5.
Two solutions of the same molecule, with concentrations of 10-3 M and 5×10-4 M, are
kept in two different cuvettes with path lengths 1 cm and 2 cm, respectively. If the
absorbance for 1st sample is 1.2, what will be the absorbance for the second sample?
a. 1.0
b. 1.2
c. 2.4
d. 6.0
The Beer-Lambert Law governs how absorbance (A) relates to concentration (c) and path length (l) in spectrophotometry, expressed as A = εcl, where ε is the molar absorptivity constant for the molecule.
For two solutions of the same molecule, the ratio of absorbances simplifies to:
A₂/A₁ = (c₂/c₁) × (l₂/l₁)
A₂/A₁ = (c₂/c₁) × (l₂/l₁)
Problem Breakdown
- First sample: concentration c₁ = 10⁻³ M, path length l₁ = 1 cm, measured absorbance A₁ = 1.2
- Second sample: c₂ = 5×10⁻⁴ M (half of c₁) and l₂ = 2 cm (double l₁)
The concentration halves absorbance contribution, but doubled path length compensates exactly, yielding A₂ = 1.2 × 0.5 × 2 = 1.2.
Option Analysis
a. 1.0: Incorrect; underestimates by ignoring path length increase, as if l₂ = 1 cm (yielding 1.2 × 0.5 = 0.6, not matching).
b. 1.2: Correct; concentration halves but path length doubles, maintaining A₂ = A₁ per Beer-Lambert proportionality.
c. 2.4: Wrong; assumes path length effect without concentration reduction (1.2 × 2).
d. 6.0: Invalid; confuses factors like doubling both without halving concentration first.
