JEE Chemistry Organic Chemistry Some Basic Principles and Techniques Notes Set 13

Isomers and Homologues

Isomers have the same molecular formula but different structures and therefore different physical and chemical properties (CH3CH2OH and CH3OCH3; CH3COOH and HCOOCH3). Homologues belong to the same functional series and differ by a CH2 unit, that is, by 14 mass units (CH3OH and CH3CH2OH).
Structural (constitutional) isomers differ in the way atoms are linked. Stereoisomers have the same linkage but differ in the arrangement of atoms in space.

Structural Isomerism

Chain isomerism: different carbon skeletons with the same functional group (butane and 2-methylpropane). Alkanes C1–C3 have no chain isomers, C4H10 has 2, C5H12 has 3 and C6H14 has 5.
Position isomerism: the same skeleton and functional group but a different position of the group, the multiple bond or a substituent (butan-1-ol and butan-2-ol).
Functional isomerism: different functional groups for the same formula (alcohol and ether, aldehyde and ketone, acid and ester, cyanide and isocyanide).
Metamerism: different alkyl groups on the two sides of a polyvalent atom or group such as –O–, –S–, –NH– or –CO– (methoxypropane and ethoxyethane).
Ring-chain isomerism: an open-chain compound and a ring compound of the same formula (propene and cyclopropane). Counting tips: C4H10O has 7 structural isomers (4 alcohols and 3 ethers) and C4H11N has 4 primary amines.

Geometrical Isomerism

Restricted rotation about a double bond (or in a ring) gives cis–trans isomers when each doubly bonded carbon carries two different groups. The cis isomer has similar groups on the same side; the trans isomer has them on opposite sides.
E/Z system: rank the two groups on each carbon by CIP priority; if the higher-priority groups are on the same side the isomer is Z (zusammen), if on opposite sides it is E (entgegen).
Properties: cis isomers are usually more polar (greater dipole moment) and have higher boiling points; trans isomers are more symmetrical and often have higher melting points. Symmetrical polyenes have fewer isomers than 2^n, for example hexa-2,4-diene has 3.

Optical Isomerism

A molecule is optically active when it is chiral, that is, not superimposable on its mirror image. The usual cause is a stereocentre: a carbon bonded to four different groups. A molecule with a plane or centre of symmetry is achiral.
A polarimeter measures the angle of rotation α. Dextrorotatory (d or +) rotates light clockwise; laevorotatory (l or −) rotates it anticlockwise. Specific rotation: \( [\alpha]=\frac{\alpha}{l\,c} \) with l in dm and c in g/mL; it does not depend on the concentration used.
Enantiomers are non-superimposable mirror images with equal and opposite rotations and identical other physical properties. Diastereomers are stereoisomers that are not mirror images and differ in physical properties. A racemic mixture has equal amounts of d and l and is inactive by external compensation; a meso compound has internal mirror symmetry and is inactive by internal compensation.
Enantiomeric excess: \( \%\,ee=\frac{[\alpha]_{observed}}{[\alpha]_{pure}}\times 100 \). A sample with 50% ee is 75% of the major and 25% of the minor enantiomer.

Counting Optical Isomers

For n different stereocentres: 2^n stereoisomers (2^(n−1) enantiomeric pairs). Example: 2,3-dichloropentane has 4; an aldopentose has 8; open-chain glucose has 16.
For n identical-end stereocentres, n even: total = 2^(n−1) + 2^((n/2)−1) of which 2^((n/2)−1) are meso. Two centres gives 3 (tartaric acid, 2,3-dichlorobutane), four centres gives 10. For n odd the total is 2^(n−1) (2,3,4-trichloropentane has 4).
Fischer projection rules: one interchange of two groups gives the enantiomer; two interchanges restore the original; rotation by 180° in the plane keeps the molecule the same, rotation by 90° gives the enantiomer. R/S: arrange the groups by CIP priority (atomic number, then duplicated atoms for multiple bonds), look with the lowest priority group away, and trace the rest from highest to lowest: clockwise is R, anticlockwise is S.

Optical Activity Without a Chiral Carbon

Compounds with consecutive (cumulated) double bonds and an even number of pi bonds are chiral if each end carries two different groups because the end groups lie in perpendicular planes (CH3CH=C=CHCH3 is chiral). Those with an odd number of pi bonds have planar end groups and show cis–trans isomerism instead. Spiranes with an even number of rings behave like the even case; those with an odd number of rings show geometrical isomerism.
Ortho-substituted biphenyls with bulky groups cannot rotate about the central bond, become non-planar and are optically active. An open-chain amine with three different groups on nitrogen is chiral but optically inactive at room temperature because the nitrogen inverts rapidly; if nitrogen is held in a ring, inversion is blocked and the compound can be active.

Conformational Isomerism

Rotation about a single bond produces different arrangements called conformations (rotamers). The dihedral (torsion) angle is the angle between groups on two adjacent bonded atoms. Conformations are shown by sawhorse and Newman projections. Conformers cannot be isolated at room temperature because the barriers are small.
Ethane: staggered is the minimum-energy form and eclipsed is the maximum; the energy difference (rotational barrier) is about 12 kJ/mol and is due to torsional strain between the bonding pairs of eclipsed C–H bonds. Torsional strain is absent in staggered forms.
Butane about the C2–C3 bond: anti (180°) is the most stable, then gauche (60°), then partially eclipsed (120°), and fully eclipsed (0°) is the least stable. Stability order: anti > gauche > partially eclipsed > fully eclipsed. Van der Waals strain is greatest when the methyl groups are close. Open-chain compounds have no angle strain.

Worked Examples

Worked Example 1. Find the number of stereoisomers of \( \ce{CH3-CH(OH)-CH(OH)-CH2-CH3} \).
Answer:
Chiral carbons: C2 and C3, both bonded to four different groups; the two ends of the chain are different (CH3 and C2H5), so the molecule is unsymmetrical.
Stereoisomers = 2² = 4: two pairs of enantiomers, no meso form.
4

Worked Example 2. A solution of 1 g of an optically active compound in 10 mL, placed in a 2 dm tube, gives an observed rotation of +4°. Find the specific rotation.
Answer:
Concentration c = 1/10 = 0.1 g/mL.
[\(\alpha\)] = 4 / (2 × 0.1) = 20.
+20°

Worked Example 3. Name the type of isomerism between \( \ce{CH3-CH2-CH2-CHO} \) and \( \ce{CH3-CO-CH2-CH3} \).
Answer:
Both are C4H8O but one is an aldehyde and the other a ketone.
Functional isomerism.