Beer-Lambert Law

Applied Science: BTEC Level 3 National Extended Diploma, topic 2.2.2

The Beer-Lambert Law

The Beer-Lambert law tells us about the absorption of light by a solution.

The Beer-Lambert law gives the equation for the absorption of light $A$ as:
$A = \epsilon bc$
Where $\epsilon$ is the molar absorptivity of the solution, $b$ is the path length of the light as it moves through the solution, and $c$ is the concentration of the solution.

The molar absorptivity $\epsilon$ is a measure of how much a particular wavelength of light is absorbed by one mole of a substance.

The single largest application of the spectrophotometer is for quantitative analysis.
The prerequisite for such analysis is a known absorption spectrum of the compound under investigation.
Of particular importance is the maximum absorption (at λmax), which can be easily obtained by plotting absorbance vs. wavelength at a fixed concentration.
Next, a series of solutions of known concentration are prepared and their absorbance is measured at λmax.

Plotting absorbance vs. concentration, a calibration curve can be determined and fit using linear regression (least-squares fit).
An unknown concentration can be deduced by measuring absorbance at the absorption maximum and comparing it to the standard curve.
Caution: The Beer-Lambert Law is only obeyed (the standard curve is linear) for reasonably dilute solutions.
Only those points in the linear range of the standard curve may be used for accurate concentration determination.

Typical results are shown in the table for the absorbance of [Ti(H₂O)₆]³⁺ measured at 490 nm.

After plotting absorbance vs concentration, we can see that if a solution has a measured absorbance of 0.450 its concentration is 1.5 mg/mL.