Entropy decrease

The second law reqmres that the entropy of an isolated system either increase or, in the limit, where the system has reached an equilibrium state, remain constant. For a closed (but not isolated) system it requires that any entropy decrease in either the system or its surroundings be more than compensated by an entropy increase in the other part or that in the Emit, where the process is reversible, the total entropy of the system plus its surroundings be constant. 

To melt ice we have to put heat into the system. This increases the system entropy via eqn. (5.20). Physically, entropy represents disorder and eqn. (5.20) tells us that water is more disordered than ice. We would expect this anyway because the atoms in a liquid are arranged much more chaotically than they are in a crystalline solid. When water freezes, of course, heat leaves the system and the entropy decreases. 

For reven sible systems, evolution almost always leads to an increase in entropy. The evolution of irreversible systems, one the other hand, typically results in a decrease in entropy. Figures 3.26 and 3.27 show the time evolution of the average entropy for elementary rules R32 (class cl) and R122 (class c3) for an ensemble of size = 10 CA starting with an equiprobable ensemble. We see that the entropy decreases with time in both cases, reaching a steady-state value after a transient period. This dc crease is a direct reflection of the irreversibility of the given rules,... 

Numerical simulations of the k = oo case reveal a sharp phase transition at Ac = 0.27 [wootters]. Simulations also suggest that the spread in values of entropy decreases with increasing k, and that the width of the transition region probably goes as k f [woot90]. 

The entropy decreases, as expected for a sample that has been compressed into a smaller volume at constant temperature. 

In a reaction in which the number of product molecules is equal to the number of reactant molecules, (e.g., A + B —> C + D), entropy effects are usually small, but if the number of molecules is increased (e.g., A —> B + C), there is a large gain in entropy because more arrangements in space are possible when more molecules are present. Reactions in which a molecule is cleaved into two or more parts are therefore thermodynamically favored by the entropy factor. Conversely, reactions in which the number of product molecules is less than the number of reactant molecules show entropy decreases, and in such cases there must be a sizable decrease in enthalpy to overcome the unfavorable entropy change. 

The problem asks for the total entropy change, which includes A S for the water and A S for the freezer compartment. When water freezes, heat flows from the water to its surroundings, the freezer compartment (see Eigure 14-61. Thus, q is negative for the water, whose entropy decreases. At the same time, q is positive for the freezer compartment, whose entropy increases. 

For the purpose of illustrating the application of the thermodynamic equation of state to experimental data, consider the plot given in Fig. 84 for the retractive force, measured at fixed length, against the absolute temperature for a hypothetical elastic substance. The slope at any temperature T gives the important quantity —(dS/dL)T,p according to Eq. (12) an increase in / with T at constant L shows immediately, therefore, that the entropy decreases with increase in length... 

The number of moles decreases from 1.5 mol of gas to 1 mol. Assuming equivalent entropies per mole, the entropy decreases. AS will be negative, so we do not expect a spontaneous process. 

Entropy decreases when reacting ions are of opposite sign, while it increases when reacting ions are of same sign. Explain ... 

The entropy factor should also be considered since cyclization results in a more ordered structure. The C5 cyclization of n-hexane involves an entropy decrease of about 15-17 entropy units (e.u.). The corresponding values for cyclohexane and benzene formation are about 25 and 38-45 e.u., respectively. These values are comparable with calculated values of adsorption entropy (29). Thus, adsorption of a molecule to be cyclized may supply a considerable part of the entropy change in other words, adsorption should take place in a geometry favorable for cyclization. This is one of the main roles of the catalyst. 

In Table XI, rate constants for a number of prototype metathesis reactions are presented. As is evident from this table, atom metatheses are characterized by A factors of the order 10 ° cm /s-mol. This A value corresponds to an entropy decrease ( — AS ) of about 20-30 cal/mol-K associated with the formation of the transition state (TS) and can be explained by considering the following ... 

In contrast, polyatomic radical metathesis reactions have A factors that are slightly lower, typically in the range 10 -10 cm /s-mol, suggesting entropy decreases in the range 30-40 cal/mol-K. This again is expected in view of the preceding discussion, since the absolute entropies of radicals are larger than those of atoms. 

The differential molar entropies can be plotted as a function of the coverage. Adsorption is always exothermic and takes place with a decrease in both free energy (AG < 0) and entropy (AS < 0). With respect to the adsorbate, the gas-solid interaction results in a decrease in entropy of the system. The cooperative orientation of surface-adsorbate bonds provides a further entropy decrease. The integral molar entropy of adsorption 5 and the differential molar entropy are related by the formula = d(n S )ldn for the particular adsorbed amount n. The quantity can be calculated from... 

C) All reactions proceed spontaneously in the direction that increases the entropy (disorder) of the system plus surroundings. The entropy of a gas increases when its pressure decreases at constant temperature, while the entropy decreases when pressure increases. The more we expand a gas, the more space the gas molecules will have and so the less ordered they will be. 

Activation parameters determined for CgHsCCl insertions into 44 and 37 (in benzene solution) were = 2.9 and 3.2 kcal/mol, with AS = —25.6 and —24.2 e.u., respectively. These activation energies are slightly greater than those observed in additions of CeHsCCl to alkenes, but the very negative entropies of activation are comparable to those observed in CeHsCCl additions, and reflect the entropy decrease that occurs when two reactant molecules combine to form a single product molecule. ... 

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