3.11 Beer-Lambert Law

What the Beer-Lambert Law says

The Beer-Lambert Law relates how much light a solution absorbs to its concentration: A = εbc, where A is absorbance (unitless), ε is the molar absorptivity (L/mol·cm, constant for a given substance/wavelength), b is the path length (cm), and c is concentration (mol/L). Absorbance increases linearly with concentration.

Using absorbance to find concentration

A spectrophotometer measures absorbance of light passing through a colored solution at a specific wavelength (usually where absorbance is maximized). By preparing solutions of known concentration, plotting a calibration curve of A vs. c, and finding the line's slope (εb), you can determine the concentration of an unknown sample from its measured absorbance.

Practical considerations

Since A = εbc is a straight line through the origin, doubling concentration doubles absorbance (at constant b). Solutions that absorb too strongly (very high A) fall outside the linear range and must be diluted before measurement. Path length and wavelength must stay constant when comparing samples.

Key terms

Beer-Lambert Law equation

A = εbc, relating absorbance (A) to molar absorptivity (ε), path length (b), and concentration (c).

Molar absorptivity (ε)

A constant specific to a substance and wavelength describing how strongly it absorbs light (units: L/mol·cm).

Path length (b)

The distance light travels through the sample, usually the width of the cuvette (cm).

Calibration curve

A plot of absorbance vs. known concentrations used to determine an unknown solution's concentration; slope = εb.

Spectrophotometer

An instrument that measures the absorbance of light by a solution at a specific wavelength.

Try an AP-style question

A = εbc. If concentration doubles, what happens to absorbance?

1. It stays the same
2. It doubles
3. It halves
4. It quadruples