Question

Fish-liver oil is a good source of vitamin \(\mathrm{A},\) whose concentration is measured spectrometrically at a wavelength of \(329 \mathrm{nm}\) (a) Suggest a reason for using this wavelength. (b) In what region of the spectrum does this wavelength lie? (c) When \(0.1232 \mathrm{~g}\) of fish-liver oil is dissolved in \(500 . \mathrm{mL}\) of solvent, the absorbance is 0.724 units. When \(1.67 \times 10^{-3} \mathrm{~g}\) of vitamin \(\mathrm{A}\) is dissolved in \(250 . \mathrm{mL}\) of solvent, the absorbance is 1.018 units. Calculate the vitamin A concentration in the fish-liver oil.

Short answer

The wavelength 329 nm is used because it is the peak absorbance of vitamin A, which lies in the UV region. The concentration of vitamin A in the fish-liver oil is 0.0193 g/g.

Step-by-step solution

Understanding the use of 329 nm wavelength

The wavelength of 329 nm is chosen because vitamin A has its maximum absorbance (peak absorbance) at this wavelength. This ensures that the measurement is accurate and specific to vitamin A, minimizing the interference from other substances.

Spectrum Region Identification

The wavelength of 329 nm falls within the ultraviolet (UV) region of the electromagnetic spectrum, which ranges from approximately 10 nm to 400 nm.

Calculate the Molar Absorptivity (ɛ) for Vitamin A

Using the Beer-Lambert Law: \[ A = ɛ \times c \times l \]Rearrange to solve for molar absorptivity (ɛ): \[ ɛ = \frac{A}{c \times l} \]Given: \[ A = 1.018 \]\[ c = \frac{1.67 \times 10^{-3} \text{ g}}{250 \text{ mL}} \text{ Vitamin A} \] (we assume l is 1 cm) Convert concentration to g/mL: \[ c = \frac{1.67 \times 10^{-3}}{0.25} = 6.68 \times 10^{-3} \text{ g/mL} \]So, \[ ɛ = \frac{1.018}{(6.68 \times 10^{-3} \text{ g/mL}) \times 1 \text{ cm}} \]\[ ɛ = 152.4 \text{ mL/(g cm)} \]

Calculate the Concentration of Vitamin A in Fish-Liver Oil

Again using Beer-Lambert Law: \[ c = \frac{A}{ɛ \times l} \]Given: \[ A = 0.724 \]Using the molar absorptivity calculated, and assuming path length l is 1 cm: \[ c = \frac{0.724}{152.4 \times 1} = 4.75 \times 10^{-3} \text{ g/mL} \]This is the concentration in the solution. Now convert this to the concentration in the fish-liver oil: \[ 4.75 \times 10^{-3} \text{ g/mL} \times 500 \text{ mL} = 2.375 \text{ g} \]\[ \text{Concentration of Vitamin A in the fish-liver oil} = \frac{2.375 \text{ g}}{0.1232 \text{ g}} = 0.0193 \text{ g/g} \]

Key concepts

spectrophotometry

Spectrophotometry is a technique used to measure the amount of light absorbed by a solution. This helps in determining the concentration of a substance in that solution. The core principle is the Beer-Lambert Law, which relates the absorbance with concentration using the formula: \( A = ɛ \times c \times l \).
Here:

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