Which of the following is a direct expression of Beer's Law relating absorbance to concentration and path length?

• A. A = abc
• B. A = 2-log%T
• C. A = log (100/%T)
• D. Abs of unknown / Abs of standard = Conc of unknown/ Conc of standard

Answer: (A)

Beer's law shows how absorbance scales with how much solute is present and how far the light travels through the sample. The direct expression is A = εbc, where ε is the molar absorptivity, b is the path length, and c is the concentration. If you simplify by renaming ε as a, it becomes A = abc, which is exactly the form that directly ties absorbance to concentration and path length.

The other ways of writing it come from rearranging or reframing the same idea. Expressing absorbance in terms of transmittance uses A = -log T, and when you work with percent transmittance (%T) you get A = log(100/%T). That still follows Beer's law but relates A to how much light passes through rather than directly to concentration and path length. The ratio form, Abs unknown / Abs standard = Conc unknown / Conc standard, follows from Beer's law when ε and b are the same for both measurements; it’s a useful comparative relation but not the direct expression linking A to c and b.