Questions: Beer–Lambert Law and Optical Absorbance

Question 1

A solution has a transmittance of 10% (T = 0.10). What is its absorbance?

• A. 0.10
• B. 0.90
• C. 1.0
• D. 2.3

Answer: (C)

A = -log(T) = -log(0.10) = -(-1) = 1.0. Transmittance and absorbance are related by a logarithm, not linearly. A common error is confusing A = 1 - T, which would give 0.90 — but that formula does not exist in Beer's law.

Question 2

Plotting percent transmittance (%T) versus concentration for a series of standards will produce a straight line if Beer's law holds.

• T. True
• F. False

Answer: False

Beer's law states that ABSORBANCE (A = -log T) is linear with concentration, not percent transmittance. Because A = -log(%T/100), %T varies exponentially with concentration, producing a curve — not a line. Always plot absorbance when verifying Beer's law linearity.

Question 3

Why does Beer's law break down at high analyte concentrations?

Model answer: At high concentrations, solute-solute interactions alter the effective molar absorptivity, and the assumption of independent, non-interacting absorbers fails. Additionally, polychromatic light causes deviations because different wavelengths have different ε values, and the average transmittance becomes nonlinear with concentration.

Beer's law derivation assumes non-interacting absorbers and truly monochromatic radiation. Both assumptions degrade at high concentration. Understanding these deviations is practical: analysts must verify linearity over the calibration range and restrict measurements to the validated linear region.