Question

A $20 \,cm$ length of a certain solution causes right-handed rotation of $38^\circ$. A $30\, cm$ length of another solution causes left-handed rotation of $24^\circ$. The optical rotation caused by $30\, cm$ 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

The Correct Option is C

For liquid $A$ $L_{1}=20 \,cm , \theta_{1}=38^{\circ}$ ; concentration $=C_{1}$ Specific rotation $ \alpha_{1}=\frac{\theta_{1}}{L_{1} C_{1}} $ $=\frac{38^{\circ}}{20 \times C_{1}}$ Similarly, for liquid $B$ $L_{2}=30 cm \theta_{2}=-24^{\circ}$, 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}': C_{2}'=1: 2 $ $\theta=\left[\alpha_{1} C_{1}'+\alpha_{2} C_{2}'\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{2 C_{2}}{3}\right\} \times 30 $ $=19^{\circ}-16^{\circ}=3^{\circ}$ Thus, the optical rotation of mixture is $+3^{\circ}$ in right hand direction