Principles of Beer-Lambert Law and Voltammetry

The Beer-Lambert Law

The Beer-Lambert law describes the linear relationship between the absorbance of light and the concentration of an absorbing species. The relationship is defined by the formula: A = εlc, where:

• A is the absorbance (unitless).
• ε is the molar absorptivity or extinction coefficient.
• l is the path length of the light through the sample.
• c is the concentration of the absorbing species.

This law establishes a direct correlation between absorbance and concentration under specific conditions, such as using a dilute solution and monochromatic light. It is a fundamental principle used for quantitative analysis in methods like UV-Vis spectroscopy and infrared spectroscopy. In a linear calibration plot where the path length is 1 cm, absorbance (A) is the dependent variable ('y'), and the molar absorptivity (ε) represents the slope, allowing for the determination of an unknown concentration.

Limitations of the Law

Despite its utility, the Beer-Lambert law has several limitations and potential sources of deviation:

• High Concentrations: The law assumes a linear relationship, but deviations often occur at high concentrations due to molecular interactions.
• Polychromatic Radiation: The law is strictly valid for monochromatic light; using a wider band of wavelengths can cause non-linearity.
• Interference: The law is designed for solutions with a single absorbing species. Real-world samples may contain multiple species, leading to interference.
• Environmental Factors: The relationship may not hold true if temperature and pressure change significantly.
• Other Effects: Accuracy can also be impacted by light scattering effects, instrumental limitations, chemical interferences, and variations in path length.

Awareness of these constraints is crucial, and corrections or alternative methods may be necessary in specific situations.

Voltammetry

Voltammetry is an electrochemical method that applies a constant and/or varying potential at an electrode's surface and measures the resulting current with an electrode system. This technique can reveal the reduction potential of an analyte and its electrochemical reactivity. In practical terms, this method is non-destructive because only a very small amount of the analyte is consumed (electrolytically reduced or, less commonly, oxidized) at the two-dimensional surface of the electrodes.

Electrode System

• Working Electrode (WE): This is where the redox activity of interest occurs. Common materials include Platinum (Pt), Gold (Au), Silver (Ag), Carbon (C), semiconductors, and Mercury (Hg), which is effective for reductions in water.
• Auxiliary Electrode (AE): Also known as the counter electrode, it catches the current flow from the WE to complete the circuit. It is typically made of similar materials as the WE but has a larger surface area.
• Reference Electrode (RE): This electrode maintains a constant potential and is used to establish the potential of the WE. A common example is the Silver/Silver Chloride (Ag/AgCl) electrode.

Quantitative Analysis Methods

Common methods for quantitative analysis using voltammetry include:

• Direct calibration method
• Standard addition method
• Internal standard method