§ C-19 Stereochemistry: Geometric (cis–trans, Z/E) & Chiral Optical Isomerism (R/S) (Grade 10–11 · Stereochemistry)
Comparing dipole polarity of cis/trans alkene isomers and optical rotation of plane-polarized light by chiral R/S-enantiomers. Chiral enantiomers relate to one another like left and right hands: sharing identical bond connectivity, they rotate plane-polarized light in opposite directions.
Theory Summary & Scientific Mechanism
Stereoisomers share the exact same molecular formula and bond connectivity but differ in the three-dimensional orientation of their atoms in space. The two primary classes are **geometric (*cis–trans* or Z/E) isomers and chiral optical isomers (enantiomers)**.
Geometric isomerism in alkenes (e.g., 1,2-dichloroethene CHCl=CHCl) arises because the lateral π-bond locks rotation around the C=C axis (barrier ≈ 268 kJ/mol). In the cis (Z) isomer, both electronegative chlorine atoms lie on the same side of the double bond, producing a net molecular dipole μₙet = 1.90 D. In the trans (E) isomer, the C–Cl dipoles point antiparallel and cancel identically (μₙet = 0 D).
Optical isomerism (chirality) occurs when a tetrahedral sp³ carbon atom **C^* (chiral stereocenter)** is bonded to four different substituents (e.g., lactic acid CH₃–C^*H(OH)–COOH). The resulting (R)- and (S)-enantiomers are non-superimposable mirror images that rotate plane-polarized light by equal and opposite angles according to Biot’s law: α = [α]_D²⁰· l· c.
Everyday Analogy
Your left and right hands have identical fingers, yet a left glove will not fit your right hand! Likewise, chiral (R)- and (S)-enantiomers around an asymmetric carbon C^* are non-superimposable mirror images that rotate polarized light in opposite directions.
Interactive Question & Derivation
Why does *trans*-1,2-dichloroethene (E-isomer) have zero net dipole moment (μ = 0 D), while chiral (R)- and (S)-enantiomers rotate plane-polarized light in opposite directions?
- A: In the *trans* isomer the two polar C–Cl bond dipoles point antiparallel and cancel out; (R)- and (S)-enantiomers contain an asymmetric sp³ carbon C^* bonded to 4 different groups, forming non-superimposable mirror images
- B: The *trans* isomer lacks covalent bonds, while (R)- and (S)-enantiomers have different molar masses
- C: *Cis* and *trans* isomers interconvert freely at room temperature without breaking the π-bond
Study Hint: In the *trans* (E) isomer opposing bond dipoles cancel (μ = 0), whereas chiral (R)- and (S)-enantiomers with 4 different groups on C^* are non-superimposable mirror images.
Proof & Explanation: The rigid C=C double bond (σ + π, rotation barrier 268 kJ/mol) locks substituents in place: bond dipoles add in the *cis* (Z) isomer (μ = 1.90 D) and cancel in the *trans* (E) isomer (μ = 0 D). Optical isomerism arises when a tetrahedral carbon C^* bears four different groups: mirror-image (R)- and (S)-enantiomers rotate polarized light by +α and -α.
Key Equations & 3D Simulation Parameters
α = [α]_D²⁰· l· c, μ_cis = 1.90 D, μₜrans = 0 D
- Stereoisomer (1=cis-Z, 2=trans-E, 3=R-enantiomer, 4=S-enantiomer): 1 … 4 (default: 1)
- Polarimeter solution concentration c: 0.1 … 1 g/mL (default: 0.5 g/mL)
- Polarimeter tube length l: 0.5 … 3 dm (default: 2 dm)
- 3D molecular model rotation speed ω: 0 … 2 rad/s (default: 0.8 rad/s)