Question

Calculate the molar absorptivity of crystal violet using the absorbance value of the crystal violet solution determined in the lab and Beer’s law. How does this value compare with the value of 87,000 M^-1 cm^-1 at 590 nm reported in literature?

Absorbance value used in lab: 590 nm.

If not enough information to solve, please explain how I would go about solving this.

Answer 1

Ans. Beer-Lambert’s Law, A = e C L             - equation 1,              

where,

                       A = Absorbance

                       e = molar absorptivity at specified wavelength (M^-1cm^-1)

                        L = path length (in cm)

                        C = Molar concentration of the solute

# To calculate molar absorptivity, the value of A, C and L must be known.

Absorbance, A is experimentally determined using spectrophotometer.

Concertation, C of the final aliquot (whose Abs is measured) is known (or, can be calculated) because it is prepared from a standard stock solution.

Path length, L is generally 1.0 cm in standard spectrophotometer.

# Since, A, C and L are not mentioned in the question, a hypothetical example is presented.

# Let you have following experimental values-

            A = 0.3637 at 590 nm

            C = 4.736 x 10^-7 M

            L = 1.0 cm

Putting the values in equation 1-

            e = A/ CL = 0.3637 / (4.736 x 10^-6 M x 1.0 cm) = 76795 M^-1 cm^-1

Therefore, experimentally determined molar absorptivity of crystal violet at 590 nm = 76795 M^-1 cm^-1.

# Comparison:

% error in e = [(Theoretical value – Experimental value) / Theoretical value] x 100

                        = [(87000 M^-1 cm^-1 – 76795 M^-1 cm^-1) / 87000 M^-1 cm^-1] x 100

                        = 11.73 %