JEE Chemistry Isomerism Notes Set 03

Stereoisomers

Stereoisomers have the same molecular formula and the same connectivity of atoms but differ in the arrangement of atoms in space. Their physical, chemical and biological properties can differ strongly: fumaric acid is a normal metabolite, while maleic acid is toxic.
Configurational isomers (geometrical and optical) cannot be interconverted at room temperature and can be separated. Conformational isomers interconvert by rotation about single bonds and are normally not separable.

Geometrical Isomerism

Condition 1: restricted rotation, which comes from a C=C, C=N or N=N bond or from a ring.
Condition 2: two different groups on each atom of the restricted bond. A carbon carrying two identical groups ends the possibility.
Examples: but-2-ene (cis and trans), the syn and anti oximes of aldehydes and unsymmetrical ketones, azobenzene, and 1,2-dimethylcyclopropane (cis and trans).
Cycloalkenes are normally cis. The smallest trans cycloalkene stable enough to isolate is trans-cyclooctene; cyclodecene exists in both forms.

Number of geometrical isomers: for n stereogenic double bonds with different end groups, \( 2^n \). When the two ends of a polyene are identical, the count is lower because of symmetry (for n even, \( 2^{n-1}+2^{(n/2)-1} \); for n odd, \( 2^{n-1}+2^{(n-1)/2} \)).

Cis-Trans and E-Z Names

cis and trans compare similar groups. E and Z use the Cahn-Ingold-Prelog (CIP) priorities: if the two higher-priority groups are on the same side the isomer is Z (zusammen); on opposite sides, E (entgegen).
CIP rules in brief: 1. higher atomic number wins at the first point of difference; 2. heavier isotope wins (T > D > H); 3. if the first atoms tie, compare the atoms they carry, set by set; 4. double and triple bonds are treated as duplicated atoms; 5. a bonded atom outranks a lone pair.
Example: \( \ce{-COOCH3} \) (O,O,O) outranks \( \ce{-CHO} \) (O,O,H); \( \ce{-CH2Cl} \gt \ce{-CH2OH} \gt \ce{-CH2CH3} \gt \ce{-CH3} \).

Properties of Geometrical Isomers

Chirality and Optical Activity

A molecule is chiral when it cannot be superimposed on its mirror image. The usual cause is a carbon with four different groups (a chiral or asymmetric centre), but chirality can also come from an axis (C=C=C compounds, hindered biphenyls) or a plane. A chiral molecule has no plane or centre of symmetry (an axis of symmetry may be present).
Optically active compounds rotate plane-polarised light, measured with a polarimeter. Rotation to the right (clockwise) is dextrorotatory, d or (+); to the left, laevorotatory, l or (-). The sign of rotation has no simple relation to R/S or D/L labels.
Specific rotation: \( [\alpha] = \dfrac{\alpha_{obs}}{l\,c} \) with l in dm and c in g/mL. It is a characteristic constant of the compound at a given temperature, wavelength and solvent, and does not change when the concentration is changed.

R/S and D/L Configuration

R/S: rank the four groups by CIP priority, orient the molecule with the lowest priority (usually H) pointing away from you, and trace 1 to 2 to 3. Clockwise is R (rectus), anticlockwise is S (sinister). If the lowest-priority group is toward you, reverse the answer.
Fischer projection: horizontal bonds point towards the viewer, vertical bonds away. Swapping two groups inverts the configuration; rotating the projection by 180 degrees in the plane keeps it, but rotating by 90 degrees inverts it.
D/L: in a Fischer projection with the most oxidised carbon at the top, the compound is D if the OH (or NH2) on the lowest chiral carbon is on the right, L if on the left. D/L is a relative configuration based on glyceraldehyde.

Elements of Symmetry

Plane of symmetry (POS): divides the molecule into two mirror-image halves. Centre of symmetry (COS): every atom has an identical atom at the opposite point through the centre. Axis of symmetry (Cn): rotation by 360/n degrees gives an identical arrangement.
A molecule with a POS or a COS is achiral. A molecule with only a rotation axis can still be chiral (for example trans-1,2-dimethylcyclopropane has a C2 axis and is chiral).

Enantiomers, Diastereomers and Meso Compounds

A racemic mixture, an equimolar mixture of two enantiomers, shows no rotation (external compensation) and can be resolved into its enantiomers by reaction with a pure chiral reagent, which gives separable diastereomers.

Optical Purity and Counting Stereoisomers

Enantiomeric excess (ee) = optical purity = \( \dfrac{|R-S|}{R+S}\times 100 \) = \( \dfrac{[\alpha]_{mixture}}{[\alpha]_{pure}}\times 100 \).
For a molecule with n different stereogenic centres: total stereoisomers = \( 2^n \), all optically active. For a symmetrical molecule with n centres: for n even, \( 2^{n-1}+2^{(n/2)-1} \) stereoisomers, of which \( 2^{(n/2)-1} \) are meso and \( 2^{n-1} \) are active; for n odd, \( 2^{n-1} \) stereoisomers and \( 2^{n-1}-2^{(n-1)/2} \) are active.
Tartaric acid, for example, has 3 stereoisomers: (R,R), (S,S) and meso (R,S); only 2 are optically active. Add the geometrical possibilities of each double bond to the product, and count chiral C=C=C axes as stereogenic elements.

Optical Activity Without a Chiral Carbon

Compounds with a C=C=C unit and two different groups at each end are chiral by axis, and so are hindered biphenyls with bulky ortho substituents. Spiro compounds with suitable ends also show axial chirality.
Nitrogen amines usually undergo fast pyramidal inversion, so their enantiomers interconvert and cannot be isolated. Quaternary ammonium salts, phosphines and sulphoxides with three different groups are configurationally stable.

Conformations of Ethane and Butane

Rotation about a C-C single bond produces conformations. The Newman projection shows the front carbon as a point with three bonds and the back carbon as a circle.
Ethane: staggered (most stable) and eclipsed (about 12 kJ/mol higher, from torsional strain, the repulsion between eclipsed bond pairs); infinitely many conformations lie between them.
Butane about C2-C3, in order of decreasing stability: anti (methyls 180 degrees apart), gauche (60 degrees), partially eclipsed, fully eclipsed (methyls at 0 degrees, highest energy, torsional plus van der Waals strain).
Intramolecular hydrogen bonding can stabilise a gauche form, as in 2-fluoroethanol, ethylene glycol and 3-hydroxypropanal.

Cyclohexane

Stability: chair (strain free, all bonds staggered, 111 degree angles) > twist boat > boat (flagpole hydrogen repulsion and eclipsed side bonds) > half chair (highest energy, a transition state).
In the chair, each carbon has one axial and one equatorial position; a ring flip exchanges them. Substituents prefer the equatorial position because axial groups suffer 1,3-diaxial interactions.
In dimethylcyclohexanes: 1,2 trans is ee or aa, cis is ae; 1,3 cis is ee or aa, trans is ae; 1,4 trans is ee or aa, cis is ae. The most stable conformer of a trans-1,4 or cis-1,3 disubstituted ring is the diequatorial chair.