Natural Tendencies Toward Equilibrium

2 THE NATURE OF THE SECOND LAW Natural Tendencies Toward Equilibrium 

It is desirable to find some common measure (preferably a quantitative measure) of the tendency to change and of the direction in which change can occur. In the 1850s, Clausius and Kelvin independently formulated the second law of thermodynamics, and Clausius invented the term entropy S (from the Greek word TpoTT-rj, which means transformation), to provide a measure of the transformational content or the capacity for change. In this chapter, we will develop the properties of this function and its relationship to the direction and extent of natural processes as expressed in the second law of thermodynamics. 

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Although there is a natural tendency toward equilibrium of the solute concentration on both sides of the membrane, such an equilibrium is rare in a living system, and selective permeability of the plasma membrane therefore assures the required distribution of metabolically important material inside and outside the cell. Kinetic studies of solute transport often permit characterization of the type of transmembrane movement involved (Neame and Richards, 1972). As outlined by Csaky (1965), a given substance can cross the cell membrane in several different ways free diffusion, diffusion through pores, pinocytosis, and carrier-mediated transport. 

Solutions are homogeneous mixtures and can be gases, liquids, or solids. Two gases, for example, will mix in all proportions to give a gaseous solution, because gases are miscible in one another. Often one substance will dissolve in another only to a limited extent. The maximum amount that dissolves at equilibrium is the solubility of that substance. Solubility is explained in terms of the natural tendency toward disorder (say, by the mixing of two substances) and by the tendency to result in the... 

This is undoubtedly a consequence of the limited availability of detailed experimental information (box 6). Nevertheless, gas-surface phenomena provide a more natural arena for statistical and thermodynamic analyses because of their increased complexity, large numbers of degrees of freedom, and tendencies toward equilibrium. 

Some monomers with no tendency toward homopolymerization are found to have some (not high) activity in copolymerization. This behavior is found in cationic copolymerizations of tetrahydropyran, 1,3-dioxane, and 1,4-dioxane with 3,3-bis(chloromethyl)oxetane [Dreyfuss and Dreyfuss, 1969]. These monomers are formally similar in their unusual copolymerization behavior to the radical copolymerization behavior of sterically hindered monomers such as maleic anhydride, stilbene, and diethyl fumarate (Sec. 6-3b-3), but not for the same reason. The copolymerizability of these otherwise unreactive monomers is probably a consequence of the unstable nature of their propagating centers. Consider the copolymerization in which M2 is the cyclic monomer with no tendency to homopolymerize. In homopolymerization, the propagation-depropagation equilibrium for M2 is completely toward... 

Nature at times employs a clever mechanism in controlling the pH in natural water systems. It does so by controlling the partial pressure of C02 gas. The C02aq, a product of microbiological respiration, has a tendency to move toward equilibrium with the C02 gas in the atmosphere ... 

When a system contains two or more components whose concentrations vary from point to point, there is a natural tendency for mass to be transferred, minimizing the concentration differences within the system and moving it towards equilibrium. The transport of one component from a region of higher concentration to that of a lower concentration is called mass transfer. 

The glassy state is nonequilibrium in nature and exhibits a tendency to rmdergo structural relaxation toward equilibrium. This tendency of the glassy state to relax structurally toward equilibrium is often referred to as structural recovery. It was observed, however, that the progress towards structural recovery with time varies significantly between a down-quench and an up-quench. This is referred to as asymmetry of structural recovery. The norrlinearlty of the process is described by the following equation [16] ... 

Many of the studies undertaken recently have centred on the reversibility of the oxygen binding and on the nature of the adducts formed. Using the isomeric diethyl-enetriaminemonoacetic acids (L) as ligands, stable cobalt(n) complexes are formed which on oxygenation show no measurable tendency towards irreversible oxidation to the cobalt(m) state. Thermodynamic equilibrium constants may be defined by the equation... 

The above-mentioned common example of water formation also points out the limits of the equilibrium theory. In biochemistry this theory is very useful in explaining energetics and the nature of biocatalysis, but it would be a gross mistake to assume that the organism is anywhere near chemical equilibrium (AF = 0). L. V. Bertalanffy put it succinctly A closed system at equilibrium neither needs energy for its maintenance, nor can energy be obtained from it. The chemical equilibrium, for this reason, is unable to produce work. In order for a system to perform work, it must not be at equilibrium, but rather it must tend toward equilibrium. And in order for the system to be able to persist in its tendency, it must be kept in a steady state. Such is the situation with the organism, whose constant capacity for work is insured by the fact that it is an open system. ... 

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