Geometrical Isomerism in Alkenes

Because rotation about a carbon-carbon double bond is restricted (breaking it would mean breaking

the pi bond), the two substituents attached to each doubly-bonded carbon are frozen in a fixed

spatial relationship to each other -- unlike a single bond, where the groups can rotate freely

past one another. When each of the two double-bond carbons carries two different groups, this

gives rise to two distinct, non-interconvertible spatial arrangements called geometrical (or cis-trans) isomers.

The condition for geometrical isomerism: an alkene $\text{R}_1\text{R}_2\text{C}{=} \text{CR}_3\text{R}_4$ shows cis-trans isomerism only if $\text{R}_1 \neq \text{R}_2$ AND

$\text{R}_3 \neq \text{R}_4$ -- i.e. neither doubly-bonded carbon may carry two identical

groups. Ethene itself ($\text{H}_2\text{C}{=}\text{CH}_2$) fails this test on both carbons and

so shows no geometrical isomerism; propene ($\text{CH}_3\text{CH}{=}\text{CH}_2$) fails it on

the terminal $\text{=CH}_2$ carbon (two identical H's) and likewise shows none. But-2-ene,

$\text{CH}_3\text{CH}{=}\text{CHCH}_3$, satisfies the condition on both carbons (each carries

one $\text{CH}_3$ and one H, which are different) and exists as two isomers: cis-but-2-ene,

with both methyl groups on the same side of the double bond, and trans-but-2-ene, with the

methyl groups on opposite sides.

Naming and properties. The older cis/trans labels describe whether the two "main" or

higher-priority groups are on the same side (cis, Latin "on this side") or opposite sides (trans,

"across") of the double bond; the more rigorous IUPAC E/Z system (used for more complex cases with

more than two different substituent types) assigns priorities to each carbon's two substituents by

atomic number and calls the isomer Z ("zusammen", together) if the two higher-priority groups are

on the same side, and E ("entgegen", opposite) if they are on opposite sides. The two isomers are

genuinely different compounds with different physical properties: cis-but-2-ene has a net

molecular dipole moment (the two methyl groups' bulk and electron-donating effect do not cancel) …