Question

If a compound has ε=50 cm^−1 m^−1, what is the lowest concentration of the compound that is still expected to be in the linear range of a calibration plot? Assume a cuvette with a path length of 1 cm. Report your answer in m, but do not include units in your answer.

a) 50mol/m^3
b) 0.02mol/m^3
c)0.5 mol/m^3
d)2mol/m^3

Answer 1

The lowest concentration expected to be in the linear range for a compound with an extinction coefficient of 50 cm⁻¹ m⁻¹ and a cuvette path length of 1 cm is 0.02 mol/m³, which corresponds to answer option b).

Step-by-step explanation:

The question asks about determining the lowest concentration of a compound that would be expected to fall within the linear range of a calibration plot, given an extinction coefficient (ε) of 50 cm⁻¹ m⁻¹ and a cuvette path length of 1 cm. When dealing with Beer's Law, the absorbance (A) is directly proportional to the concentration (c) of the solution and the path length (l), which is summarized by the equation A = εcl. To remain within the linear range, typically an absorbance between 0.1 and 1.0 is ideal. Assuming a maximum absorbance value of 1, the highest concentration (c) while still maintaining a linear relationship can be calculated by rearranging Beer's Law to c = A/εl. With A set at 1, a path length (l) of 1 cm, and ε of 50 cm⁻¹ m⁻¹, the concentration would be c = 1/(50 cm⁻¹ m⁻¹ × 1 cm) = 0.02 m. Therefore, the answer is 0.02 mol/m³, which means option b) 0.02mol/m³ is expected to be the lowest concentration in the linear range of a calibration plot.