beer's Law

Meaning: Beer's law (often called the Beer–Lambert law) relates how much light a sample absorbs to how much absorbing substance the light passes through. More absorbing molecules in the beam, from higher concentration or a longer path, means more light absorbed. In UV-Vis spectroscopy, this lets you find an unknown concentration from a measured absorbance. Each compound has its own molar absorptivity at a given wavelength, so measurements are usually made at λmax, where absorbance is greatest and sensitivity is best.

Equation: A = εlc, where A is absorbance (unitless), ε is molar absorptivity (L·mol⁻¹·cm⁻¹, or m²/mol in strict SI), l is path length (cm, or m in SI), and c is concentration (mol/L, or mol/m³ in SI). Also A = −log(T), where T is transmittance, the fraction of light that passes through (unitless).

On the MCAT: A passage gives a calibration curve of absorbance versus concentration for standards. You read off an unknown's concentration, or predict what happens when you dilute the sample or use a cuvette of a different width. Doubling l or c doubles A. A tenfold drop in transmittance raises A by 1. Questions may also ask why a conjugated compound absorbs in the visible range.

Common confusion: Absorbance is linear in concentration, but transmittance is not. It falls exponentially, as T = 10⁻ᴬ. Beer's law also holds best for dilute solutions, and a calibration plot can curve at high concentration.