Entropy and Physical Changes

Although chemists deal primarily with the chemical changes of matter, physical changes are also very important. In this section we will consider how the entropy of a substance depends on its temperature and on its physical state. 

For an isothermal process we have seen that the change in entropy is defined by the relationship 

We can calculate AS for a change in temperature from T1 to T2 by summing infinitesimal increments in entropy at each temperature T  

Entropy Changes Associated with Changes of State 

At the normal melting point or boiling point of a substance the two states of matter present at that temperature and at 1 atm pressure are in equilibrium. That is, the two states can coexist indefinitely if the system is isolated (left totally undisturbed). Recall that a reversible process can occur only at equilibrium. Thus, since a change of state from solid to liquid at the substance s melting point is a reversible process, we can calculate the change in entropy for this process by using the equation 

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Vibrational energy states are too well separated to contribute much to the entropy or the energy of small molecules at ordinary temperatures, but for higher temperatures this may not be so, and both internal entropy and energy changes may occur due to changes in vibrational levels on adsoiption. From a somewhat different point of view, it is clear that even in physical adsorption, adsorbate molecules should be polarized on the surface (see Section VI-8), and in chemisorption more drastic perturbations should occur. Thus internal bond energies of adsorbed molecules may be affected. 

The combination of Eqs. (150) and (151) provides a rate expression for the dehydrogenation/hydrogenation reactions that is dependent on the values of k, and Kx (as well as the overall equilibrium constant, Kcq). Estimates of these kinetic parameters can be made in terms of physically meaningful quantities such as entropies and enthalpy changes. Transition state theory gives the following expression for ky. 

Energy, Enthalpy, and Entropy Changes Involving Ideal Cases and Physical Changes... 

Describe the change in entropy of the following chemical and physical changes, using the information on pages 716 and 717. a) Wood burns and forms carbon dioxide and water vapor, b) Dry ice sublimes at room temperature and forms carbon dioxide gas. c) Liquid oxygen freezes. 

Compensation effects have been reported for the rates of a large number of catalytic reactions and adsorption-desorption processes. Our present interests focus in particular on the study of such effects in physical adsorption equilibria by Everett [D.H. Everett, Trans. Faraday Soc., 46, 942 (1950)], who reported a linear relationship between the entropy and enthalpy changes on adsorption. Thus,... 

The key concept of entropy as an assessment of dispersal of matter and of energy is carefully developed to provide a firm foundation for later ideas including heat changes that accompany chemical and physical changes, prediction of reactions, and chemical bond stability. Throughout this chapter, many fundamental terms are rigorously defined, discussed, and illustrated for use throughout later studies of chemistry. 

The second law of thermodynamics states that the total entropy of the universe tends to increase. This usually means that for a chemical reaction or a physical change to take place, the entropy of the system (the reactants) and their surroundings must increase. Some chemical reactions and physical changes appear to have a decrease in entropy but this is because the entropy of the surroundings increases by a greater amount, giving an overall increase in entropy in the universe (Figure 15.31). The system is the sample or reaction mixture. Outside the... 

Table 15.5 Qualitative entropy changes (of the system) for some common reactions and physical changes...

Entropy determines the direction of chemical and physical change. A chemical system proceeds in a direction that increases the entropy of the universe—it proceeds in a direction that has the largest number of energetically equivalent ways to arrange its components. 

In many physical changes, the entropy increase is the major driving force. This situation applies when two liquids with similar intermolecular forces, such as benzene (C6H< ) and tol-... 

Why Do We Need to Know This Material The second law of thermodynamics is the key to understanding why one chemical reaction has a natural tendency to occur bur another one does not. We apply the second law by using the very important concepts of entropy and Gibbs free energy. The third law of thermodynamics is the basis of the numerical values of these two quantities. The second and third laws jointly provide a way to predict the effects of changes in temperature and pressure on physical and chemical processes. They also lay the thermodynamic foundations for discussing chemical equilibrium, which the following chapters explore in detail. 

RADICALC Bozzelli, J. W. and Ritter, E. R. Chemical and Physical Processes in Combustion, p. 453. The Combustion Institute, Pittsburgh, PA, 1993. A computer code to calculate entropy and heat capacity contributions to transition states and radical species from changes in vibrational frequencies, barriers, moments of inertia, and internal rotations. 

The process shown in Figure 7.5 is certainly a favourable change. Yet no exchange of energy is involved. The condition that influences this change is called entropy. It is an important condition in all physical and chemical changes. 

The principle that different structural domains, moieties, or features of a molecular substance contribute separately and additively to a property of a substance. In 1840, G. H. Hess introduced the Law of Constant Heat Summation, a relation that allows one to calculate the heat of a reaction from collected measurements of seemingly different reactions, as long as the summation of a series of reactions yields the same overall chemical reaction as the one of interest. Thermodynamic additivity requires that if two components, A and B, contribute independently to some process, then the total change in free energy (or enthalpy or entropy) is the sum of components, AG = AGa + AGb. In view of its broad use in examining chemical and physical principles, Benson has even offered the view that additivity is the fourth law of thermodynamics. 

The second law of thermodynamics states that the total entropy of a chemical system and that of its surroundings always increases if the chemical or physical change is spontaneous. The preferred direction in nature is toward maximum entropy. Moving in the direction of greater disorder in an isolated system is one of the two forces that drive change. The other is loss of heat energy, AH. 

The site entropy is thus a sensible candidate for describing fluid relaxation outside the immediate vicinity of the glass transition. In a more precise language, is actually an entropy density, and the maximum in Sc T) derives from an interplay between changes in the entropy and fluid density as the temperature is varied. Explicit calculations demonstrate that the maximum in Sc T) disappears in the limit of an incompressible fluid, which is physically achieved in the limit of infinite pressure. The pressure dependence of Sc T) is described in Section X, where it is found that the maximum in Sc T) becomes progressively shallower and 7a becomes larger with increasing pressure. 

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