Entropy changes, chemical reactions

Chemical Reactions Entropy Changes and Free Energy... 

In a chemical reaction, the change in enthalpy and the change in entropy are determined by the nature of the compounds involved. 

For chemical reactions, the change of entropy production with time P is... 

If the fuel cell system is in thermal and mechanical equilibrium and operates at constant pressure and temperature, through a chemical reaction whose changes of free energy, enthalpy end entropy are, respectively, AG, AH, and AA, the intrinsic maximum efficiency, q, is given by ... 

For a chemical reaction, any change of the entropy of the system provoked by a reaction is accompanied by a change of the entropy in the surrounding. If the generated (or consumed) heat is reversibly transferred from or into the system, the change of the entropy becomes zero, which is expressed by the free enthalpy (Cibbs function) as ... 

The are many ways to define the rate of a chemical reaction. The most general definition uses the rate of change of a themiodynamic state function. Following the second law of themiodynamics, for example, the change of entropy S with time t would be an appropriate definition under reaction conditions at constant energy U and volume V ... 

Transient, or time-resolved, techniques measure tire response of a substance after a rapid perturbation. A swift kick can be provided by any means tliat suddenly moves tire system away from equilibrium—a change in reactant concentration, for instance, or tire photodissociation of a chemical bond. Kinetic properties such as rate constants and amplitudes of chemical reactions or transfonnations of physical state taking place in a material are tlien detennined by measuring tire time course of relaxation to some, possibly new, equilibrium state. Detennining how tire kinetic rate constants vary witli temperature can further yield infonnation about tire tliennodynamic properties (activation entlialpies and entropies) of transition states, tire exceedingly ephemeral species tliat he between reactants, intennediates and products in a chemical reaction. 

Chemistry can be divided (somewhat arbitrarily) into the study of structures, equilibria, and rates. Chemical structure is ultimately described by the methods of quantum mechanics equilibrium phenomena are studied by statistical mechanics and thermodynamics and the study of rates constitutes the subject of kinetics. Kinetics can be subdivided into physical kinetics, dealing with physical phenomena such as diffusion and viscosity, and chemical kinetics, which deals with the rates of chemical reactions (including both covalent and noncovalent bond changes). Students of thermodynamics learn that quantities such as changes in enthalpy and entropy depend only upon the initial and hnal states of a system consequently thermodynamics cannot yield any information about intervening states of the system. It is precisely these intermediate states that constitute the subject matter of chemical kinetics. A thorough study of any chemical reaction must therefore include structural, equilibrium, and kinetic investigations. 

In principle, the second law can be used to determine whether a reaction is spontaneous. To do that, however, requires calculating the entropy change for the surroundings, which is not easy. We follow a conceptually simpler approach (Section 17.3), which deals only with the thermodynamic properties of chemical systems. 

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. 

The steric environment of the atoms in the vicinity of the reaction centre will change in the course of a chemical reaction, and consequently the potential energy due to non-bonded interactions will in general also change and contribute to the free energy of activation. The effect is mainly on the vibrational energy levels, and since they are usually widely spaced, the contribution is to the enthalpy rather than the entropy. When low vibrational frequencies or internal rotations are involved, however, effects on entropy might of course also be expected. In any case, the rather universal non-bonded effects will affect the rates of essentially all chemical reactions, and not only the rates of reactions that are subject to obvious steric effects in the classical sense. 

In addition to chemical reactions, the isokinetic relationship can be applied to various physical processes accompanied by enthalpy change. Correlations of this kind were found between enthalpies and entropies of solution (20, 83-92), vaporization (86, 91), sublimation (93, 94), desorption (95), and diffusion (96, 97) and between the two parameters characterizing the temperature dependence of thermochromic transitions (98). A kind of isokinetic relationship was claimed even for enthalpy and entropy of pure substances when relative values referred to those at 298° K are used (99). Enthalpies and entropies of intermolecular interaction were correlated for solutions, pure liquids, and crystals (6). Quite generally, for any temperature-dependent physical quantity, the activation parameters can be computed in a formal way, and correlations between them have been observed for dielectric absorption (100) and resistance of semiconductors (101-105) or fluidity (40, 106). On the other hand, the isokinetic relationship seems to hold in reactions of widely different kinds, starting from elementary processes in the gas phase (107) and including recombination reactions in the solid phase (108), polymerization reactions (109), and inorganic complex formation (110-112), up to such biochemical reactions as denaturation of proteins (113) and even such biological processes as hemolysis of erythrocytes (114). 

Entropy changes are important in every process, but chemists are particularly interested in the effects of entropy on chemical reactions. If a reaction occurs under standard conditions, its entropy change can be calculated from absolute entropies using the same reasoning used to calculate reaction enthalpies from standard enthalpies of formation. The products of the reaction have molar entropies, and so do the reactants. The total entropy of the products is the sum of the molar entropies of the products multiplied by their stoichiometric coefficients in the balanced chemical equation. The total entropy of the reactants is a similar sum for the reactants. Equation... 

We use a short version of the seven-step method. The problem asks for the entropy and enthalpy changes accompanying a chemical reaction, so we focus on the balanced chemical equation and the thermodynamic properties of the reactants and products. 

The entropy of any chemical substance increases as temperature increases. These changes in entropy as a function of temperature can be calculated, but the techniques require calculus. Fortunately, temperature affects the entropies of reactants and products similarly. The absolute entropy of every substance increases with temperature, but the entropy of the reactants often changes with temperature by almost the same amount as the entropy of the products. This means that the temperature effect on the entropy change for a reaction is usually small enough that we can consider A Sj-eaction he independent of temperature. 

Gases that participate in chemical reactions typically are at pressures different from one bar. Substances in solution are likely to be at concentrations different from one molar. For example, a biochemist who wants to know what processes are spontaneous under physiological conditions will find that the substances dissolved in biological fluids are rarely at one molar concentration. How does AG vary with changes in molarity and pressure Recall that enthalpy is virtually independent of concentration but that entropy obeys Equation ... 

Macrostates are collections of microstates [9], which is to say that they are volumes of phase space on which certain phase functions have specified values. The current macrostate of the system gives its structure. Examples are the position or velocity of a Brownian particle, the moments of energy or density, their rates of change, the progress of a chemical reaction, a reaction rate, and so on. Let x label the macrostates of interest, and let x(r) be the associated phase function. The first entropy of the macrostate is... 

What a catalyst does is change the reaction pathway to one with a lower energy however, one must remember that the rate of a chemical reaction depends on two things the rate constant, which contains energy terms (both enthalpy and entropy), and concentration terms. 

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