Question

A $20cm$ length of a certain solution causes right-handed rotation of $38^{\circ }$. A $30cm$ length of another solution causes left-handed rotation of $24^{\circ }$. The optical rotation caused by $30cm$ length of a mixture of the above solutions in the volume ratio $1:2$ is

• A. right handed rotation of $14^{\circ }$
• B. left handed rotation of $14^{\circ }$
• C. right handed rotation of $3^{\circ }$
• D. left handed rotation of $3^{\circ }$

Answer 1

Answer: (C)

For liquid $A$
$L_1=20cm,{\theta }_1=38^{\circ }$ ; concentration $=C_1$
Specific rotation ${\alpha }_1=\frac{{\theta }_1}{L_1{C}_1}$
$=\frac{38^{\circ }}{20\times C_1}$
Similarly, for liquid $B$
$L_2=30cm{\theta }_2=-24^{\circ }$, concentration $=C_2$
Specific rotation ${\alpha }_2=\frac{{\theta }_2}{L_2{C}_2}$
$=\frac{\left(-24^{\circ }\right)}{30\times C_2}$
The mixture has 1 part of liquid $A$ and 2 parts of liquid $B$
$\therefore C_1^{\prime }:C_2^{\prime }=1:2$
$\theta =\left[{\alpha }_1{C}_1^{\prime }+{\alpha }_2{C}_2^{\prime }\right]l$
$=\left\{\frac{38^{\circ }}{20\times C_1}\times \frac{C_1}{3}+\frac{\left(-24^{\circ }\right)}{30\times C_2}\times \frac{2C_2}{3}\right\}\times 30$
$=19^{\circ }-16^{\circ }=3^{\circ }$
Thus, the optical rotation of mixture is $+3^{\circ }$ in right hand direction