Entropies of Chemical Reactions

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. 

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... 

V. Equilibrium Constants of Chemical Reactions — Gibbs Energy, Enthalpy, Entropy for Reactions... 

The validity of quantum-chemical kinetics of low-temperature reactions, the existence of the limit of chemical reaction rate,6 and the applicability of the previously mentioned general principle of cold formation of low-entropy products can be illustrated by recent finding of formaldehyde polymers in interstellar space.10... 

What I emphasize is that you can have no care at all about the decrease of entropy in chemical reactions as long as they proceed near absolute zero. 

Systems at constant temperature and pressure, which are common laboratory conditions, have a tendency toward lower enthalpy and higher entropy. A chemical reaction is driven toward the formation of products by a negative value of AH (heat given off) or a positive value of AS (more disorder) or both. When AH is negative and AS is positive, the reaction is clearly favored. When AH is positive and AS is negative, the reaction is clearly disfavored. 

The direction of chemical reaction will be determined by the free energy, AG, not the enthalpy, AH. However, in the present ruction the entropy term, A5, is apt to be comparatively small and since AG AH — TAS, the (tea energy ml) be dominated by the amhaJpy at moderate temperatures. 

As we stated earlier, diS > 0. Generalizing the concept of affinity of chemical reactions, the rate of entropy production can be written as7... 

Remind students to multiply 1 the standard molar entropy of each reactant and product by the appropriate coefficient from the balanced chemical equation when calculating the standard entropy of a reaction. 

Hatley and Blair [3.69] presented mean Tg data for anhydrous carbohydrates (Table 3.1), which vary in the literature owing to measurement and interpretation differences. Small amounts of water may depress the data substantially. The physical stability of amorphous formulations below Tg is generally accepted, and a collapse can be avoided. This does not always apply to the chemical stability. If the temperature is reduced below T, the configurational entropy diminishes until it reaches zero. This T0 (also shown in Table 3.1) is called the zero mobility temperature at which the molecular motion stops. The authors define three areas of chemical reactions above Tg, chemical reactions are generally possible at T, reactions such as aggregation, which require substantial molecular motion, stop and between Tg and T0, reactions involv-... 

The existence of an energy balance is not sufficient to answer all questions about a chemical reaction. Does a given reaction take place at all If so, to what extent does it proceed Questions relating to the processes and extent of chemical reactions require the introduction of some new thermodynamic functions which, like E and //, are properties of the state of the system. These new functions are entropy, S, and Gibbs free energy, G. In order to answer these and other questions, a mathematical statement of the second law of thermodynamics is required ... 

Kinetic properties (rates of chemical reactions) and thermodynamic properties (equilibrium constants, energy, entropy) are described by a large number of different mathematical relations, which are usually just presented for the student to memorize. Part of the reason for this is the complexity associated with a full treatment of these properties these subjects are taught in graduate chemistry and physics courses at every major university, and multivariate calculus is needed to formulate a rigorous treatment. Unfortunately, simple memorization does not provide much intuition. 

However, using entropy as a criterion of whether a biochemical process can occur spontaneously is difficult, as the entropy changes of chemical reactions are not readily measured, and the entropy change of both the system and its surroundings must be known. These difficulties are overcome by using a different thermodynamic function, free energy (G), proposed by Josiah Willard Gibbs which combines the first and second laws of thermodynamics ... 

Using the procedure of Eq. (7), the entropy change of chemical reaction (2) can be written as... 

The concept of affinity introduced in the foregoing chapter (section 3.5) can apply to all the physicochemical changes that occur irreversibly. Let us now discuss the physical meaning of the affinity of chemical reactions. As mentioned in the foregoing, we have in Eq. 3.27 the fundamental inequality in entropy balance of irreversible processes as shown in Eq. 4.1 ... 

Chemical reaction. To perform detailed exergy analyses of chemical reactions, information about composition of both reactants and products is required. Then the changes in enthalpy, entropy, exergy, and the direction factor for the reaction process can be calculated. For primary dicussions for the reaction system synthesis, however, the standard direction factor D° defined by the following equation may be utilized. 

Gibbs free energy describes the spontaneity of chemical reactions in terms of enthalpy, entropy, and temperature. Negative values signify a spontaneous reaction, while positive values are nonspontaneous. A free energy of zero denotes equilibrium conditions. 

In order to remain alive, in other words, organisms must be in a perpetual state of activity (their cells work even when they sleep), and must continuously pump out the excess entropy of their reactions. In the words of Erwin Schrodinger (1944), they eat not only matter but also order. Towards the end of the nineteenth century, in conclusion, a living organism came to be seen essentially as a thermodynamic machine, i.e. as a chemical machine that must be continuously active in order to obey the laws of thermodynamics. 

Both the classical and statistical equations [Eqs. (5.22) and (5.23)] yield absolute values of entropy. Equation (5.23) is known as the Boltzmann equation and, with Eq. (5.20) and quantum statistics, has been used for calculation of entropies in the ideal-gas state for many chemical species. Good agreement between these calculations and those based on calorimetric data provides some of the most impressive evidence for the validity of statistical mechanics and quantum theory. In some instances results based on Eq. (5.23) are considered more reliable because of uncertainties in heat-capacity data or about the crystallinity of the substance near absolute zero. Absolute entropies provide much of the data base for calculation of the equilibrium conversions of chemical reactions, as discussed in Chap. 15. 

Engineering systems mainly involve a single-phase fluid mixture with n components, subject to fluid friction, heat transfer, mass transfer, and a number of / chemical reactions. A local thermodynamic state of the fluid is specified by two intensive parameters, for example, velocity of the fluid and the chemical composition in terms of component mass fractions wr For a unique description of the system, balance equations must be derived for the mass, momentum, energy, and entropy. The balance equations, considered on a per unit volume basis, can be written in terms of the partial time derivative with an observer at rest, and in terms of the substantial derivative with an observer moving along with the fluid. Later, the balance equations are used in the Gibbs relation to determine the rate of entropy production. The balance equations allow us to clearly identify the importance of the local thermodynamic equilibrium postulate in deriving the relationships for entropy production. 

Nonisothermal reaction-diffusion systems represent open, nonequilibrium systems with thermodynamic forces of temperature gradient, chemical potential gradient, and affinity. The dissipation function or the rate of entropy production can be used to identify the conjugate forces and flows to establish linear phenomenological equations. For a multicomponent fluid system under mechanical equilibrium with n species and A r number of chemical reactions, the dissipation function 1 is... 

For a multicomponent fluid system under mechanical equilibrium with n species and Nr number of chemical reactions, the entropy production function is... 

For nonequilibrium systems far from global equilibrium, the second law does not impose the sign of entropy variation due to the terms djS and d S, as illustrated in Figure 12.2. Therefore, there is no universal Lyapunov function. For a multicomponent fluid system with n components, entropy production in terms of conjugate forces Xu flows Jj, and / number of chemical reactions is... 

Now, according to the transition-state theory of chemical reaction rates, the pre-exponential factors are related to the entropy of activation, A5 , of the particular reaction [A = kT ere k and h are the Boltzmann and Planck constants, respectively, and An is the change in the number of molecules when the transition state complex is formed.] Entropies of polymerization are usually negative, since there is a net decrease in disorder when the discrete radical and monomer combine. The range of values for vinyl monomers of major interest in connection with free radical copolymerization is not large (about —100 to —150 JK mol ) and it is not unreasonable to suppose, therefore, that the A values in Eq. (7-73) will be approximately equal. It follows then that... 

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