Q15. A solution of a compound shows an absorbance of 0.275 at 275 nm in a cuvette with 0.1 dm light path. The molar absorptivity (ε275 = 4 × 104 M-1 cm-1). The concentration of the compound is ____ × 10-5 M (rounded off to closest integer).
A solution shows an absorbance of 0.4 at 275 nm in a 0.1 dm cuvette, with a molar absorptivity of 4×104 M-1 cm-1. The concentration is 10-5 M.
Beer-Lambert law concentration calculation determines unknown solute levels in spectrophotometry, vital for CSIR NET life sciences. This method uses absorbance (A), molar absorptivity (ε), and path length (b) via A = εbc to find concentration (c).
Problem Breakdown
The query involves a solution with absorbance A = 0.4 at 275 nm wavelength, measured in a 0.1 dm (1 cm) path length cuvette. Molar absorptivity ε = 4×104 M-1 cm-1.
Rearrange Beer-Lambert law for concentration: c = A/(εb).
Substitute values: c = 0.4/(4×104)×1 = 10-5 M, or 0.00001 M.
Step-by-Step Solution
- Convert units: 0.1 dm = 1 cm path length b.
- Compute: εb = 4×104 M-1 cm-1 × 1 cm = 4×104 M-1.
- Then c = 0.4 / 4×104 = 1×10-5 M.
- Round -log₁₀(c) = 5 to nearest integer, so 10-5 M.
Common Options Explained
CSIR NET problems often include distractors:
- 10-4 M: Mistake dividing by ε only (ignores b=1 cm).
- 10-6 M: Error using b=0.1 cm instead of 1 cm.
- 10-3 M: Wrong ε as 4×10³ or absorbance misread.
- Correct: 10-5 M: Matches precise calculation.
Applications in Life Sciences
Beer-Lambert law concentration calculation quantifies DNA/proteins at 260/280 nm in biotech. For CSIR NET, practice verifies linearity (A < 1-2) and units.
Final Answer
Concentration = 10-5 M
