Page 139 - Instant notes

Thermodynamics of ions in solution 125

This expression simply emphasizes that changes in the activity coefficient of the cation
cannot be calculated without changes in the activity coefficient of the anion, as anions
cluster around cations and cations cluster around anions. If it is assumed that the effects
of clustering on the two activity coefficients are approximately equal (as well as the
parameter B for both ions), then the activity coefficient for an individual ion is given by:

−3
At very low dilution (typically when I<0.001 mol dm ), the first term in the denominator
of the equation dominates the second term, and produces the simplified Debye-Hückel
limiting law (which removes the ion dependent parameter B from the expression):

−3
At higher values of I<1 mol dm , the assumption of weak interactions between ions
made in deriving the Debye-Hückel expression becomes increasingly untenable. Activity
coefficients in this regime generally fit the expression:

where C is an empirical parameter which can be adjusted to fit the data. This extra term is
introduced to take account of the increasing importance of short-range ion-ion and ion-
solvent forces and this equation is often called the Debye-Hückel extended law. The
applicability of these equations to calculating mean activity coefficients is demonstrated
in Fig. 1, where calculated values can be seen to fit experimentally determined values
−3
(see Topic E5) closely. For I>1 mol dm , where short-range interactions dominate and
ions have increasingly incomplete solvation, theoretical calculation of activity coefficient
data is notoriously unreliable.