Question

The activity of a free ion may be controlled by equilibrium with a solid phase that contains that ion. The activity of Al3+(aq) in equilibrium with gibbsite at pH 4 is 10-5.5. Calculate the change in concentration of Al3+(aq) if the ionic strength of the background solution (dominated by NaCl) shifts from 6 mM (6 x 10-3 M) to 60 mM (60 x 10-3 M).

Answer 1

The activity of any species is defined as the product of the concentration of the species in solution and a solution-dependent activity coefficient.

   (1)

where a_i is the activity of species i and is the acitivity coefficient.

Here, the species of interest is Al³⁺ and we know that

(2)

at pH = 4 in equilibrium with Gibbsite (a mineral form of Al(OH)₃).

The activity coefficients for Al³⁺ can be calculated using the extended Debye-Hueckel equation at the different ionic strengths.

At ionic strength,

(3)

Therefore, (4)

Here z is the charge and alpha is the effective diameter of the hydrated ion in nanometers at 25^oC. The values for the effective diameter is taken from the following article Kielland, J. J. Am. Chem. Soc. 1937, 59, 1675–1678.

Similarly, for ,

(5)

Thus,    (6)

Using the obtained activity coefficients and and the activity of Al³⁺ in the definition of ionic strength in equation (1), we obtain, for an ionic strength of 6 mM,

(7)

(8)

and for an ionic strength of 60 mM,

   (9)

Thus, the change in concentration of Al³⁺ equals

(10)