Spectrophotometric Determination of the Equilibrium Constant of a Reaction

The experiment determined the equilibrium constant for the formation of the FeSCN2+ complex. Using a spectrophotometer, the absorbance of FeCl3, KSCN and HCl standard solutions of known concentration was measured and graphed to determine the absorptivity coefficient. This coefficient was then used to calculate the actual concentrations of the FeSCN2+ complex. Having the initial concentration of Fe3+ and SCN- ions along with the complex, the equilibrium constant can be determined.

INTRODUCTION
The equilibrium constant (Keq) relates the concentrations of the reactants and products in a reaction in equilibrium. However, the Keq cannot be determined with calculations because only the concentrations of reactants are known. By using a spectrophotometer, the products’ properties can show the concentration of the product using Beer-Lambert’s Law, which relates Absorbance and concentration.

METHODOLOGY

250 ml of 0.1M HCl, 100 ml of 0.002M KSCN and 100 ml of 0.002M FeCl3 was prepared. These were separated into two sets of solutions, standard and analysis, with varying combinations of concentration (see table 1). Standard 5 has the most concentration of the analyte FeSCN2+ and is used as the standard for maximum absorption. The wavelength used that will yield the maximum absorption of standard 5 was recorded and is to be used in all subsequent solutions. First, we cleaned the cuvette (container of solution to be analyzed by the spectrophotometer). We rinsed it with water, rinsed it with standard blank and then filled it to the brim with the same. We placed it in the spectrophotometer and set it to autozero.

This is the blank, and its purpose is gauge the absorbance of the solvent alone, without FeSCN2+. By determining the wavelength at which the constituents of the solvent is fully detected, we can set a “zero value” where at this wavelength reading only the solvent is detected and zero molars of FeSCN2+ is detected. From this point we can get an absorbance for and only for FeSCN2+ without accounting for the solvent because we set it at a wavelength beyond the absorbance of the solvent. It is important to use the entire solvent (including FeCl3 and HCl) as the blank and not just water, because these also have a detectable absorbance that may be interpreted as the absorbance of the analyte.

See Appendix Table A3 for details

From these data, and value for ε can be found.

Knowing the molar absorptivity coefficient, we can directly determine the concentration of FeSCN2+ for the standards, without making assumptions; herein lies some of the limitations of Beer-Lambert’s Law. It is unlikely for the production of FeSCN2+ to consume all of the SCN-. This would mean some color might be cause by the reactants and not the products. Another inconsistency is that too much concentration of FeSCN2+ might cause it to react with the solvent thus altering its ability to absorb and reflect light.

CONCLUSION AND RECOMMENDATIONS
Beer-Lambert’s Law can be used to determine the Keq of a reaction forming a substance that produces a distinguishable color. We repeated the same procedure in recording absorbances for the analysis, but still using the wavelength recorded from standard 5. (See table 1)

RESULTS AND DISCUSSION
In order to find the equilibrium constant, we must know the concentration of the reactants and products in reaction. A beam of white light is a bundle of photons moving in different wavelengths. From 380nm to 740nm, the light can be sensed by the naked eye as colors. A spectrophotometer shines a beam of light on a sample. If the sample has particular color, say red, the red color is created by absorbing particular wavelength from the beam of light. The non-absorbed wavelengths are read by the device, and the sample’s absorbance of light can be determined. According to Beer-Lambert’s Law, the absorbance (A) can be related to the path length (b) which is distance the light will travel through the sample (or the cross-sectional distance of the cuvette, the molar concentration (c) of a particular substance in solution, and the molar absorptivity coefficient (ε) of the substance in equation:

A=εbc Kc = [FeSCN2+] / [Fe3+][SCN-]

The combination FeCl3, KSCN and HCl, yields a net ionic equation of Fe3+ + SCN- -> FeSCN2+. Although HCl has no effect of the reaction process, it was added to make sure the reaction proceeded fully to form as much of the analyte FeSCN2+ as possible. It was chosen specifically because it is a strong acid that dissociates easily in water. The free H+ will help dissociate FeCl3 and KSCN without affecting the reaction because Cl- is already present in the reaction.

We use a set of solutions (analysis) to determine ε. Using the limiting reactant SCN-, it was assumed that there was 100% yield of FeSCN2+. Since they have a 1:1 stoichiometric ratio, the concentration of FeSCN2+ was assumed to be the same as that of SCN-. FeCl3 is used in several different volumes to see the trend as concentration is increased, starting with 0 ml.

REFERENCES

* Silberberg M.. Principles of General Chemistry: 2nd Ed. Mcgraw-Hill Companies Inc., New York. 2010 * Humphrey, Baird, Robinson. Chemistry. Allyn and Bacon Inc, Massachusetts. 1986 * Oppapers.com, 2011, June 12, http://www.oppapers.com/essays/The-Spectrophotometric-Determination-Of-An-Equilibrium/580874 * Pharmaxchange.info, Akul Mehta, 2012, May 14, http://pharmaxchange.info/press/2012/05/ultraviolet-visible-uv-vis-spectroscopy-%E2%80%93-limitations-and-deviations-of-beer-lambert-law/