Q.33 The absorbance of a solution of tryptophan measured at
280 nm in a cuvette of 2.0 cm path length is 0.56 at pH 7.
The molar extinction coefficient (ε) for tryptophan at 280 nm is
5600 M^-1cm^-1 at pH 7.
The concentration of tryptophan (in µM) in the solution is ________

Tryptophan concentration is calculated using the Beer-Lambert law, yielding 50 µM for the given conditions. This value aligns with standard biochemical principles for amino acid quantification at 280 nm.

Beer-Lambert Law Basics

Absorbance (A) relates to concentration (c) via A = ε × c × l, where ε is the molar extinction coefficient (5600 M⁻¹cm⁻¹) and l is path length (2.0 cm). Rearrange to c = A / (ε × l) = 0.56 / (5600 × 2) M. This computes to 5 × 10⁻⁵ M, or 50 µM.​

Step-by-Step Calculation

First, compute ε × l = 5600 M⁻¹cm⁻¹ × 2.0 cm = 11,200 M⁻¹. Then, c = 0.56 / 11,200 = 0.00005 M = 50 µM. At pH 7, tryptophan’s ε remains valid as stated, ensuring accurate protein/amino acid quantification via UV spectroscopy.​

Options Analysis

Options: a) 30 µM, b) 40 µM, c) 50 µM, d) 90 µM.

• a) 30 µM errors from ignoring path length (c = 0.56 / 5600 ≈ 0.0001 M or 100 µM, halved wrongly).

• b) 40 µM mismatches arithmetic (e.g., using ε=7000).

• c) 50 µM correct per exact formula.

• d) 90 µM assumes 1 cm path (0.56 / (5600 × 1) × 10⁶ / 20 wrongly adjusted).​