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 0.1596 g of fish-liver oil is dissolved in 305 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

The relation between concentration and absrobance is known as Beer Lambert's law

Absrobance = concentration x path length X absroptivity

Or A = εcl

here we will take concentration in g / L

If we are performing the test in the same instrument for same compound then

Absroptivity ε = constant

l = path length is also constant

hence we can say that

Absrbance = constant X concentration

Alos

(absrobance at one concentration) / concentration 1 = absorbance at other conentration / concentration 2

Concentration 1 = 1.67 × 10⁻³ g of vitamin A is dissolved in 250. mL

Concentration 1 = 1.67 X 10^-3 / 0.250 = 0.00668 g / L

Absrobance 1 = 1.018

Concentration 2 = ?

Absorbance 2 = 0.724

Putting values

1.018 / 0.00668 g / L = 0.724 / concentration 2

concentration 2 = 0.00475 g / L

this is the concentration of vitamin A in 0.1596 g of fish-liver oil dissolved in 305mL

So mass of vitamin A in given fish oil of volume 305mL = 0.00475 X 0.350 = 0.00166 grams

Hence concentration of vitamin A in the given mass of 0.1596g of fish liver oil will be = Mass of vitamin A / Mass of fish liver oil

concentration of Vitamin A = 0.00166/0.1596 = 0.0104g vitamin A / gram of oil