Absorbance and Molar Absorptivity

 

Absorbance (A):

• Definition: Absorbance measures the amount of light absorbed by a solution at a specific wavelength. It is a unitless quantity that indicates how much light is absorbed by the molecules in the solution when light passes through it.

• Formula:$$A={\log }_{10}\left(\frac{I_0}{I}\right)$$Where:
  • $A$ = absorbance
  • $I_0$ = intensity of the incident light
  • $I$ = intensity of the transmitted light after passing through the sample
• Beer-Lambert Law: Absorbance is directly proportional to the concentration of the absorbing species and the path length of the light passing through the solution.$$A=ϵ\cdot c\cdot l$$Where:
  • $A$ = absorbance
  • $ϵ$ = molar absorptivity (L·mol⁻¹·cm⁻¹)
  • $c$ = concentration of the solution (mol/L)
  • $l$ = path length of the light through the sample (cm)

Molar Absorptivity (ε):

• Definition: Molar absorptivity, also known as the extinction coefficient, is a constant that relates the absorbance of a solution to the concentration of the absorbing species and the path length. It reflects how strongly a chemical species absorbs light at a given wavelength.
• Units: The units of molar absorptivity are typically L·mol⁻¹·cm⁻¹.
• Dependence: Molar absorptivity depends on the wavelength of light used. Different substances absorb light differently at different wavelengths, and molar absorptivity varies accordingly.
• Significance: A higher molar absorptivity means the substance absorbs more light per unit concentration and path length, while a lower value means it absorbs less.

Key Points:

1. Proportional Relationship: Absorbance increases with an increase in concentration or path length, assuming the molar absorptivity remains constant.
2. Use in Quantification: The Beer-Lambert law is commonly used in spectroscopy to determine the concentration of a solution by measuring its absorbance.
3. Limitations: Deviations from the Beer-Lambert law can occur at very high concentrations due to molecular interactions, changes in refractive index, or scattering effects.

These concepts are widely used in spectrophotometric analysis to understand the interactions between light and matter, especially in chemical, biological, and pharmaceutical studies.