Page 45 - Vogel's TEXTBOOK OF QUANTITATIVE CHEMICAL ANALYSIS

THE UW OF MASS ACTION 2.2

where k, is a constant known as the rate constant or rate coefficient, and the
square brackets (see footnote Section 2.21) denote the concentrations (mol L- ')
of the substances enclosed within the brackets.
Similarly, the rate of conversion of C and D is given by:

At equilibrium, the two rates of conversion will be equal:

or k, x [A] x [BI = k, x [Cl x [Dl

K is the equilibrium constant of the reaction at the given temperature.
The expression may be generalised. For a reversible reaction represented by:

where pl, p,, p, and q, , q,, q3 are the stoichiometric coefficients of the reacting
species, the condition for equilibrium is given by the expression:

This result may be expressed in words: when equilibrium is reached in a reversible
reaction, at constant temperature, the product of the concentrations of the
resultants (the substances on the right-hand side of the equation) divided by
the product of the concentrations of the reactants (the substances on the
left-hand side of the equation), each concentration being raised to a power equal
to the stoichiometric coefficient of the substance concerned in the equation for
the reaction, is constant.
The equilibrium constant of a reaction can be related to the changes in Gibbs
Free Energy (AG), enthalpy (AH) and entropy (AS) which occur during the
reaction by the mathematical expressions:
AGe = - RTlnKe = -2.303RTlogl, Ke

In these expressions, the superscript symbol (8) indicates that the quantities
concerned relate to a so-called 'standard state'. For the derivation and the
significance of these expressions, a textbook of physical chemistry' should
be consulted, but briefly a reaction will be spontaneous when AG is negative,
it will be at equilibrium when AG is zero, and when AG is positive the reverse
reaction will be spontaneous. It follows that a reaction is favoured when heat
is produced, i.e. it is an exothermic reaction so that the enthalpy change AH is
negative. It is also favoured by an increase in entropy, that is when AS is positive.
A knowledge of the values of the equilibrium constants of certain selected systems
can be of great value to the analyst; for example in dealing with acid-base
interactions, with solubility equilibria, with systems involving complex ions,