Question

Which alkenes exist as pairs of cis,trans isomers? For each that does, draw the trans isomer. (a) \(\mathrm{CH}_{2}=\mathrm{CHBr}\) (b) \(\mathrm{CH}_{3} \mathrm{CH}=\mathrm{CHBr}\) (c) \(\mathrm{BrCH}=\mathrm{CHBr}\) (d) \(\left(\mathrm{CH}_{3}\right)_{2} \mathrm{C}=\mathrm{CHCH}_{3}\) (e) \(\left(\mathrm{CH}_{3}\right)_{2} \mathrm{CHCH}=\mathrm{CHCH}_{3}\)

Short answer

Answer: Alkenes (b), (c), and (e) have cis,trans isomers, and the trans isomers are as follows: (b) \(\mathrm{CH}_{3}\mathrm{CH}=\underset{Br}{\mathrm{C}}\overset{\mathrm{H}}{\mathrm{C}}\mathrm{H}\) (c) \(\underset{Br}{\mathrm{C}}\overset{\mathrm{H}}{\mathrm{C}}\underset{H}{\mathrm{C}}\overset{\mathrm{Br}}{\mathrm{C}}\mathrm{H}\) (e) \(\mathrm{C}\left(\mathrm{CH}_{3}\right)_{2}\overset{\mathrm{H}}{\mathrm{C}}\underset{H}{\mathrm{C}}\mathrm{CH}_{3}\)

Step-by-step solution

Identifying Double Bonds and Stereocenters

For an alkene to have cis and trans isomers, there must be a carbon-carbon double bond (C=C) with at least two different substituents on each carbon atom of the double bond. In other words, the carbon atoms must be stereocenters. (a) \(\mathrm{CH}_{2}=\mathrm{CHBr}\): No stereocenters since one carbon atom has two similar substituents (hydrogens). (b) \(\mathrm{CH}_{3} \mathrm{CH}=\mathrm{CHBr}\): Stereocenters present. (c) \(\mathrm{BrCH}=\mathrm{CHBr}\): Stereocenters present. (d) \(\left(\mathrm{CH}_{3}\right)_{2} \mathrm{C}=\mathrm{CHCH}_{3}\): No stereocenters since one carbon atom has two similar substituents (methyl groups). (e) \(\left(\mathrm{CH}_{3}\right)_{2} \mathrm{CHCH}=\mathrm{CHCH}_{3}\): Stereocenters present.

Drawing the trans Isomers

The following are the trans isomers for the alkenes with stereocenters: (b) \(\mathrm{CH}_{3} \mathrm{CH}=\mathrm{CHBr}\) The trans isomer: \(\mathrm{CH}_{3}\mathrm{CH}=\underset{Br}{\mathrm{C}}\overset{\mathrm{H}}{\mathrm{C}}\mathrm{H}\) (c) \(\mathrm{BrCH}=\mathrm{CHBr}\) The trans isomer: \(\underset{Br}{\mathrm{C}}\overset{\mathrm{H}}{\mathrm{C}}\underset{H}{\mathrm{C}}\overset{\mathrm{Br}}{\mathrm{C}}\mathrm{H}\) (e) \(\left(\mathrm{CH}_{3}\right)_{2} \mathrm{CHCH}=\mathrm{CHCH}_{3}\) The trans isomer: \(\mathrm{C}\left(\mathrm{CH}_{3}\right)_{2}\overset{\mathrm{H}}{\mathrm{C}}\underset{H}{\mathrm{C}}\mathrm{CH}_{3}\) The final answer: Trans isomers are present in alkenes (b), (c), and (e): (b) \(\mathrm{CH}_{3}\mathrm{CH}=\underset{Br}{\mathrm{C}}\overset{\mathrm{H}}{\mathrm{C}}\mathrm{H}\) (c) \(\underset{Br}{\mathrm{C}}\overset{\mathrm{H}}{\mathrm{C}}\underset{H}{\mathrm{C}}\overset{\mathrm{Br}}{\mathrm{C}}\mathrm{H}\) (e) \(\mathrm{C}\left(\mathrm{CH}_{3}\right)_{2}\overset{\mathrm{H}}{\mathrm{C}}\underset{H}{\mathrm{C}}\mathrm{CH}_{3}\)