Question

Fish-liver oil is a good source of vitamin A, which is measured spectrophotometrically, after correcting for background, at a wavelength of 329 nm. When 0.1713 g of fish-liver oil is dissolved in 545 mL of solvent, the absorbance is 0.724 units. When 1.67 × 10−3 g of vitamin A is dissolved in 250. mL of solvent, the absorbance is 1.018 units. Calculate the vitamin A concentration in the fish-liver oil.

Answer 1

For pure vitamin A

mass vitamin A = 1.67 x 10^-3 g

volume of solvent = 250. mL = 0.250 L

mass concentration of Vitamin A = (mass Vitamin A) / (volume of solvent in liters)

mass concentration of Vitamin A = (1.67 x 10^-3 g) / (0.250 L)

mass concentration of Vitamin A = 6.68 x 10^-3 g/L

According to Beer's law

Absorbance = (molar absorptivity) * (path length of cell) * (concentration)

For same material, molar absorptivity is constant and path length is also assumed constant

Hence, Absorbance is directly proportional to concentration

or, A₁ / C₁ = A₂ / C₂

C₂ = C₁ * (A₂ / A₁)

where C₁ = mass concentration of Vitamin A = 6.68 x 10^-3 g/L

C₂ = mass concentration of Vitamin A in fish-liver oil

A₁ = absorbance of pure Vitamin A = 1.018

A₂ = absorbance of Vitamin A in fish-liver oil = 0.724

C₂ = 6.68 x 10^-3 g/L * (0.724 / 1.018)

C₂ = 4.75 x 10^-3 g/L

Vitamin A concentration in the fish-liver oil = 4.75 x 10^-3 g/L