Mystery Yellow Dye

Question

When cleaning a laboratory, you find a bottle with a label reading “Yellow dye, ϵ = 1.07x10⁴ (cm^-1⋅M^-1)”. When 7.0 mg is dissolved in 295 mL, an absorbance of 0.553 was found. What is the molecular weight of the mystery dye?

Answer 1

Molecular weight (molar mass) = grams / moles. We know the grams (7.0 mg = 7.0x10^-3 g), so we need to find the moles.

Use the Beer Lambert Law: A = ϵcl

A= absorbance = 0.553

ϵ = extinction coefficient = 1.07x10⁴ cm^-1M^-1

c = concentration = moles / L = ?

l = path length = 1 cm (not given in the question, but this is typical)

Solving for concentration in moles/L we have...

0.553 = (1.07x10⁴ cm^-1M^-1)(c)(1)

C = 5.17x10^-5 M = 5.17x10^-5 moles / L

Since we have 295 mls (0.295 L), we can find moles present:

5.17x10^-5 moles / L x 0.295 L = 1.52x10^-5 moles

Molecular weight (molar mass) = grams / moles = 7.0x10^-3 g / 1.52x10^-5 moles

Molecular weight (molar mass) = 463 g / mole