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.