Spontaneity Conditions

We started the last chapter with the question, Will a process occur spontaneously We found that it is the total entropy change of the universe—the system and the surroundings—that determines spontaneity. If AS niv is greater than zero, the process is spontaneous. However, it may not always be convenient to determine the entropy change of both the system and the environment. To have a spontaneity condition that depends on the system would be more convenient for assessing chemical reactions. It would also be convenient if this spontaneity condition were useful under conditions that are common for chemical reactions, mainly fixed temperature and fixed pressure. In this chapter, we will determine such a spontaneity condition and apply it to physical and chemical systems. 

We will begin the chapter by discussing the limitations of entropy. We will then define the Gibbs energy and the Helmholtz energy. What we will ultimately show is that for most chemical processes, the Gibbs energy provides a strict test for the spontaneity or nonspontaneity of that process. 

The Gibbs and Helmholtz energies, both named after prominent thermodynam-icists, are the last energies that will be defined. Their definitions, coupled with the appropriate use of partial derivation, allow us to derive a rich set of mathematical relationships. Some of these mathematical relationships let the full force of thermodynamics be applied to many phenomena, like chemical reactions and chemical equilibria and—importantly—predictions of chemical occurrences. These relationships are used by some as proof that physical chemistry is complicated. Perhaps they are better seen as proof that physical chemistry is widely applicable to chemistry as a whole. 

8 TheChemicai Potentiai and Other Partiai Moiar Quantities 

Unless otherwise noted, all art on this page is Cengage Learning 2014. 

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The NIH shift has been found to occur during aromatic hydroxylations catalyzed by enzymes present in plants, animals, fungi and bacteria. It is thus evident that the acid catalyzed (or spontaneous) isomerization of oxepins-arene oxides is a very important type of in vivo reaction. It should be emphasized that the NIH shift may occur under either acid-catalyzed or neutral (spontaneous) conditions (76ACR378). The direct chemical oxidation of aromatic rings has also yielded both phenols (obtained via the NIH shift) and arene oxides (80JCS(P1)1693>. 

Why did we not introduce equation 4.3 as a spontaneity condition earlier First, it depends on our definition of entropy, which we did not get to until the previous chapter. Second—and more importantly—it requires a process that is isentropic that is, where dS = 0 infinitesimally and AS = 0 for the overall process. One can imagine how difficult it must be to perform a process on a system and ensure that the order, on an atomic and molecular level, does not change. (Contrast that with how easy it is to devise a process where dV is zero or, equivalently, A for the entire process equals 0.) To put it bluntly, equation 4.3 is not a very useful spontaneity condition. 

Again, this is not a useful spontaneity condition unless we can keep the system isen-tropic. Because p and S must be constant in order for the enthalpy change to act as a spontaneity condition, p and S are the natural variables for enthalpy. Equation 4.4 does suggest why many spontaneous changes are exothermic, however. Many processes occur against a constant pressure that of the atmosphere. Constant pressure is half of the requirement for enthalpy changes to dictate spontaneity. However, it is not sufficient, because for many processes the entropy change is not zero. 

Note that in the above example, all of the processes may be spontaneous. However, only the last two must be spontaneous by the laws of thermodynamics as we know them. The difference between may and must is important for science. Science recognizes that anything might occur. It focuses, however, on what will occur. These spontaneity conditions help us determine what will occur. 

This equation implies certain natural variables, namely, T and p, such that the following spontaneity condition is... 

This is the spontaneity condition we have been looking for We therefore make the following, perhaps premature, statements. For a system, under conditions of constant pressure and temperature, for any process. 

Would this be considered a spontaneous process Because the pressure is not kept constant, the strict application of AG as a spontaneity condition is not warranted. However, gases do tend to go from high pressure to low pressure, given the opportunity. We might expect that this process is in fact spontaneous. 

List the sets of conditions that allow dS, dil, and dH of a process in a system act as a spontaneity condition. 

Explain why conditions for using AS > 0 as a strict spontaneity condition imply that AU and AH both equal zero. 

Explain why the spontaneity conditions given in equations 4.3 and 4.4 are in terms of the general derivatives dil and dH and not some partial derivative of U and H with respect to some other state variable. 

In this introductory chapter, we define chemical equilibrium. The Gibbs energy is the energy that is most useful to us, because processes at constant T and p (conditions that are easily established) have dG as a spontaneity condition. Therefore, we relate the idea of chemical equilibrium to the Gibbs energy. Chemical reactions go only so far toward completion, and we define extent as a means of expressing how far a reaction proceeds as pure reactants proceed toward products. We use extent to help define chemical equilibrium. 

There is one thing to notice about the signs on the electromotive force. Because AG is related to the spontaneity of an isothermal, isobaric process (that is, AG is positive for a nonspontaneous process, negative for a spontaneous process, and zero for equilibrium) and because of the negative sign in equation 8.21, we can establish another spontaneity test for an electrochemical process. If E is positive for a redox process, it is spontaneous. If E is negative, the process is not spontaneous. If E is zero, the system is at (electrochemical) equilibrium. Table 8.1 summarizes the spontaneity conditions. 

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