Question

Reaction of R-2-bromobutane with aqueous KOH follows two parallel reactions, one by $S_{N}2$ (complete inversion) and other by $S_{N}1$ (complete racemization). Specific optical activity for R-2-butanol is $-{13.50}^{\circ }/gmL$ per dm length of the polarimeter.


If in a 10 cm tube polarimeter, 10 ml of R-2-bromobutane along with KOH is filled, then after complete reaction of R-2-bromobutane, the mass of all alcohols formed is found equal to 5 g of which 1 g is of R-2-butanol. Then, the total optical rotation (in degree) of the solution is

Answer 1

Optical rotaion of the products formed by $S_{N}1$ reaction is zero due to complete racemization.
Since 1g of R-2-butanol is formed which must be from $S_{N}1$. So the racemized product will be of 2 g.
That means 3 g of S-2-butanol will be formed by $S_{N}2$.
$\therefore$ Total optical rotaion of the solution
$={13.5}^{\circ }\times \frac{3}{10}={4.05}^o$