Thermodynamics, statistical

Statistical Thermodynamics of Adsorbates. First, from a thermodynamic or statistical mechanical point of view, the internal energy and entropy of a molecule should be different in the adsorbed state from that in the gaseous state. This is quite apart from the energy of the adsorption bond itself or the entropy associated with confining a molecule to the interfacial region. It is clear, for example, that the adsorbed molecule may lose part or all of its freedom to rotate. 

Statistical thermodynamics tells us that Cv is made up of four parts, translational, rotational, vibrational, and electronic. Generally, the last part is zero over the range 0 to 298 K and the first two parts sum to 5/2 R, where R is the gas constant. This leaves us only the vibrational part to worry about. The vibrational contr ibution to the heat capacity is 

S. A. Sairan, Statistical Thermodynamics of Surfaces, Interfaces and Membranes, Addison-Wesley, Reading, MA, 1994. 

Keizer J 1987 Statistical Thermodynamics of Nonequilibrium Processes (New York Springer) 

Ben-Naim A 1992 Statistical Thermodynamics for Chemists and Biologists (London Plenum) 

Irikura, K. K. Essential Statistical Thermodynamics in Computational Thermochemistry, In Irikura, K. K. Erurip, D. J. Eds., 1998. Computational Thermochemistry. American Chemical Society, Washington, DC. 

By the standard methods of statistical thermodynamics it is possible to derive for certain entropy changes general formulas that cannot be derived from the zeroth, first, and second laws of classical thermodynamics. In particular one can obtain formulae for entropy changes in highly di.sperse systems, for those in very cold systems, and for those associated, with the mixing ofvery similar substances. 

Gilson et al., 1997] Gilson, M., Given, J., Bush, B., and McCammon, J. The statistical-thermodynamic basis for computation of binding affinities A critical review. Biophys. J. 72 (1997) 1047-1069 

R. Fowler and E. A. Guggenheim, Statistical Thermodynamics, Cambridge University Press, Cambridge, England, 1952, p. 437. 

Lavenda B H 1985 Nonequilibrium Statistical Thermodynamics (New York Wley) oh 3 

Lavenda B FI 1985 Nonequilibrium. Statistical Thermodynamics (New York Wiley) 

A2.1.7.4 THIRD STATEMENT (SIMPLE LIMITS AND STATISTICAL THERMODYNAMICS) 

From the third law of thermodynamics, the entiopy 5 = 0 at 0 K makes it possible to calculate S at any temperature from statistical thermodynamics within the hamionic oscillator approximation (Maczek, 1998). From this, A5 of formation can be found, leading to A/G and the equilibrium constant of any reaction at 298 K for which the algebraic sum of AyG for all of the constituents is known. A detailed knowledge of A5, which we already have, leads to /Gq at any temperature. Variation in pressure on a reacting system can also be handled by classical thermodynamic methods. 

Chandler D 1987 Introduction to Modern Statistical Mechanics (Oxford Oxford University Press) Hill T L 1960 Introduction to Statistical Thermodynamics (Reading, MA Addison-Wesley) 

Mason E A and Spurling T H 1969 The VIrlal Equation of State (Oxford Pergamon) McQuarrie D A 1973 Statistical Thermodynamics (Mill Valley, CA University Science Books) 

S. Ross and I. D. Morrison, Colloidal Systems and Interfaces, Wiley, New York, 1988. S. A. Saffan, Statistical Thermodynamics of Surfaces, Interfaces and Membranes, Addison-Wesley, Reading, MA, 1994. 

In another sense the title is too restrictive, implying that only pure, phenomenological thermodynamics are discussed herein. Actually, this is far from true. Both thermodynamics and statistical thermodynamics comprise the contents of the chapter, with the second making the larger contribution. But the term statistical is omitted from the title, as it is too intimidating. 

The treatment of heat capacity in physical chemistry provides an excellent and familiar example of the relationship between pure and statistical thermodynamics. Heat capacity is defined experimentally and is measured by determining the heat required to change the temperature of a sample in, say, 

Thus from an adsorption isotherm and its temperature variation, one can calculate either the differential or the integral entropy of adsorption as a function of surface coverage. The former probably has the greater direct physical meaning, but the latter is the quantity usually first obtained in a statistical thermodynamic adsorption model. 

It is curious that he never conuuented on the failure to fit the analytic theory even though that treatment—with the quadratic fonn of the coexistence curve—was presented in great detail in it Statistical Thermodynamics (Fowler and Guggenlieim, 1939). The paper does not discuss any of the other critical exponents, except to fit the vanishing of the surface tension a at the critical point to an equation 

K (66.46 e.u.) with the spectroscopic value calculated from experimental data (66.41 0.009 e.u.) (295, 289) indicates that the crystal is an ordered form at 0°K. Thermodynamic functions of thiazole were also determined by statistical thermodynamics from vibrational spectra (297, 298). 

In general, it seems more reasonable to suppose that in chemisorption specific sites are involved and that therefore definite potential barriers to lateral motion should be present. The adsorption should therefore obey the statistical thermodynamics of a localized state. On the other hand, the kinetics of adsorption and of catalytic processes will depend greatly on the frequency and nature of such surface jumps as do occur. A film can be fairly mobile in this kinetic sense and yet not be expected to show any significant deviation from the configurational entropy of a localized state. 

It is not particularly difficult to introduce thermodynamic concepts into a discussion of elasticity. We shall not explore all of the implications of this development, but shall proceed only to the point of establishing the connection between elasticity and entropy. Then we shall go from phenomenological thermodynamics to statistical thermodynamics in pursuit of a molecular model to describe the elastic response of cross-linked networks. 

The preceding derivation, being based on a definite mechanical picture, is easy to follow intuitively kinetic derivations of an equilibrium relationship suffer from a common disadvantage, namely, that they usually assume more than is necessary. It is quite possible to obtain the Langmuir equation (as well as other adsorption isotherm equations) from examination of the statistical thermodynamics of the two states involved. 

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