a. Four(one double bond, two `G.I`. and one asymmetric `C` atom. Two optical isomers, total four).
(I) and (II), and (III) and (IV) are enantiomers,
(I) and (III), (II) and (IV), (I) and (IV), and (II) and (III) are diastereomers.
b. Nil, since there is no asymmetric `C` atom.
c. four, two
d. ii.
e. i. `2-3-` Dihydroxy butane , this name is wrong. It should be butan `-2,3-`diol.
`CH_(3).^(**)CHOH .^(**)CHOH.CH_(3)` where `(**)` shows asymmetric `C` atoms. Thus, the compound has optical isomers.
ii. `3-`phenyl`-2`- propenoic acid:
`underset(H)underset(|)overset(C_(6)H_(5))overset(|)(C)=underset(H)underset(|)(C)-COOH`. It has two geometrical isomers.
`underset("cis form")(C_(6)H_(5)-underset(HOOC-C-H)underset(||)(C)-H) " " underset("trans form")(C_(6)H_(5)-underset(H-C-COCH)underset(||)(C)-H)`
f. i.
Number of asymmetric `C` atoms`=2`
Different terminal groups:`(-COOH)` and `(Me)`
Number of (O.I.A) racemic form `=(4)/(2)=2`
(racemate mixtrue)
`:.` Total optical isomers `=4`
Optically inactive forms `=2`
ii.
Number of asymmetric `C` atoms `=2` Same terminal groups, `-(COOH)`
Number of O.I.A `= 2^(n-1)=2^(2-1)=2^(1)=2`
Number of `(O.I.A)` meso form `=2^((n-2)//2)= 2^(@)=1`
Number of `(O.I.A)` racemic form `=(2)/(2)=1`
Total optical isomers`=2+1=3`
Note: For stereoisomerism in cyclic compounds.
