Reaction Gibbs energy

The most important themiodynamic property of a substance is the standard Gibbs energy of fomiation as a fimetion of temperature as this infomiation allows equilibrium constants for chemical reactions to be calculated. The standard Gibbs energy of fomiation A G° at 298.15 K can be derived from the enthalpy of fomiation AfT° at 298.15 K and the standard entropy AS° at 298.15 K from... 

The chemical potential, plays a vital role in both phase and chemical reaction equiUbria. However, the chemical potential exhibits certain unfortunate characteristics which discourage its use in the solution of practical problems. The Gibbs energy, and hence is defined in relation to the internal energy and entropy, both primitive quantities for which absolute values are unknown. Moreover, p approaches negative infinity when either P or x approaches 2ero. While these characteristics do not preclude the use of chemical potentials, the appHcation of equiUbrium criteria is faciUtated by the introduction of a new quantity to take the place of p but which does not exhibit its less desirable characteristics. 

The standard Gibbs energy change of reaction, is used ia the calculation of equilibrium compositions the standard heat of reaction, is used iu... 

The general criterion of chemical reaction equiUbria is the same as that for phase equiUbria, namely that the total Gibbs energy of a closed system be a minimum at constant, uniform T and P (eq. 212). If the T and P of a siagle-phase, chemically reactive system are constant, then the quantities capable of change are the mole numbers, n. The iadependentiy variable quantities are just the r reaction coordinates, and thus the equiUbrium state is characterized by the rnecessary derivative conditions (and subject to the material balance constraints of equation 235) where j = 1,11,.. ., r ... 

In the case of a siagle-phase, multicomponent system undergoiag just a single reaction, the total Gibbs energy is as foUows ... 

Quantity K is the chemical reaction equilibrium constant for reactionyj and AG° is the corresponding standard Gibbs energy change of reaction (eq. 237). Although called a constant, fC is a function of T, but only of T. 

Generalized charts are appHcable to a wide range of industrially important chemicals. Properties for which charts are available include all thermodynamic properties, eg, enthalpy, entropy, Gibbs energy and PVT data, compressibiUty factors, Hquid densities, fugacity coefficients, surface tensions, diffusivities, transport properties, and rate constants for chemical reactions. Charts and tables of compressibiHty factors vs reduced pressure and reduced temperature have been produced. Data is available in both tabular and graphical form (61—72). 

The standard Gibbs-energy change of reaction AG° is used in the calculation of equilibrium compositions. The standard heat of reaclion AH° is used in the calculation of the heat effects of chemical reaction, and the standard heat-capacity change of reaction is used for extrapolating AH° and AG° with T. Numerical values for AH° and AG° are computed from tabulated formation data, and AC° is determined from empirical expressions for the T dependence of the C° (see, e.g., Eq. [4-142]). 

Complex Clieinical-Reaction Equilibria When the composition of an equilibrium mixture is determined by a number of simultaneous reactions, calculations based on equilibrium constants become complex and tedious. A more direct procedure (and one suitable for general computer solution) is based on minimization of the total Gibbs energy G in accord with Eq. (4-271). The treatment here is... 

When the kinetics are unknown, still-useful information can be obtained by finding equilibrium compositions at fixed temperature or adiabatically, or at some specified approach to the adiabatic temperature, say within 25°C (45°F) of it. Such calculations require only an input of the components of the feed and produc ts and their thermodynamic properties, not their stoichiometric relations, and are based on Gibbs energy minimization. Computer programs appear, for instance, in Smith and Missen Chemical Reaction Equilibrium Analysis Theory and Algorithms, Wiley, 1982), but the problem often is laborious enough to warrant use of one of the several available commercial services and their data banks. Several simpler cases with specified stoichiometries are solved by Walas Phase Equilibiia in Chemical Engineering, Butterworths, 1985). 

A more general, and for the moment, less detailed description of the progress of chemical reactions, was developed in the transition state theory of kinetics. This approach considers tire reacting molecules at the point of collision to form a complex intermediate molecule before the final products are formed. This molecular species is assumed to be in thermodynamic equilibrium with the reactant species. An equilibrium constant can therefore be described for the activation process, and this, in turn, can be related to a Gibbs energy of activation ... 

This is a 4 2 reaction, and is thus pressure dependent. However, it is necessary to compute the equilibrium partial pressure of some alternative gaseous species, such as SiCls, and other hydrocarbons such as C2H2 and for this a Gibbs energy minimization calculation should be made. 

This estimated Gibbs energy of the uansporting reaction is,... 

The oxidation of nickel-copper alloys provides an example of die dependence of the composition of the oxide layer on the composition of the alloy. Nickel-copper alloys depart from Raoult s law, but as a first approximation can be taken as ideal. The Gibbs energy change for the reaction... 

The hrst successful study which clarihed the mechanism of roasting, was a study of the oxidation of pyrite, FeSa, which is not a typical industrial process because of the availability of oxide iron ores. The experiment does, however, show die main features of roasting reactions in a simplihed way which is well supported by the necessaty thermodynamic data. The Gibbs energy data for the two sulphides of iron are,... 

A catalyst is a substance that increases the rate of a reaction without modifying the overall standard Gibbs energy change in the reaction the process is called catalysis, and a reaction in which a catalyst is involved is known as a catalyzed reaction. ... 

Furthermore, equilibria hold for ions and electrons. In every case, the Gibbs energy of the defect reaction has to provide a minimum for the equilibrium concentrations ... 

The standard Gibbs free energy of reaction, AG°, is defined like the Gibbs free energy of reaction but in terms of the standard molar Gibbs energies of the reactants and products ... 

Use Appendix 2A to determine (a) the standard reaction enthalpy (b) the standard entropy (c) the standard Gibbs energy at 25°C for the re-forming reaction of methane. 

Figure 13. The Gibbs energy available from a reaction, A B, depends on its displacement from equilibrium when IB)/IA) = K. The AC value is plotted against the mass-action ratio, and this is the value when B1/ A] is maintained constant in the steady state if the rate of substrate supply and substrate removal is constant.

---