Isomerism for JEE Advanced

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1. Introduction to Isomerism Isomers are compounds that have the same molecular formula but different arrangements of atoms in space. This difference leads to distinct physical and chemical properties. Molecular Formula: Same for all isomers. Arrangement of Atoms: Different. Properties: Different. Isomerism is broadly classified into two main types: Structural Isomerism (Constitutional Isomerism): Different connectivity of atoms. Stereoisomerism: Same connectivity but different spatial arrangement of atoms. 2. Structural Isomerism Structural isomers have the same molecular formula but differ in the sequence in which their atoms are linked. They possess different IUPAC names. 2.1. Chain Isomerism (Skeletal Isomerism) Compounds having the same molecular formula but differing in the arrangement of the carbon chain (straight vs. branched). Example: $C_4H_{10}$ n-butane: $CH_3-CH_2-CH_2-CH_3$ isobutane (2-methylpropane): $CH_3-CH(CH_3)-CH_3$ 2.2. Position Isomerism Compounds having the same molecular formula and carbon skeleton but differing in the position of a functional group, substituents, or multiple bonds (double/triple bonds). Example 1: $C_3H_8O$ (Alcohols) Propan-1-ol: $CH_3-CH_2-CH_2-OH$ Propan-2-ol: $CH_3-CH(OH)-CH_3$ Example 2: $C_4H_8$ (Alkenes) But-1-ene: $CH_2=CH-CH_2-CH_3$ But-2-ene: $CH_3-CH=CH-CH_3$ 2.3. Functional Group Isomerism Compounds having the same molecular formula but differing in the functional group present. Example 1: $C_2H_6O$ Ethanol (Alcohol): $CH_3-CH_2-OH$ Dimethyl Ether (Ether): $CH_3-O-CH_3$ Example 2: $C_3H_6O_2$ Propanoic acid (Carboxylic acid): $CH_3-CH_2-COOH$ Methyl acetate (Ester): $CH_3-COO-CH_3$ Common pairs: Alcohols and Ethers Aldehydes and Ketones Carboxylic acids and Esters Cyanides and Isocyanides Nitroalkanes and Alkyl nitrites Primary, Secondary, Tertiary amines (sometimes) 2.4. Metamerism Compounds having the same molecular formula and functional group, but differing in the nature of alkyl groups attached to the polyvalent functional group atom (e.g., -O-, -S-, -COO-, -CO-, -NH-). Example: $C_4H_{10}O$ (Ethers) Diethyl ether: $CH_3-CH_2-O-CH_2-CH_3$ Methyl n-propyl ether: $CH_3-O-CH_2-CH_2-CH_3$ 2.5. Tautomerism A special type of functional isomerism where two functional isomers exist in dynamic equilibrium with each other. The isomers (tautomers) differ in the position of a proton and a double bond. Keto-enol Tautomerism: Most common type. Involves the migration of a proton ($H^+$) and a $\pi$-bond. Conditions: Presence of an $\alpha$-hydrogen atom with respect to a carbonyl group. Stability: Enol form is generally less stable than keto form, except when stabilized by: Aromaticity (e.g., Phenol) Intramolecular H-bonding (e.g., $\beta$-dicarbonyl compounds) Resonance stabilization Example: Acetone $$ CH_3-CO-CH_3 \rightleftharpoons CH_2=C(OH)-CH_3 $$ Keto form (more stable) $\rightleftharpoons$ Enol form (less stable) Other types: Nitro-aci tautomerism, Imine-enamine tautomerism, etc. 2.6. Ring-Chain Isomerism Compounds having the same molecular formula where one isomer has an open-chain structure and the other has a cyclic structure. Example: $C_3H_6$ Propene: $CH_3-CH=CH_2$ Cyclopropane: A three-membered carbon ring. 3. Stereoisomerism Stereoisomers have the same molecular formula and connectivity but differ in the spatial arrangement of their atoms. They have the same IUPAC name, differing only by prefixes (e.g., cis-, trans-, R-, S-, D-, L-). Conformational Isomerism: Interconvertible by rotation around single bonds. Configurational Isomerism: Not interconvertible without breaking and reforming bonds. Geometrical Isomerism (cis-trans) Optical Isomerism (enantiomers, diastereomers) 3.1. Conformational Isomerism (Conformers/Rotamers) Different spatial arrangements of atoms that can be interconverted by rotation around single bonds. These are not true isomers as they are rapidly interconverting at room temperature. Newman Projections: Used to visualize conformers by looking down a C-C bond. Ethane: Staggered conformation (most stable, dihedral angle $60^\circ$): Torsional strain is minimized. Eclipsed conformation (least stable, dihedral angle $0^\circ$): Maximum torsional strain. Butane (along $C_2-C_3$ bond): Anti (most stable): Two largest groups (methyl) are $180^\circ$ apart. Minimum steric strain. Gauche (less stable): Two largest groups are $60^\circ$ apart. Steric strain due to gauche interaction. Eclipsed (least stable): Methyls are $0^\circ$ apart. Maximum steric strain and torsional strain. Partially eclipsed: Methyls are $120^\circ$ apart. Cyclohexane Conformations: Chair form: Most stable. No angle strain or torsional strain. All bonds are staggered. It resembles a beach chair with axial and equatorial positions for substituents. Boat form: Less stable than chair due to flagpole interactions and eclipsed interactions. Resembles a boat. Twist-boat form: Intermediate stability between chair and boat. 3.2. Configurational Isomerism Isomers that cannot be interconverted by simple rotation around single bonds. Bond breaking and reforming is required. 3.2.1. Geometrical Isomerism (cis-trans isomerism) Arises due to restricted rotation around a double bond or in a cyclic structure. Conditions for Alkenes: Each carbon of the double bond must be attached to two different groups. $C_1 \ne C_2$ and $C_3 \ne C_4$ for $C_1C_2=C_3C_4$ If $a \ne b$ and $c \ne d$ for $R_a R_b C = C R_c R_d$. cis-isomer: Identical groups on the same side of the double bond. trans-isomer: Identical groups on opposite sides of the double bond. Generally more stable due to less steric hindrance. Example: But-2-ene cis-But-2-ene: $CH_3$ groups on same side. trans-But-2-ene: $CH_3$ groups on opposite side. E/Z Notation: Used when there are no identical groups. Based on Cahn-Ingold-Prelog (CIP) priority rules. Z (Zusammen = together): Higher priority groups are on the same side. E (Entgegen = opposite): Higher priority groups are on opposite sides. Cyclic Compounds: Can exhibit cis-trans isomerism if there are two groups on different carbons of the ring. cis-1,2-dimethylcyclopropane: Both $CH_3$ groups are on the same face of the ring. trans-1,2-dimethylcyclopropane: $CH_3$ groups are on opposite faces of the ring. Oximes: Show syn/anti isomerism, similar to cis/trans. 3.2.2. Optical Isomerism Compounds that rotate plane-polarized light are called optically active. This arises from the presence of chirality. 3.2.2.1. Chirality Chiral molecule: A molecule that is non-superimposable on its mirror image. Does not possess a plane of symmetry, center of symmetry, or alternating axis of symmetry. Chiral center (Stereocenter): An atom (usually carbon) bonded to four different groups. Achiral molecule: A molecule that is superimposable on its mirror image. Possesses at least one element of symmetry (plane of symmetry, center of symmetry). 3.2.2.2. Enantiomers Stereoisomers that are non-superimposable mirror images of each other. Possess identical physical properties (melting point, boiling point, density, solubility) except for the direction of rotation of plane-polarized light. React differently with other chiral molecules. Optical activity: Dextrorotatory (d or +): Rotates plane-polarized light to the right (clockwise). Levorotatory (l or -): Rotates plane-polarized light to the left (anticlockwise). Racemic mixture: An equimolar mixture of a pair of enantiomers. Optically inactive due to external compensation (rotation by one enantiomer is cancelled by the equal and opposite rotation of the other). Resolution: The process of separating a racemic mixture into its pure enantiomers. 3.2.2.3. Diastereomers Stereoisomers that are not mirror images of each other. May or may not be optically active. Possess different physical and chemical properties (melting point, boiling point, solubility, reactivity). Often arise in compounds with more than one chiral center. Example: Tartaric acid ($HOOC-CH(OH)-CH(OH)-COOH$) (R,R)-Tartaric acid and (S,S)-Tartaric acid are enantiomers. (R,R)-Tartaric acid and (R,S)-Tartaric acid (meso) are diastereomers. 3.2.2.4. Meso Compounds Molecules that contain chiral centers but are optically inactive due to the presence of an internal plane of symmetry or center of symmetry. They are superimposable on their mirror images. Example: Meso-tartaric acid. Even though it has two chiral carbons, it has a plane of symmetry passing through the middle, making it achiral and optically inactive. 3.2.2.5. Number of Stereoisomers For a molecule with 'n' distinct chiral centers, the maximum number of possible stereoisomers is $2^n$. If meso compounds are possible, the number of stereoisomers will be less than $2^n$. Formula for number of optical isomers (when no meso compound): $2^n$. Formula for number of optical isomers (when meso compound exists for even 'n'): $2^{n-1} - 2^{(n/2)-1}$ (total pairs of enantiomers) + $2^{(n/2)-1}$ (meso forms). Total = $2^{n-1}$. Formula for number of optical isomers (when meso compound exists for odd 'n'): $2^{n-1}$. 3.2.2.6. Configuration (R/S Notation) Cahn-Ingold-Prelog (CIP) priority rules are used to assign R (Rectus/Right) or S (Sinister/Left) configuration to chiral centers. Assign Priorities: Higher atomic number directly attached to the chiral center gets higher priority. If atoms are the same, move to the next atoms along the chain until a point of difference is found. Double/triple bonds are treated as if they are bonded to an equivalent number of single-bonded atoms. Orient the Molecule: Place the lowest priority group (usually H) away from the viewer (on a dashed wedge in 3D, or on a vertical line in a Fischer projection). Determine Direction: Trace a path from priority 1 to 2 to 3. Clockwise direction: R configuration. Counter-clockwise direction: S configuration. Fischer Projections: Vertical lines represent bonds going away from the viewer. Horizontal lines represent bonds coming towards the viewer. If the lowest priority group is on a horizontal line, reverse the R/S assignment determined. 3.2.2.7. D/L Notation Used primarily for carbohydrates and amino acids. Based on the configuration of the highest-numbered chiral center relative to glyceraldehyde. D-isomer: -OH group (or $NH_2$ group for amino acids) on the right side of the lowest chiral carbon in Fischer projection. L-isomer: -OH group (or $NH_2$ group) on the left side of the lowest chiral carbon. D/L notation does NOT directly relate to (+) or (-) optical rotation. 4. Isomerism in Specific Compounds 4.1. Alkenes Geometrical isomerism (cis/trans or E/Z) is common. Terminal alkenes (e.g., propene) do not show geometrical isomerism. 4.2. Cycloalkanes Geometrical isomerism (cis/trans) when two or more substituents are present on different carbons. Chirality can exist in substituted cyclopropanes, cyclobutanes, etc. 4.3. Alcohols and Ethers Can be functional group isomers ($C_n H_{2n+2} O$). Position isomerism for -OH group. Chain isomerism for carbon skeleton. Optical isomerism if a chiral carbon is present. 4.4. Aldehydes and Ketones Functional group isomers ($C_n H_{2n} O$). Position isomerism for ketones. Chain isomerism. Tautomerism (keto-enol). 4.5. Carboxylic Acids and Esters Functional group isomers ($C_n H_{2n} O_2$). Chain isomerism. Optical isomerism if chiral center exists. 4.6. Amines Primary, secondary, and tertiary amines can be functional group isomers (e.g., $C_3H_9N$). Position isomerism for primary amines. Chain isomerism. Optical isomerism if chiral. (Note: amine inversion can make chiral amines optically inactive unless inversion is restricted). 4.7. Biphenyls and Allenes Biphenyls: If substituted at ortho positions with bulky groups, rotation around the C-C bond joining the two rings can be restricted, leading to atropisomerism (a type of stereoisomerism without a chiral center). The molecule becomes chiral. Allenes: Compounds with two adjacent double bonds ($C=C=C$). If the two ends of the allene are substituted with different groups, they can be chiral and exhibit optical isomerism even without a chiral carbon. Example: 2,3-pentadiene ($CH_3-CH=C=CH-CH_3$) is achiral. Example: 2,3-heptadiene ($CH_3-CH=C=CH-CH_2CH_2CH_3$) is chiral. 4.8. Spiro Compounds Compounds where two rings share one common carbon atom. Can exhibit chirality similar to allenes if appropriately substituted. 5. Degree of Unsaturation (DU) / Index of Hydrogen Deficiency (IHD) A useful tool to determine the number of rings or $\pi$-bonds in a molecule given its molecular formula. Formula for $C_c H_h N_n O_o X_x$ (X = halogen): $$ DU = c + 1 - \frac{h}{2} + \frac{n}{2} - \frac{x}{2} $$ Each double bond or ring accounts for one DU. Each triple bond accounts for two DUs. Example: $C_6H_6$ (Benzene) $$ DU = 6 + 1 - \frac{6}{2} = 7 - 3 = 4 $$ (Benzene has 3 double bonds and 1 ring, total 4 DU). 6. Important Considerations for JEE Advanced Identify all possible isomers: Practice systematically drawing structural and stereoisomers for a given molecular formula. Chirality without chiral carbon: Remember allenes, biphenyls, and spiro compounds. Stability of conformers: Understand energy profiles for ethane and butane, and chair flips in cyclohexane. Distinguishing isomers: Relate structural differences to physical/chemical property differences. Reaction stereochemistry: How reactions (e.g., $S_N1$, $S_N2$, $E1$, $E2$, additions to alkenes) affect stereochemistry (retention, inversion, racemization). Optical purity/Enantiomeric excess (ee): $$ ee = \frac{|[\alpha]_{obs}|}{[\alpha]_{pure}} \times 100\% = \frac{|D - L|}{D + L} \times 100\% $$ Where $D$ and $L$ are the amounts of dextro and levo enantiomers.