Spectrophotometric Determination of the Equilibrium Constant of a Reaction

Date Performed: January 6, 2011

ABSTRACT

The objective of the experiment was to determine the equilibrium constant of the reaction forming ferric thiocyanate through the use of Spectrophotometry. For the calibration, five standard solutions were prepared, then their respective absorbance values that were obtained through the use of the spectrophotometer, were plotted versus the concentration of the analyte so that a calibration curve would be obtained. The calibration curve was then used to determine the molar absorptivity coefficient. The unknown solutions were then tested, resulting in absorbance values. The molar absorptivity coefficient obtained in the calibration curve and the absorbance values were used to determine the equilibrium concentrations of all the species involved in the reaction. These concentrations were then used to calculate the equilibrium constant. An equilibrium constant of 54.0 was found. Compared to the literature value of 890 there was a 177.11% difference. Even if there was a high percent difference, this was enough to prove that spectrophotometry can be used to determine the equilibrium constant of a given reaction.

INTRODUCTION

In this experiment spectrophotometry was used which involves an instrument called a spectrophotometer. A spectrophotometer is a light measuring device that measures intensity as a function of the light source wavelength. The amount of light that had passed through the system is called the transmittance. The amount of light absorbed by the system is called the absorbance. However, the absorbance of [Fe(SCN)]2+ is the one that the experiment is concerned with.

The concept of the Q, the reaction quotient is needed. There are infinitely many Q’s for a given reaction. The reaction quotient at state where the rate of the forward reaction and the reverse reaction are equal is called the Keq. The equal reaction rates means equal production of products and reactants which would result in constant ratio of products and reactants, thus there is only one Keq for a given reaction.

In the first part of the experiment, calibration was performed. Calibration was done by testing five standard samples with known [Fe(SCN) 2+]eq with a spectrophotometer to get their absorbances. A calibration curve was then constructed. The calibration curve was obtained when the values of the equilibrium concentrations of [Fe(SCN)]2+ and their respective absorbance values were plotted. After obtaining the calibration curve, linear regression was used to find the equation of the best fit line of the plot of the points. The εb is the slope m of the best fit line, absorbance is the y value, and the equilibrium concentration is the x value.

In the next part of the experiment, absorbance readings from five unknown solutions (with unknown [Fe(SCN)2+]eq’s) were taken. The [Fe(SCN) 2+]eq was obtained by substituting the absorbance to the equation of the best fit line. Then [Fe(SCN)2+]eq was then subtracted from the initial concentrations of Fe3+ and SCN- to get their respective equilibrium concentrations. The main objective of the experiment was to find the equilibrium constant of the reaction:

[1] Fe3+ + SCN- ↔ [Fe(SCN)]2+

Equation 1 produces a blood red complex. To determine this equilibrium constant, the following equation was used:

[2] Keq = [Fe(SCN)2+]eq/ [Fe3+]eq[SCN-]eq

RESULTS AND DISCUSSION

There are two existing light sources within a UV-VIS spectrophotometer, one for each (UV and visible light) spectrum. The usual light source used to generate visible light is the tungsten-halogen lamp emitting 200-340 nm wavelengths (Boyer, 1993). The UV source can be either a high-pressure hydrogen lamp or deuterium lamp. When measuring absorbance at the UV spectrum, the other lamp has to be turned off. The same goes when measuring visible light absorbance. This is to prevent interference of unnecessary wavelengths in the incident light on the sample. Following the light source is a monochromator, the purpose of which is to filter light and select a specific wavelength by using either a prism or a diffraction grating. After the monochromator is a series of lenses, slits, mirrors, and filters that act as an optical system to concentrate, increase spectral purity of, and direct monochromatic light towards the sample chamber with cuvettes containing solutions to be tested. However, since the instrument has only a single beam, every time the wavelength has to be changed a blank reading must precede any sample reading. The light-sensitive detector follows the sample chamber and measures the intensity of light transmitted from the cuvette and passes the information to a meter that records and displays the value to the operator on an LCD screen. There are two general designs of spectrophotometers, single-beams and double-beams. When using any kind of spectrophotometer, one must perform auto-zero.

The absorbance measured from the spectrophotometer can be related to the concentration of the analyte by the Beer-Lambert’s Law (Beer-Lambert-Bouguer’s Law):

[3] A = εbC,

Where:

A = measured absorbance

ε = wavelength – dependent molar absorptivity coefficient

b = path length (cm)

C = molar concentration

The linearity of the Beer-Lambert law’s is limited by chemical and instrumental factors alike. Hence, there are deviations from the law on certain conditions, here are some: