Question

A molecule is known to have a molar absorptivity of 18,650 at a certain wavelength. A spectrometer is tuned to this wavelength and used to measure the absorbance of a solution of this substance in a b = 1 cm cuvette. The indicated absorbance of the sample was 1.04. The tested solution used in the experiment was prepared by dissolving 100 mg of the substance into a 100 mL volumetric flask. What is the molecular weight of the substance / molecule tested?

Answer 1

Answer:

17,932.69 g/mol is the molecular weight of the substance.

Explanation:

Using Beer-Lambert's law :

Formula used :

$A=\epsilon \times c\times l$

where,

A = absorbance of solution = 1.04

c = concentration of solution =?

l = length of the cell = 1 cm

$\epsilon$ = molar absorptivity of this solution = 18,650 $M^{-1} cm^{-1}$

Now put all the given values in the above formula, we get the molar absorptivity of this solution.

$1.04=18,650 M^{-1} cm^{-1}\times c)\times (1cm)$

c = $5.576\times 10^{-5} M$

$Concentration=\frac{\text{Mass of compound}}{\text{Molecular mass of compound}\times V}$

V = Volume of the solution in L

Molecular weight of the substance = x

V = 100 mL = 0.1 L

Mass of the substance = 100 mg = 0.1 g

$5.576\times 10^{-5} M=\frac{0.1 g}{x\times 0.1 L}$

x = 17,932.69 g/mol

17,932.69 g/mol is the molecular weight of the substance.