Question

An unknown amount of a compound with a molecular mass of 285.71 g/mol is dissolved in a 10-mL volumetric flask. A 1.00-mL aliquot of this solution is transferred to a 25-mL volumetric flask and enough water is added to dilute to the mark. The absorbance of this diluted solution at 355 nm is 0.511 in a 1.000-cm cuvette. The molar absorptivity for this compound at 355 nm is ε355 = 5873 M–1 cm–1.

What is the concentration of the compound in the cuvette?

Answer 1

Using the Beer-Lambert law and the given absorbance, molar absorptivity, and path length, the concentration of the compound in the cuvette is found to be 2.175 x 10⁻³ M after accounting for the dilution factor.

Step-by-step explanation:

To determine the concentration of the compound in the cuvette after dilution, use the Beer-Lambert law, which relates absorbance (A), molar absorptivity (ε), concentration (c), and path length (l). The formula is A = εcl. Given that the absorbance (A) is 0.511, the molar absorptivity (ε) at 355 nm is 5873 M⁻¹ cm⁻¹, and the path length (l) is 1.000 cm (standard for cuvettes), we can solve for the concentration (c).

​​​​​​​​​​​​​​​By rearranging the formula, the concentration is found: c = A / (εl), which simplifies to c = 0.511 / (5873 × 1.000), yielding c = 8.7 x 10⁻µ M in the diluted solution within the 25-mL volumetric flask.

To find the concentration in the original 10-mL volumetric flask before the first dilution, one must account for the dilution factor which is the total volume after dilution (25 mL) divided by the volume of the aliquot taken (1 mL). Thus, the dilution factor is 25. Multiplying the concentration of the diluted solution by this factor gives the concentration in the original flask: 8.7 x 10⁻µ M × 25 = 2.175 x 10⁻³ M. This is the concentration of the compound in the cuvette.