Question

Specific rotation of sugar solution is 0.01 S.I. units $200 kg{m}^{-3}$ of impure sugar solution is taken in a polarimeter tube of length 0.25 m and an optical rotation of 0.4 rad is observed. The percentage of purity of sugar in the sample is
A. 80 %
B. 89 %
C. 11 %
D. 20 %

Answer 1

Hint: To solve this question, use the formula for specific rotation which is in terms of observed rotation, length of the tube and concentration of the solution. Substitute the values in the formula and find the concentration of the solution. Then, divide this obtained value of concentration by amount of impure sugar solution. This will give the amount of pure sugar. Multiplying this value by 100 will give the percentage of purity of sugar in the sample.

Complete Solution :
Formula used:
$[\alpha]= \dfrac {\alpha}{l \times c}$

Given: Specific rotation, [$\alpha$] = 0.01
Amount of impure sugar solution, ${S}_{impure}$ = $200 kg{m}^{-3}$
Length of the tube, l = 0.25 m
Observed rotation, $\alpha$ = 0.4 rad
The formula for specific rotation is given by:
$[\alpha]= \dfrac {\alpha}{l \times c}$ …(1)
Where, $[\alpha]$ is the specific rotation
$\alpha$ is the observed rotation
l is the length of the tube
c is the concentration of solution
Substituting values in the equation. (1) we get,
$0.01= \dfrac {0.4}{0.25 \times c}$

Rearranging the above equation we get,
$c= \dfrac {0.4}{0.25 \times 0.01}$
$\Rightarrow c= \dfrac {0.4}{ 0.0025}$
$\Rightarrow c= 160 {kg}/{{m}^{3}}$
Purity of sugar solution can be calculated by,
${S}_{pure}= \dfrac {c}{{S}_{impure}} \times 100$
Substituting values in above equation we get:
${S}_{pure}= \dfrac {160}{200} \times 100$
$\Rightarrow {S}_{pure} = 0.8 \times 100$
$\Rightarrow {S}_{pure} = 80%$
Thus, the percentage of purity of sugar in the sample is 80%.

So, the correct answer is “Option A”.

Note: Specific rotation of a solution depends on the wavelength of the light. The variation of specific rotation with wavelength can be used to determine the absolute configuration of certain compounds. Specific rotation is a substance-specific physical parameter which is determined by a polarimeter. The value of specific rotation not only depends on the wavelength of the light but also depends on the temperature as well as the concentration of the solution.