# Spectrophotometric Determination of the Ligand/metal Ratio and Kf in a Complex Ion

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Spectrophotometric Determination of the Ligand/Metal Ratio and Kf in a Complex Ion

Objectives: Three methods of spectrophotometric techniques were used in this experiment to determine the ligand: mole ratio for coordinate compounds in solution. The three methods used included the Mole Ratio Method, the Slope Ratio Method, and JobÐŽÐ‡s Method of Continuous Variation. JobÐŽÐ‡s Method was used to determine the stability constant, Kf, for the reaction. The Slope Ratio Method was used to determine the molar absorptivity, ¦Ð*, for the ligand-metal complex.

Introduction: Transition metals form coordinate covalent bonds with Lewis bases to make coordination complexes. The anion or neutral compound reacting with the metal are called ligands. A general reaction for the formation of the complex follows:

One of the characteristics of transition metal complexes is that they absorb light in the visible region of the spectrum. The instrument used for analysis is a spectrophotometer. The instrument works by passing a beam of light through a cuvette, which contains the solution in a closed chamber. The beam passes through the sample and into a detector. The detector measures the intensity of the light that was passed through the solution, as a measurement of percent transmittance. Photons are passed through the solution and the absorbing species transitions to a higher energy state. Because the species is in and excited state and unstable, the photons are then released and the species returns to the ground energy state. Photons are released randomly from the absorbing species, which means as the concentration of the absorbing species increases, the amount of photons reaching the detector decreases. The equation to convert transmittance to absorbance is:

Spectrophotometric analysis and the application of BeerÐŽÐ‡s Law were used to determine the ligand: mole ratios, molar absorptivity, and the stability constant for the reaction. According to BeerÐŽÐ‡s Law, absorbance is proportional to the product of the molar absorptivity constant, the path length, and the concentration of the absorbing species. The equation is as follows:

Where: ¦Ð* = molar absorptivity, M-1cm-1

¦Ð'= path length, cm

C= concentration of absorbing species

The absorbance of the species can now be used in BeerÐŽÐ‡s Law expression, which in turn can be manipulated to calculate the stoichiometric coefficients of a reaction, ¦Ð*, for the absorbed species, and Kf of the reaction.

In Part A of the experiment the Mole Ratio and Slope Ratio methods were used to determine the ligan/metal ratio. The stoichiometric coefficients for the metal (Fe(III)) and ligand (1,10-phenanthroline), were determined using the Mole Ratio Method. For the Mole Ratio method, multiple solutions were prepared. The concentrations of the metal were constant while the ligand concentrations were varied. At lower concentrations of ligand there were insufficient amounts to form maximum amounts of complex; the ligand was the limiting reagent. As the concentration of ligand was increased, so did the absorbance of the complex. The absorption will increase until the stoichiometric amount ligand has been added for a specific amount metal. Once the stoichiometric amount of ligand was added the absorbance of the complex will plateau. The point where the two linear portions of the graph intercept is the stoichiometric ratio of ligand/metal (b/a).

In the Slope Ratio method the absorbance was measured with the ligand concentration being held constant in one trial, and the metal concentration being held constant in the other trial. According to BeerÐŽÐ‡s Law, when the absorbance is plotted as a function of the ligand concentration, with excess metal, a linear relationship is obtained. The slope of the plot is represented by the following equation:

With ligand limiting

Where b represents the stoichiometric coefficient of the ligand. When the absorbance is plotted as a function of the metal concentration, with excess ligand, a linear relationship is obtained again. The slope of this plot is represented by the following equation:

With metal limiting

Where a represents the stoichiometric coefficient of the metal. Since ¦Ð* and ¦Ð' are in both relationships, they cancel out and leave the following relationship:

After determining the stoichiometric coefficients, BeerÐŽÐ‡s Law was rearranged to calculate the experimental value of ¦Ð*.

In Part B, JobÐŽÐ‡s Method of Continuous Variation was used to calculate the stoichiometric coefficients of the metal and ligand, and to calculate the stability constant, Kf, for the formation of the complex. The equation for the formation of the complex is shown below:

The procedure called for two solutions that varied the concentrations of the metal and ligand, but the formal concentrations remained constant. The highest concentration of the complex was determined when the absorbance was plotted as a function of the mole fraction of thiocyanate. The stoichiometric coefficient was calculated using:

The value of XSCN- can then be determined by fitting the data with a second order polynomial curve and then differentiating the absorbance with respect to XSCN-. Once the mole fraction of the thiocyanate is calculated, the maximum absorbance value can be determined by substituting its value back into the polynomial equation. By knowing the stoichiometric coefficients, the value of Kf can be calculated using the following equation:

In order to solve the previous equation for Kf, the concentration of the complex has to be calculated. By taking to sets of data point, 0-3 and 10-7, from the JobÐŽÐ‡s Method plot, and fitting them with a linear curve, the two lines should intersect at the x-value of the maximum experimental absorbance. This value is a representative of the theoretical maximum absorbance, which would occur if the reaction went to completion. Because the reaction is in equilibrium, the theoretical maximum absorbance will be greater than the experimental

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