Page 51 - Vogel's TEXTBOOK OF QUANTITATIVE CHEMICAL ANALYSIS

ACTlVlTY AND ACTlVlTY COEFFICIENT 2.5

AlCl,, or SO, in an inert solvent cause colour changes in indicators similar to
those produced by hydrochloric acid, and these changes are reversed by bases
so that titrations can be carried out. Compounds of the type of BF, are usually
described as Lewis acids or electron acceptors. The Lewis bases (e.g. ammonia,
pyridine) are virtually identical with the Br~nsted-Lowry bases. The great
disadvantage of the Lewis definition of acids is that, unlike proton-transfer
reactions, it is incapable of general quantitative treatment.
The implications of the theory of the complete dissociation of strong
electrolytes in aqueous solution were considered by Debye, Hückel and Onsager,
and they succeeded in accounting quantitatively for the increasing molecular
conductivity of a strong electrolyte producing singly charged ions with decreasing
concentration of the solution over the concentration range 0-0.002M. For full
details, textbooks of physical chemistry must be consulted.
It is important to realise that whilst complete dissociation occurs with
strong electrolytes in aqueous solution, this does not mean that the effective
concentrations of the ions are identical with their molar concentrations in any
solution of the electrolyte: if this were the case the variation of the osmotic
properties of the solution with dilution could not be accounted for. The variation
of colligative, e.g. osmotic, properties with dilution is ascribed to changes in the
activity of the ions; these are dependent upon the electrical forces between the
ions. Expressions for the variations of the activity or of related quantities,
applicable to dilute solutions, have also been deduced by the Debye-Hückel
theory. Further consideration of the concept of activity follows in Section 2.5.

2.5 ACTlVlTY AND ACTlVlTY COEFFICIENT
In the deduction of the Law of Mass Action it was assumed that the effective
concentrations or active masses of the components could be expressed by the
stoichiometric concentrations. According to thermodynamics, this is not strictly
true. The rigorous equilibrium equation for, Say, a binary electrolyte:

where a, #, a,-, and a,, represent the activities of A+, B-, and AB respectively,
and Kt is the true or thermodynamic, dissociation constant. The concept of
activity, a thermodynamic quantity, is due to G. N. Lewis. The quantity is
related to the concentration by a factor termed the activity coefficient:
Activity = Concentration x Activity coefficient

Thus at any concentration
a,+ = y,, .[A+], a,- = y,.. [B-1, and a,, = y,,. [AB]
where y refers to the activity coefficients,* and the square brackets to the

*The symbol used is dependent upon the method of expressing the concentration of the solution.
The recommendations of the IUPAC Commision on Symbols, Terminology and Units (1969) are
as follows: concentration in moles per litre (molarity), activity coefficient represented by y,
concentration in mols per kilogram (molality), activity coefficient represented by y, concentration
expressed as mole fraction, activity coefficient represented by f: