Question

In Chapter 6I of Analytical Chemistry 2.1, the author shows two beakers in Figure 6.15 on pg. 242: One is filled with a relatively dark orange iron (III) thiocyanate complex, and one with added supporting electrolyte, resulting in a lighter colored iron (III) thiocyanate complex. The determination of the equilibrium constant for the formation of the iron (III) thiocyanate complex, often performed in general chemistry lab, is shown in the following reaction:

Fe³⁺_(aq) + SCN^–_(aq) ↔ FeSCN²⁺_(aq)

The concentration-based formation constant for this reaction (μ = 1.0 M) has been reported to be 113. Determine the thermodynamic formation constant for the iron (III) thiocyanate complex and support your answer by relating it to the experimental observation in Figure 6.15 on page 242. Assume that the hydrated ion diameter for FeSCN²⁺ is 0.20 nm.

Analytical Chemistry 2.1

http://dpuadweb.depauw.edu/harvey_web/eTextProject/version_2.1.html

Answer 1

To the reaction given:

The expresion for the equilibrium constant based on concentrations is:

and the expresion for the equilibrium constant based on activities is:

Activities are given by the equation:

Substituting it in equation (2) for every specie in the equilibrium:

Rearranging terms:

Notice that the previous equation is:

The activity coefficients for every specie is given by the Debye-Hückel equation:

where Zi is the charge of the ion, and i is the hydrated ion diameter in nanometers.

For Fe(SCN)⁺² we have:

Substituting in equation (4):

For Fe⁺³ we have:

Substituting in equation (4):

For SCN^- we have:

Substituting in equation (4):

Substituting all the activity coefficients in equation (3) we have the thermodynamic formation constant: