Beer-Lambert Law
The Beer-Lambert law A = elc relates light absorbance to concentration for spectrophotometry analysis.
Learn with examples.
The Formula
The Beer-Lambert law states that the absorbance of light by a solution is directly proportional to the concentration of the absorbing species and the path length of light through the solution. It is the fundamental equation behind spectrophotometry.
The law combines contributions from Pierre Bouguer (1729), Johann Heinrich Lambert (1760), and August Beer (1852). It works well for dilute solutions (typically below 0.01 M) where solute molecules do not interact significantly. At higher concentrations, deviations occur due to molecular interactions.
Absorbance (A) is a logarithmic measure: A = −log(I/I₀), where I₀ is incident light intensity and I is transmitted light intensity. A = 1 means 90% of light is absorbed. A = 2 means 99% is absorbed. This logarithmic relationship allows absorbance to be directly proportional to concentration.
Variables
| Symbol | Meaning |
|---|---|
| A | Absorbance (dimensionless) |
| ε | Molar absorptivity or extinction coefficient (L/(mol·cm)) |
| l | Path length of the cuvette (cm) |
| c | Concentration of the solution (mol/L) |
Example 1
A potassium permanganate solution has ε = 2,455 L/(mol·cm) at 525 nm. A 1.0 cm cuvette gives A = 0.736. What is the concentration?
Rearrange: c = A/(ε × l) = 0.736/(2455 × 1.0)
c = 3.0 × 10⁻⁴ M (0.3 mM)
Example 2
A protein solution at 0.5 mg/mL (MW = 50,000 g/mol) has ε = 35,000 L/(mol·cm) at 280 nm. What absorbance is expected in a 1 cm cuvette?
Convert: c = 0.5 × 10⁻³ / 50,000 = 1.0 × 10⁻⁵ M
A = ε × l × c = 35,000 × 1.0 × 1.0 × 10⁻⁵
A = 0.35
When to Use It
Use the Beer-Lambert law to determine solution concentrations from light absorbance measurements.
- Measuring concentrations in analytical chemistry labs
- Quantifying protein and DNA concentrations in biochemistry
- Monitoring water quality and pollutant levels
- Clinical blood chemistry analysis