Which of these molecules can have cis and trans iso- mers?...

Which of these molecules can have cis and trans iso- mers? For those that do, write the structural formulas of the two isomers and label each cis or trans. For those that cannot have these isomers, explain why. (a) $\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{BrC}=\mathrm{CBrCH}_{3}$ (b) $\left(\mathrm{CH}_{3}\right)_{2} \mathrm{C}=\mathrm{C}\left(\mathrm{CH}_{3}\right)_{2}$ (c) $\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{IC}=\mathrm{CICH}_{2} \mathrm{CH}_{3}$ (d) $\mathrm{CH}_{3} \mathrm{ClC}=\mathrm{CHCH}_{3}$ (e) $\left(\mathrm{CH}_{3}\right)_{2} \mathrm{C}=\mathrm{CHCH}_{3}$

Which of these molecules can have cis and trans iso-
mers? For those that do, write the structural formulas of the two isomers and label each cis or trans. For those
that cannot have these isomers, explain why.
(a) $\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{BrC}=\mathrm{CBrCH}_{3}$
(b) $\left(\mathrm{CH}_{3}\right)_{2} \mathrm{C}=\mathrm{C}\left(\mathrm{CH}_{3}\right)_{2}$
(c) $\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{IC}=\mathrm{CICH}_{2} \mathrm{CH}_{3}$
(d) $\mathrm{CH}_{3} \mathrm{ClC}=\mathrm{CHCH}_{3}$
(e) $\left(\mathrm{CH}_{3}\right)_{2} \mathrm{C}=\mathrm{CHCH}_{3}$

Key Concepts

Double Bond Rigidity and Restricted Rotation

The double bond is rigid due to its pi bond component, which prevents free rotation of the bonded atoms. This restricted rotation allows for the existence of stereoisomers (cis and trans forms) when the substituents are arranged differently on either side of the double bond.

Representation of Structural Formulas

Drawing accurate structural formulas is essential for visualizing the spatial arrangement of the substituents around the double bond. Such representations help in distinguishing between cis and trans isomers, enabling a clear comparison of the relative positions of substituents and facilitating the identification of cases where geometric isomerism is possible or ruled out due to symmetrical or identical substituents.

Geometric Isomerism

Geometric isomerism, often referred to as cis-trans isomerism, arises in compounds with double bonds where the restricted rotation about the carbon–carbon double bond means that substituents can occupy different spatial positions relative to the double bond. These distinct spatial arrangements can lead to molecules exhibiting different physical and chemical properties despite having the same connectivity.

Requirement for Distinct Substituents on Double-Bonded Carbons

For geometric isomerism to occur, each carbon atom of the double bond must have two different substituents. This difference is crucial because if a carbon atom has two identical groups, there is no possibility for the distinct spatial arrangement of those groups, and thus, cis-trans isomerism cannot be observed.

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