Which equation represents the Beer–Lambert law?

• A. A = ε b c; absorbance is proportional to molar absorptivity ε, path length b, and concentration c.
• B. A = ε b / c; absorbance is inversely proportional to concentration.
• C. A = b / (ε c); absorbance equals path length divided by the product of ε and c.
• D. A = ε + b + c; absorbance is the sum of ε, b, and c.

Answer: (A)

Absorbance increases as more absorbing molecules are present and as light travels longer through the sample, so the law expresses A as a product of those factors. The equation A = ε b c captures this: ε is the molar absorptivity (how strongly the species absorbs at the chosen wavelength), b is the path length the light travels through the sample (in centimeters), and c is the concentration (in mol/L). Because absorbance reflects how much light is removed along the path, doubling either the concentration or the path length doubles the amount of light removed, which in turn increases A and reduces transmitted light (T = 10^(-A)). Forms that involve dividing by concentration or adding the terms would imply the wrong dependence on these factors, so they don’t match the observed linear relation of A with both concentration and path length.