The molar absorptivity constant of a particular chemical is 2.16 M·cm. What is the concentration of a solution made from this chemical that has an absorbance of 0.458 with a cell path length of 1.01 cm?

0.21 M

Explanation:

The method to solve this question is to use Beer's law which is expressed by

A = εcl

where A is the absorbance, ε is molar absorptivity (M⁻¹·cm⁻¹), c is the concentration M (mol/L), and l is the path length in cm.

Solving for c in the above equation

c = A / εl = 0.458 / (2.16 M⁻¹·cm⁻¹ x 1.01 cm) = 0.21 M

Note: there is an error in the units for the absorptivity constant, it should have said M⁻¹·cm⁻¹. You can check this by realizing the absorbance is unitless and when we multiply M⁻¹·cm⁻¹ with the units of concentration c (M) and path length (cm) the units cancel.