2: Determination of an Equilibrium Constant

PURPOSE

• To apply LeChatelier’s Principle to manipulate reaction conditions and drive the formation of iron(III) thiocyanate to determine its maximum concentration.
• To use spectrophotometry and Beer's Law to determine the concentration of \( \ce{ Fe(SCN)^{2+}} \) in solution and calculate the proportionality constant, k.
• To construct and analyze a calibration curve by plotting absorbance versus concentration and interpret the slope to support quantitative analysis of equilibrium mixtures.
• To calculate equilibrium concentrations of \(\ce{Fe^{3+}}\), \(\ce{SCN-}\), and \( \ce{ Fe(SCN)^{2+}} \) and use these values to determine the equilibrium constant, K_c, for the reaction.

INTRODUCTION

This experiment will allow you to determine the equilibrium constant for the formation of iron(III) thiocyanate, \( \ce{ Fe(SCN)^{2+}} \). Moreover, the experiment will require you to use LeChatelier's principle. When the reaction between iron(III), \(\ce{Fe^{3+}}\), and thiocyanate, \(\ce{SCN-}\), in aqueous solution comes to equilibrium, the system consists of the reactants and iron(III) thiocyanate. The chemical equation for this reaction is

\[ \ce{Fe^{3+}(aq)}\ +\ \ce{SCN-(aq)} \rightleftharpoons \textcolor{red}{\ce{ Fe(SCN)^{2+}(aq)}}\]

colorless colorless blood-red

The product is a complex ion that has a coordinate covalent bond between the iron(III) ion and an atom from the thiocyanate anion. The blood-red color of this complex ion is so intense that thiocyanate ions can be used to detect very small quantities of iron(III). Interestingly, iron(III) thiocyanate appears to exist solely in solution. Solid compounds containing this ion have never been isolated.

The objective of the experiment is to determine the equilibrium constant for this reaction. The equilibrium constant is given by the expression:

\[ K_{\text{c}} = \frac{ \left[ \ce{Fe(SCN)^{2+}} \right]_{\text{eq}} }{ \left[ \ce{Fe^{3+}} \right]_{\text{eq}} \left[ \ce{SCN^-} \right]_{\text{eq}} } \]

where the concentrations of the substances are at equilibrium. \( K_{\text{c}} \) can be calculated easily if these equilibrium concentrations are determined.

Because the reactants are essentially colorless, whereas the complex ion is deeply colored, you will use a spectrophotometer to monitor the absorbance due to the complex ion without interference from the reactants. The absorbance (\(A\)) is proportional to the concentration (\(c\)) of the species that absorbs the light (in this case, iron(III) thiocyanate) according to Beer's law,

\[ A = kc \]

where \(k\) is a proportionality constant. After the concentration of iron(III) thiocyanate has been measured by way of the absorbance, the concentrations of the reactants can be inferred from their starting concentrations and the concentration of the complex ion.

There is a problem, however. To determine the proportionality constant, \(k\), we must measure the absorbance of a series of solutions with known amounts of the complex ion. How can known amounts of iron(III) thiocyanate be obtained? After all, this substance is an active participant in the equilibrium with iron(III) and thiocyanate. Stoichiometric quantities of the reactants will not yield a known amount of the product.

This difficulty can be avoided by using LeChatelier's principle. LeChatelier's principle states that when more of a reactant is added to a system at equilibrium, the equilibrium will shift to produce more products. As more of the same reactant is added, even more of the product forms. It is possible to add so much of one reactant that essentially all the other reactant is converted to the product. You will use limiting quantities of thiocyanate and large amounts of iron(III) to achieve this result. The amount of iron(III) thiocyanate that is formed will then be essentially identical to the starting amount of the limiting reactant, the thiocyanate.

This experiment can be described briefly as follows. You will prepare a series of solutions with known concentrations of iron(III) thiocyanate. You will measure the absorbances of these solutions at a wavelength near 450 nm, the wavelength of maximum absorbance. When these absorbances are plotted against the concentrations of iron(III) thiocyanate, \(k\) (Beer’s Law constant) can be determined from the slope of the straight line. You will then measure the concentration of iron(III) thiocyanate produced under several different conditions in which substantial amounts of the reactants and the product are present. The equilibrium constant, \( K_{\text{c}} \), for the reaction can be calculated from the concentrations of reactants and the product for each of the different conditions.