Spectrophotometric Determination of Equilibrium Constants
Beer-Lambert Law
The foundation for relating absorbance to concentration is the Beer-Lambert Law: A = εbc, where A is absorbance, ε is the molar absorptivity (a constant specific to the substance and wavelength), b is the path length of the light through the sample, and c is the concentration of the absorbing species.
Equilibrium Constant and Absorbance
For a reaction at equilibrium involving colored species, the equilibrium constant (Keq) can be determined spectrophotometrically. The absorbance of the solution at equilibrium is directly related to the concentrations of the reactants and products. By measuring the absorbance at a suitable wavelength, the concentrations of the absorbing species can be calculated using the Beer-Lambert Law. These concentrations can then be substituted into the equilibrium expression to calculate Keq.
Experimental Procedure Considerations
- Wavelength Selection: Choose a wavelength at which one species absorbs significantly more strongly than others involved.
- Calibration: A calibration curve (absorbance vs. concentration) for the absorbing species is crucial for accurate concentration determination.
- Stoichiometry: The balanced chemical equation is essential for constructing the correct equilibrium expression.
- Temperature Control: Maintaining a constant temperature is important because equilibrium constants are temperature dependent.
- Blank Correction: The absorbance of the solvent or any non-reacting components should be subtracted from the measured absorbance.
Determining Keq from Absorbance Data
For Single Absorbing Species
If only one species absorbs significantly at the chosen wavelength, the equilibrium concentration can be calculated directly from absorbance using the Beer-Lambert Law, and then used to calculate the equilibrium constant.
For Multiple Absorbing Species
If multiple species absorb at the chosen wavelength, a more complex approach is required. This might involve using multiple wavelengths or applying simultaneous equations based on the Beer-Lambert Law for each absorbing species to solve for the individual concentrations. Analysis techniques such as matrix algebra might be needed for more intricate reaction systems.
Limitations
The accuracy of the spectrophotometric method depends on several factors, including the linearity of the Beer-Lambert Law, the accuracy of absorbance measurements, and the purity of the samples. Deviations from the Beer-Lambert Law at high concentrations can also introduce error.