Equilibrium constant and composition

Heat effects accompanying chemical reaction influence equilibrium constants and compositions as well as rates of reaction. The enthalpy change of reaction, AHr, is the difference between the enthalpies of formation of the participants. It is positive for endothermic reactions and negative for exothermic ones. This convention is the opposite of that for heats of reaction, so care should be exercised in applications of this quantity. Enthalpies of formation are empirical data, most often known at a standard temperature, frequently at 298 K. The Gibbs energies of formation, AGfl likewise are empirical data. 

Table 4.10 Equilibrium constants and compositions for solid-state reaction (4.11) (P° = lbar) for isomer X of...

Table 4.11 Equilibrium constants and compositions for ideal-gas reaction (4.14) at P° = 1 bar. x is a mol fraction of a component, is a degree of conversion...

Table 4.14 Equilibrium constants and compositions for gas-phase reaction (4.16)...

The fundamental relationship between equilibrium constant and composition is via the product of the activities of species raised to the corresponding stoichiometric coefficients ... 

In general the degree of conversion depends on temperature, pressure, the numerical value of the equilibrium constant and composition of the initial mixture n° —... 

This corresponds to a distribution of 66% anti and 34% gauche. Table 3.2 gives the relationship between free-energy difference, equilibrium constant, and percent composition of a two-component mixture. 

If these measurements are made at a pH where only the neutral molecules are present, the ratio is equal to the constant K. This restriction about pH is necessary because and are ordinarily composite, their relationship to the equilibrium constants and pA values being given by the relevant equations, ... 

The effect of temperature on the equilibrium composition arises from the dependence of the equilibrium constant on the temperature. The relation between the equilibrium constant and the standard Gibbs free energy of reaction in Eq. 8 applies to any temperature. Therefore, we ought to be able to use it to relate the equilibrium constant at one temperature to its value at another temperature. 

The distribution of metals between dissolved and particulate phases in aquatic systems is governed by a competition between precipitation and adsorption (and transport as particles) versus dissolution and formation of soluble complexes (and transport in the solution phase). A great deal is known about the thermodynamics of these reactions, and in many cases it is possible to explain or predict semi-quantita-tively the equilibrium speciation of a metal in an environmental system. Predictions of complete speciation of the metal are often limited by inadequate information on chemical composition, equilibrium constants, and reaction rates. 

This permits provisional calculation of the compositional dependence of the equilibrium constant and determination of provisional values of the solid phase activity coefficients (discussed below). The equilibrium constant and activity coefficients are termed provisional because it is not possible to determine if stoichiometric saturation has been established without independent knowledge of the compositional dependence of the equilibrium constant, such as would be provided from independent thermodynamic measurements. Using the provisional activity coefficient data we may compare the observed solid solution-aqueous solution compositions with those calculated at equilibrium. Agreement between the calculated and observed values confirms, within the experimental data uncertainties, the establishment of equilibrium. The true solid solution thermodynamic properties are then defined to be equal to the provisional values. 

Nitric oxide has a very low ionization potential and could ionize at flame temperatures. For a normal composite solid propellant containing C—H—O—N—Cl—Al, many more products would have to be considered. In fact if one lists all the possible number of products for this system, the solution to the problem becomes more difficult, requiring the use of advanced computers and codes for exact results. However, knowledge of thermodynamic equilibrium constants and kinetics allows one to eliminate many possible product species. Although the computer codes listed in Appendix I essentially make it unnecessary to eliminate any product species, the following discussion gives one the opportunity to estimate which products can be important without running any computer code. 

We want to find the equilibrium composition at the temperature T = 1000 and pressure P = 1.013x10 Pa if the system initially contains 2 moles of methane and 3 moles of water. For the given temperature and pressure the natural logarithms of the equilibrium constants and K2 expressed in terms of mole fractions are known log = 3.4789 and log 2 = -0.0304. Let n, n2,... 

More commonly, we are given the initial composition and the equilibrium constant and asked to calculate the equilibrium composition. The procedure is identical, but we write one of the unknown changes as x and use the reaction stoichiometry to find the other changes. The procedure is summarized in Toolbox 9.1 and illustrated in the examples that follow. 

Relate the equilibrium constant to compositions of the two phases. Let subscripts 1 and 2... 

Solubility calculations were added for two allophanes, for which the equilibrium constants and formulae are a function of pH. Paces (74) found cold ground waters collected from springs in granitic rocks of the Bohemian Massif of Czechoslovakia to be supersaturated with respect to kaolinite while being unsaturated with respect to amorphous silica. He interpreted this as an indication that a metastable aluminosilicate more soluble than kaolinite was controlling the concentrations of alumina and silica in these waters. This aluminosilicate was further hypothesized to be of varied chemical composition, controlled by the mole... 

Equilibrium measurements accordit g to Eq. (108) were performed at quite high concentrations of active spedes ( 0.6 mole 1 ) and it is not certain whether these measurements actually gave the equilibrium constants (and related thermodynamic parameters) or whether the determined values are tl composite coefficients involving two or more equilibria. 

---