Chemistry Laboratory #3: Spectrophotometric Determination of an Equilibrium Constant

*Adapted from "Chemistry in the Laboratory", 4th ed., J. L. Roberts, Jr., J. L. Hollenberg and J. M. Postma, Freeman, 1997.

January 23, 2001

Purpose: The objective of this lab is to measure the equilibrium constant for the formation of [Fe(H₂O)₅(SCN)]²⁺.

Introduction: To measure an equilibrium constant it is necessary to ascertain the concentrations of all species appearing in the equilibrium expression. This can be done by a variety of means such as titration, spectroscopy, or by other instrumental techniques. It is often the case that one of the species is more easily measured than the others however. When this is true, it is sometimes possible to calculate the concentrations of the remaining species using the stoichiometric relationships that exist in the balanced reaction.

In this experiment you will study the following reaction:

In this reaction the reactants are colorless but the product is an orange-red color. Thus the concentration of the product is easily measurable by absorbance spectroscopy and the applications of Beer's Law. Because the reactants are colorless, we will calculate the concentrations of both reactants using the mass balance.

You will prepare a series of solutions prepared from solutions of known concentration of Fe³⁺ and SCN^-. Assuming that no other reactions are taking place to an appreciable extent, a statements of the mass balance for both reactants is:

Since you will know the volumes and concentrations of the Fe³⁺ and SCN^- solutions used to prepare each solution, you will be able to determine the total concentrations of both species. Using Beer's Law, you will also be able to measure the concentration of Fe(H₂O)₅(SCN) ²⁺. You can then calculate [Fe(H₂O)₆³⁺] and [SCN^-] and calculate the value of K for each solution.

Procedure. Label a series of nine test tubes and prepare nine solutions of by varying the amounts of iron and thiocyanate in a mixture, as listed in the table below. (Be careful, each solution is also 0.5 M nitric acid) Use a buret to deliver the solutions to the nearest tenth of a milliliter. The analysis that follows requires that the total number of moles delivered be the same in each solution (mol_Fe + mol_SCN = 3.00 ´ 10^-5), so measure the volumes carefully. Thoroughly mix the solutions to ensure uniformity.
 

Using deionized water as a reference, measure the absorbance spectrum of each solution individually. Save the solutions until the analysis is complete - this is so you can reanalyze the solutions if you suspect the validity of some of your measurements. Finally, measure the absorbance of the 0.003 M Fe(NO₃)₃ solution and the 0.003 M KSCN solution at 450 nm. Record these values in your notebook.

After Part 1 is complete, pour all of the solutions in a beaker, neutralize with sodium bicarbonate and dispose down the drain.
 

Analysis.

Part 1: Plot the absorbance at 450 nm as a function of mole fraction of Fe³⁺, c_Fe. The mole fraction of Fe³⁺ is simply the number of moles of the iron (III) ion divided by the total number of moles in the solution, i.e., moles Fe³⁺ plus moles SCN^-.  Thus, the range on the x-axis will be from 0 (the pure SCN^- solution) to 1 (the pure Fe³⁺ solution). Include the plot in your final report.

Part 2: Graphical Estimation of the Equilibrium Constant. Calculate the concentration of [Fe(H₂O)₅(SCN)²⁺] for each solution. Use Beer's Law, where e = 4700 M^-1cm^-1 and b, the pathlength, is 1 cm, you can determine the concentration of the iron (III) thiocyanate. Note that this only works because the Fe³⁺ and the SCN^- are both colorless. If they were to absorb light, this analysis would be incorrect because the total absorbance would be due to multiple compounds.

Prepare a plot of [Fe(H₂O)₅(SCN)²⁺] as a function of mole fraction of c_Fe. It should be possible to find the best-fit curve that describes the behavior of the function. Do this using a least-squares approach on Excel as described in class. Superimpose the best fit curve on the data, using enough calculated points to give a smooth curve. Report the "optimized" value of the equilibrium constant.

Part 3. Calculate the value of K for each individual solution. Evaluate the value of the equilibrium constant, K, by using the known initial concentrations of Fe³⁺ and SCN^- and the measured concentration of iron thiocyanate complex. This is done as follows:
 

[Fe(SCN)²⁺]. Use the concentrations found above for each solution.

[Fe³⁺]. The equilibrium iron concentration is equal to the initial concentration minus the concentration of iron thiocyanate that forms during the reaction.

Note that the initial concentration of iron will not be 0.00300 M; you need to calculate the iron concentration for each sample you prepare using v₁c₁=v₂c₂.

[SCN-]. This can be calculated in the same manner as the iron. Thus,

[SCN^-]_eq =  [SCN^-]_initial - [Fe(SCN)²⁺]_eq