Chemistry

Problem

A laboratory technician is preparing to quantify a newly synthesized dye. For the chosen analytical wavelength, the dye’s molar absorptivity is

1.87 \times 10^4\,\text{L mol}^{-1}\,\text{cm}^{-1}

. A quartz cuvette with an internal path length of

0.850\,\text{cm}

is employed. A solution that is known to be

3.20 \times 10^{-5}\,\text{M}

in the dye is placed in the cuvette, and its absorbance is recorded. Answer the following. a. Part 1: (a) Calculate the expected absorbance of the solution. Show your work. b. Part 2: (b) The spectrophotometer’s detector is linear only for absorbance values between

0.050

and

1.000

. Based on your calculation in part (a), determine whether the measured absorbance will fall within the instrument’s linear range and justify your answer.

Intuitive explanation

This problem is about Beer's Law, which connects how much light a colored solution absorbs to its concentration. The key insight is that absorbance depends on three factors: how strongly the dye absorbs light (molar absorptivity $\varepsilon$ ), how far light travels through the solution (path length $b$ ), and how many dye molecules are in the way (concentration $c$ ). You're given all three pieces and just need to plug them into $A = \varepsilon bc$ to find the absorbance the technician will measure.

Intuitive explanation

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