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

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

Step-by-step explanation:

Using Beer-Lambert's law :

Formula used :

`A=\epsilon * c* 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)* c)* (1cm)`

c =
`5.576* 10^(-5) M`

`Concentration=\frac{\text{Mass of compound}}{\text{Molecular mass of compound}* 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* 10^(-5) M=(0.1 g)/(x* 0.1 L)`

x = 17,932.69 g/mol

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