Equilibrium constants of formation

The observed rate constant is kobs = kkn(k + vD)-1. For the fast reactions with k vD the rate constant is kobs = kI). In the case of a slow reaction with k vD the rate constant is k0bs = kx KAb, where KAB = k y vn is the equilibrium constant of formation of cage pairs A and B in the solvent or solid polymer matrix. The equilibrium constant KAB should not depend on the molecular mobility. According to this scheme, the rate constant of a slow bimolecular reaction kobs = kKAB(kobs kD) should be the same in a hydrocarbon solution and the nonpolar polymer matrix. However, it was found experimentally that several slow free radical reactions occur more slowly in the polymer matrix than in the solvent. A few examples are given in Table 19.1. 

In the same context as the heat of formation, the JANAF tables have tabulated most conveniently the equilibrium constants of formation for practically every substance of concern in combustion systems. The equilibrium constant of formation (KPt[) is based on the equilibrium equation of formation of a species from its elements in their normal states. Thus by algebraic manipulation it is possible to determine the equilibrium constant of any reaction. In flame temperature calculations, by dealing only with equilibrium constants of formation, there is no chance of choosing a redundant set of equilibrium reactions. Of course, the equilibrium constant of formation for elements in their normal state is one. 

Complexes of cobalt (III) containing coordinated perrhenate ion have not previously been reported. % They are of special interest because of their close relationship to the unstable perchlorate complexes and are of use in studies on the mechanism of hydrolysis. Since the equilibrium constant of formation is small and [Co(NH )5(HjO)](Re04) -2H20 is relatively insoluble, the present procedure is similar to that used previously for mom common complex ions. 

If the equilibrium constant for a given reaction is not available, it is also possible to calculate its value at any temperature by simple algebraic manipulation, if the equilibrium constants of formation of the substances present relative to their elements in their standard states are known at that temperature. All the latest, convenient thermodynamic tabulations in fact list equilibrium constants of formation and this procedure has become the standard for the calculating Kp of a general equilibrium reaction system. For example, consider the determination of the Kp of the reaction ... 

In many modern rocket propellant systems, condensable oxides are always present. Further the equilibrium constant of formation of carbon containing substances must contain graphite, since this is the form of carbon in its standard state. Thus, the condition presented by condensed phases must be considered. The equilibrium constant of formation of C02 follows from the simple reaction ... 

It is above Kp f which are listed for the equilibrium constants of formation when a condensed phase is present. Kp, f is determined from the standard free energy change of the gaseous system and the vapor pressure of the condensed phase. 

Figure 5.3.2 The equilibrium constant of formation methanol synthesis by-products from 3 1 H2 C02 mixtures at 250°C.

Stability constant — is the - equilibrium constant of formation of a - complex. The reciprocal quantity is called instability constant. Extensive compilations of various kinds of stability constants are available [i—iv]. Stability constants are reported for a given ionic strength (or extrapolated to zero ionic strength), and pH. In many cases, stability constants can be determined with the help of electrochemical techniques, e.g., -> chronopotentiometry, -> potentiometry, -> polarogra-phy, and - voltammetry, provided that the systems exhibit -> electrochemical reversibility, and some other prerequisites are fulfilled [v]. See also -> conditional equilibrium constants. 

Derivation. Apart from concentrations, the ratio of the numerator and the j th denominator term is the ratio of the products of the first j +1 forward coefficients and the first j reverse coefficients. The product of the ratios of forward and reverse coefficients of the first j steps equals the equilibrium constant of formation of Xj from the reactants or a power of it. According to the van t Hoff equation... 

Key words critically evaluated data enthalpy enthalpy of formation entropy equilibrium constant of formation Gibbs energy function Gibbs energy of formation heat capacity thermochemical tables. 

The formation functions consist of enthalpy of formation, Gibbs energy of formation, and the logarithm of the equilibrium constant of formation. Enthalpies of formation at temperatures other than 298.15 K require a knowledge of the enthalpies of the reference elements ... 

The logarithm of the equilibrium constant of formation is then found from the relation A fG T) = —RTln Kf,... 

Table IX-1 Equilibrium constants of formation of aqueous thorium sulphate complexes at 25°C, unless otherwise noted, reported in the hterature and those calculated by this...

EPR spectroscopy was employed by Rockenbauer et al [Ro 72] to study the equilibrium stability constants of low-spin cobalt(II) mixed complexes. They determined the equilibrium constants of formation of the mixed complexes of the bis(dimethylglyoximato)cobalt(II) parent complex with pyridine ligands, in methanol. It was shown that in a methanolic solution of the parent complex, two methanol molecules are coordinated along the z axis, and these methanol molecules can be replaced stepwise with pyridine. 

A further interesting feature of these investigations is that, despite the great solvent dependence of the rate constants, the equilibrium constant of formation of the mixed complex was almost the same in the different solutions. 

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