The Equilibrium Constant An Introduction

Science is based on the resuits of experiments. The development of the equilibrium concept is typical. On the basis of their observations of many chemical reactions, two Norwegian chemists, Cato Maximilian Guldberg and Peter Waage, proposed in 1864 the law of chemical equilibrium (originally called the law of mass action) as a general description of the equilibrium condition. Guldberg and Waage postulated that for a reaction of the type 

The square brackets indicate the concentrations of the chemical species at equilibrium (in units of mol/L), and X is a constant called the equiiibrium constant. Note that the equilibrium expression is a special ratio of the concentrations of the products to the concentrations of the reactants. 

Each concentration is raised to a power corresponding to its coefficient in the balanced equation. 

The law of chemical equilibrium as proposed by Guldberg and Waage is based on experimentai observations. Experiments on many reactions showed that the equiiibrium condition could always be described by this special ratio, called the equilibrium expression. 

To see how to construct an equilibrium expression, consider the reaction where ozone changes to oxygen  

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The kinetics of chlorination of ethylene, allyl chloride, 3,4-dichlorobutene, 2,3-dichlo-ropropene, and 1,2-dichloroethylene in 1,2-dichloroethane have been investigated in the presence of BU4NCI. The mathematical treatment of the results was performed with due regard to the equilibrium constants of the formation of complexes between CI2 and CP. For all the substrates at 256K, the introduction of CP into the system has been found to result in an increase in the rate of the addition. The reaction turned out to be of first order with respect to both the substrate and the salt and second order with respect to chlorine. As expected, the dependence of the reaction rate on the substiments at the double bond is compatible with the electrophilic addition, initiated by electrophilic chlorine."... 

FIGURE 1.6 The effect of temperature on the equilibrium constants. [Graph reconstructed from data by W. Stumm and J. J. Morgan, Aquatic Chemistry An Introduction Emphasizing Chemical Equilibria in Natural Waters, Wiley Interscience, New York, 1981, p. 71.]... 

As anticipated in the Introduction, for a system following Scheme 2, the equilibrium constant of the precursor dissociation must not be larger than an upper limiting value. If this holds, one obtains a lifetime of the precursor R—Y that exceeds the natural lifetime (Ad)-1 by the factor of Ac[I]o/AtR/C and this may amount to many orders of magnitude.1517... 

The subsequent introduction of Eqs. (56)-(61) into Eq. (63) eventually gives an intricate mathematical expression because the additive contributions of the microspecies belonging to the same macrospecies prevent simplification. The equilibrium constant Kg chtri depends on all... 

It is obvious from the introduction that the authors were not aware of the current literature at the time, a fact that might explain both their neglect of polynuclear complexes and the far from adequate calculation method used to calculate the equilibrium constants from the experimental Uq, v5. pH data. The reported equihbrium constants are not reliable because of an erroneous chemical model, the neglect of polynuclear species that are totally dominating the speciation under the experimental conditions used. 

As a first approximation, one may assume that C is independent of R. C is calculated at the experimental equilibrium intemuclear distance and is then the adiabatic correction to the zero of vibrational energy. In this approximation, the only contribution of the corrections to the B.O. approximation to the equilibrium constant of exchange reaction (1) will result from the quantity designated as A ELEC in the Introduction (See also eqs. (12) and (13)). In our later calculations (4), which will not be discussed in detail here, we have calculated C at several intemuclear distances. We have found that C then will contribute not only to the zero of vibrational energy but will also lead to an isotope dependent shift of the equilibrium intemuclear distance and of the various vibrational constants. However, the distance dependence of C is such in our calculations that the correction to the zero of vibrational energy so calculated at the new equilibrium intemuclear distance is. 

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