Undergraduate · 20 min

Beer–Lambert law: calibrating UV-Vis absorbance

Measure how the absorbance of a KMnO₄ solution grows linearly with concentration and path length, then read an unknown concentration straight from the calibration line.

Goal

State A = ε·l·c, explain the role of each factor, and use a calibration line to convert a measured absorbance into a concentration.

Apparatus and reagents

A stock solution of potassium permanganate, volumetric flasks for dilutions, 1 cm (and 0.5 cm) quartz or glass cuvettes and a UV-Vis spectrophotometer set near 525 nm.

Procedure

Select the standard conditions (1.0 cm cell, ε ≈ 2 250 L·mol⁻¹·cm⁻¹ at 525 nm) and note that the calibration line passes through the origin.
Hover the line: absorbance equals slope times concentration, so any measured A maps to one c — this is how an unknown is dosed.
Switch to the 0.5 cm cell: the slope halves because A is proportional to path length — doubling the path doubles the absorbance at fixed c.
Switch to the wavelength where ε is larger: a bigger molar absorptivity makes the line steeper, which means better sensitivity at low concentrations.

What to observe

Every line goes through the origin: at c = 0 there is nothing to absorb, whatever the cell or the wavelength.
Steeper slope = larger ε·l product: the same concentration gives a stronger signal, up to the detector’s linear range.

Explanation

The Beer–Lambert law A = ε·l·c is linear because each absorbing molecule removes the same fraction of photons: absorbance is additive in both thickness and concentration. It fails at high concentration (molecular interactions, stray light, polychromatic beams), which is why real calibrations stay below A ≈ 1–2.

History of the experiment

Pierre Bouguer in 1729 and Johann Heinrich Lambert in 1760 first noted that light loss grows geometrically with the thickness traversed; August Beer showed in 1852 that the absorbing species’ concentration plays the same role. Merged as the Beer–Lambert (or Bouguer–Beer–Lambert) law, it turned spectroscopy into the workhorse quantitative tool of the analytical laboratory.

Chemists behind it

Robert Bunsen