- and the D-trans-fer, symbolized by the dashed lines, coincide with the observed ones, represented by the solid lines, as = k. However, at high temperature it was assumed that a non-reactive form of the molecule dominates because of its more positive entropy, leading to k y, = kK. Thus, both the observed rate constants and the observed preexponential factors are smaller than expected. 

Positional probability is also illustrated by changes of state. In general, positional entropy increases in going from solid to liquid to gas. A mole of a substance has a much smaller volume in the solid state than it does in the gaseous state. In the solid state, the molecules are close together, with relatively few positions available to them in the gaseous... 

Since a mole of gaseous COj has the greater volume by far, the molecules have many more available positions than in a mole of solid COj. Thus gaseous COj has the higher positional entropy. 

Some liquids may become glasslike rather than crystalline solids as the temperature is lowered. In this case, the molecules exhibit considerable randomness of arrangement and can be frozen in on further cooling so as to yield a positive entropy at 0°K. Both glycerol and ethanol can be cooled to yield positive entropies in this way. 

The amount of heat that is produced by a fuel cell operating reversibly is TAS. Reactions in fuel cells that have negative entropy change generate heat (such as hydrogen oxidation), while those with positive entropy change (such as direct solid carbon oxidation) may extract heat from their... 

Dense polymer systems, such as melts, glasses, and crosslinked networks or rubber are extremely complex materials. Besides the local chemical interactions and density correlations which are common to all disordered hquids and solids, the chain conformations also play an important role. Their influence is twofold. First the intrachain entropy dominates over the positional entropy of the center of mass of the chains. This leads to the well known effect that a weak effective repulsion between different types of chains is sufficient to drive phase segregation. The static and dynamic properties of mixtures of two types of chains is an important and challenging problem, which is reviewed by Binder in Chapter 7 of this volume. Here we consider dense melts of ehains of the same chemical composition. In this case the entropy is at its maximum when the chains have a random walk structure. Since the average end-to-end distance Nfor a random... 

Other ordering systems show striking discrepancies with the predictions of the quasi-chemical theories. Cu-Pt,67 Co-Pt,38 and Pb-Tl36 are binaries the solid solutions of which exhibit a positive partial excess free energy for one of their components, as well as positive excess entropies of solution. Co-Pt goes even further in deviating from theory in that it has a positive enthalpy of solution,... 

There are three different substituted benzene compounds with the formula C6H4F2. Assume that the benzene rings pack similarly into their crystal lattices. If the positions of the H and F atoms are statistically disordered in the solid state, which isomer will have the least residual molar entropy ... 

The disorder of a system typically increases when a solid dissolves (Fig. 8.24). Therefore, in most cases, we can expect the entropy of the system to increase when a solution forms. Because TAS is positive, this increase in disorder makes a negative contribution to AG. If AH is negative, we can be confident that AG is negative overall. Therefore, we can expect most substances with negative enthalpies of solution to be soluble. 

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