Entropy molecular basis

In equation (1.17), S is entropy, k is a constant known as the Boltzmann constant, and W is the thermodynamic probability. In Chapter 10 we will see how to calculate W. For now, it is sufficient to know that it is equal to the number of arrangements or microstates that a molecule can be in for a particular macrostate. Macrostates with many microstates are those of high probability. Hence, the name thermodynamic probability for W. But macrostates with many microstates are states of high disorder. Thus, on a molecular basis, W, and hence 5, is a measure of the disorder in the system. We will wait for the second law of thermodynamics to make quantitative calculations of AS, the change in S, at which time we will verify the relationship between entropy and disorder. For example, we will show that... 

The fundamental driving force behind the remarkable elastic properties of the elastin polymer is believed to be entropic, where stretching decreases the entropy of the system and elastic recoil is driven by a spontaneous return to maximum entropy. The precise molecular basis for elasticity has not been fully elucidated and a number of models exist. Two main categories of structure-function models have been proposed those in which elastin is considered to be isotropic and devoid of structure, and those which consider elastin to be anisotropic with regions of order (Vrhovski and Weiss, 1998). 

Equation (48) is of the expected form for relations between reaction velocities and activation energies on the one hand, and between equilibrium constants and heats of reaction on the other. However, there are difficulties in the way of using (48) as a quantitative basis-for the BrOnsted relation. In the first place, the quantities E and e in the diagram refer strictly to the behavior of the system at absolute zero since no account is taken of the internal thermal energy of the molecules. In the second place experiment shows that even in a series of similar reactions the observed velocities and equilibrium constants often involve variations in entropies of activation and of reaction, and not only energy changes. These difficulties are not yet fully resolved, but there seems little doubt that diagrams such as Fig. 1 represent the essential molecular basis of the Bronsted relation. 

Entropy changes in chemical reactions also can be understood on a molecular basis. Consider, for example, the process... 

Water-soluble globular proteins usually have an interior composed almost entirely of nonpolar, hydrophobic amino acids such as phenylalanine, tryptophan, valine and leucine with polar and charged amino acids such as lysine and arginine located on the surface of the molecule. This packing of hydrophobic residues is a consequence of the hydrophobic effect, which is the most important factor that contributes to protein stability. The molecular basis for the hydrophobic effect continues to be the subject of some debate but is generally considered to be entropic in origin. Moreover, it is the entropy change of the solvent that is... 

Describe the molecular basis for entropy, including its relation to spatial and energetic configurations. Relate macroscopic directional processes to molecular mixing. 

Thermodynamics rests largely on the consohdation of many observations of nature into two fundamental postulates or laws. Chapter 2 addressed the first law— the energy of the universe is conserved. We camiot prove this statement, but based on over a hundred years of observation, we believe it to be true. In order to use this law quantitatively— that is, to make numerical predictions about a system—we cast it in terms of a thermodynamic property internal energy, u. Likewise, the second law summarizes another set of observations about nature. We will see that to quantify the second law, we need to use a different thermodynamic property entropy, s. Like internal energy, entropy is a conceptual property that allows us to quantify a law of nature and solve engineering problems. This chapter examines the observations on which the second law is based explores how the property s quantifies these observations illustrates ways we can use the second law to make numerical predictions about closed systems, open systems, and thermodynamic cycles and discusses the molecular basis of entropy. 

Ref. 205). The two mechanisms may sometimes be distinguished on the basis of the expected rate law (see Section XVni-8) one or the other may be ruled out if unreasonable adsorption entropies are implied (see Ref. 206). Molecular beam studies, which can determine the residence time of an adsorbed species, have permitted an experimental decision as to which type of mechanism applies (Langmuir-Hinshelwood in the case of CO + O2 on Pt(lll)—note Problem XVIII-26) [207,208]. 

This nonequilibrium Second Law provides a basis for a theory for nonequilibrium thermodynamics. The physical identification of the second entropy in terms of molecular configurations allows the development of the nonequilibrium probability distribution, which in turn is the centerpiece for nonequilibrium statistical mechanics. The two theories span the very large and the very small. The aim of this chapter is to present a coherent and self-contained account of these theories, which have been developed by the author and presented in a series of papers [1-7]. The theory up to the fifth paper has been reviewed previously [8], and the present chapter consolidates some of this material and adds the more recent developments. 

The third law of thermodynamics states that the entropy of a perfect crystal is zero at a temperature of absolute zero. Although this law appears to have limited use for polymer scientists, it is the basis for our understanding of temperature. At absolute zero (-273.14 °C = 0 K), there is no disorder or molecular movement in a perfect crystal. One caveat must be introduced for the purist - there is atomic movement at absolute zero due to vibrational motion across the bonds - a situation mandated by quantum mechanical laws. Any disorder creates a temperature higher than absolute zero in the system under consideration. This is why absolute zero is so hard to reach experimentally ... 

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