Question

300mm long tube containing 60cc of sugar solution produces a rotation of 9° when placed in a polarimeter. If the specific rotation is 60°. Calculate the quantity of sugar contained in the solution.

Answer 1

Hint: For solving this problem, the understanding of the general concept of polarization and polarimeters is a must. Additionally, it is very important that we know the formula of the polarimeter, which provides a relation between observed rotations, length, and specific optical rotation of the given medium.

Complete answer:
> Let’s consider all the given values and convert them to the required units
$l$\[ = 300mm{\text{ }} = 30cm{\text{ }} = 3dm\], $\theta $ $ = 9^\circ $,$[\alpha ]_A^T = 60^\circ $, volume of solution
Where, $ = 60c{m^3}$
$l = $ Length of tube,
$\theta = $ Observed optical rotation,
$[\alpha ]_A^T = $Specific rotation of given sugar solution
> According to the formula of polarimeter
$\theta = [\alpha ]_\lambda ^TlC \\
\Rightarrow C = \dfrac{\theta }{{[\alpha ]_\lambda ^Tl}} = \dfrac{{9^\circ }}{{60^\circ \times 3}} = \dfrac{1}{{20}}gc{m^{ - 3}} \\ $
> Quantity of sugar in solution$ = Concentration \times Volume$
$ \Rightarrow \dfrac{1}{{20}} \times 60 = 3gm$
Hence, the quantity of sugar in the given solution is 3gm.

Note: Polarimeter works by using the concept of polarization. Polarimeter is a very essential equipment in pharmaceutical industries, as it helps in quality control of products. Additionally, remember to always convert the length of the tube to decimeter (dm).