Page 138 - Instant notes

Physical chemistry 124

ionic concentration is sufficient to calculate the chemical potential or molar free energy
of the ion (see Topics B6, C1 and D1). At higher ionic concentrations, ionic interactions
become significant, γ i is typically less than unity and electrostatic interactions are
important in determining thermodynamic data.

Ionic strength
The overall degree of electrostatic ionic interactions is measured by using the ionic
strength of the solution, I. This is given by:

and involves adding the contribution of every ion in solution, i, using the concentration of
the ion c i and the formal charge or charge number, z i. The charge number for a general
x+
y−
cation M is x and for a general anion X is −y. For a 1:1 electrolyte where x=1 and y=1,
I is equal to the solution concentration, c. For electrolytes where x and/or y are greater
than 1, I>c, which reflects the greater electrostatic interaction of ions of higher charge
with other ions.

Calculation of activity coefficients

When the electrostatic interactions between ions and counterions are relatively weak
compared with their thermal energy, k BT (i.e. at low dilution), the distribution of ions and
potential at any distance from any ion can be calculated. The effect on the energy of the
system of the electrostatic interactions that result can then be quantified. This procedure
results in the Debye-Hückel law:

−3
which can generally be applied to solutions of I≤0.01 mol dm (for which this
assumption of relatively weak electrostatic interactions holds). A is a constant for a given
solvent (0.509 for water at 298 K), B is a constant for a given ion in a given solvent
(conveniently B is often approximately equal to 1 for most ions in water) and is the
−3
standard ionic strength (defined as being equal to 1 mol dm ). This allows the mean
activity coefficient, γ ±, to be calculated for a salt M y X x, where