The optical rotation of an optically active compound is `+20^(@)`. The length of tube is `10 cm` and the density of solution is `0.4 gm ml^(-)`. The specific rotation of the compound is:
i. `+50^(@)` ii. `+500^(@)` iii. `+5^(@)` iv. `+0.5^(@)`
b. Which of the following are optically active compounds and why?
i. Butan-1-ol ii. 2-Chlorobutane
II. Lactive acid iv. 3-Chloropentane
c. Which of the following are optically active and why?
i. `CH_(3)CH(Cl)CH_(3)`
ii. `CH_(3)CH_(2)CH(CH_(3))COOH`
iii. `CH_(3)CH_(2)CH(NH_(2))CH_(3)`
iv. `CH_(2)OHCH_(2)OH`
d. Which of the following are optically active and why?
i. Propan-1-ol , ii. Butan-2-ol
iii. Heptan-4-ol , iv. 3-Aminohexane
v. 2-Chloropentane , vi. 2,2-Dichloropropane
e. Mark `(**)` on the asymmetric carbon atom, if any, in the following compounds:
(i) `CH_(3)-CHCl-CH_(2)-CH_(3)`, ii. `CH_(3)-CHOH-CH_(3)`.

Explanation

a. i. `10cm=1 dm, [alpha]=(+120^(@))/(1xx0.4)= +50^(@)`
b. The structural formulas of the given compounds are as under :
(i). `CH_(3)CH_(2)CH_(2)CH_(2)OH` (Butan-1-ol)
Butan-1-ol is not optically acive since it does not contain any asymmetric carbon atom. Hence the molecule is achiral.
ii. `CH_(3)-.^(**)overset(Cl)overset(|)CH-CH_(2)-CH_(3)` (2-Chlorobutane)
`2`-Chlorobutane is a chiral molecule since it contains an asymmetric carbon atom marked with an asterisk. Hence, it is optically active.
iii. `CH_(3)-.^(**)overset(OH)overset(|)CH-CH_(2)-COOH`
Lactic acid contains one asymmetric carbon atom and its molecule is chiral. Thus, it shows optical activity.
iv. `CH_(3)CH_(2)-overset(OH)overset(|)CH-CH_(2)CH_(3)` (3-Chloropentane)
`3`- Chloropentane is a symmetrical moleucle since it does not contain an asymmetric carbon atom. Hence it does not show optical activity.
c. (ii) and (iii) have asymmetric `C` atom.
d. (ii), (iv) and (v) have asymmetric `C` atom.
e. i. has asymmetric `C` atom, `CH_(3)-overset(**)CH(Cl)-CH_(2)CH_(3)`