See image — Isomerism and Stereochemistry Chemistry Question

💡 Solution & Explanation

Concept: Diastereomers are stereoisomers that are not mirror images of each other. They differ in configuration at one or more (but not all) stereocenters, or they differ in one type of stereoisomerism (e.g., one center differs while another remains the same, or E/Z geometry differs while the chiral center remains the same). Step 1: Identify the stereoelements in (R)-4-bromo-cis-2-hexene. - It has a double bond between C2 and C3 with cis (Z) geometry. - It has a chiral center at C4 with R configuration. So this compound has two stereocenters/stereoelements: (cis, R). Step 2: Definition of diastereomers. Two compounds are diastereomers if they are stereoisomers (same connectivity/constitution) but not enantiomers. They must differ at some but not all stereoelements. Step 3: Evaluate each option. (a) (S)-4-bromo-cis-2-hexene: Same constitution, same double bond geometry (cis), opposite configuration at C4 (S vs R). This differs at ALL stereoelements if we consider only two: cis stays the same but R→S changes. Wait — cis is the same, R→S is different. This means they differ at exactly one stereoelement (C4 configuration) while the other (double bond geometry) remains the same. This makes them diastereomers? Actually, let's reconsider: if cis is the same and R vs S differ, these are diastereomers. But conventionally, (R)-4-bromo-cis-2-hexene and (S)-4-bromo-cis-2-hexene are enantiomers only if those are the only two stereoelements and they are mirror images. Since the molecule has a double bond (cis) AND a chiral center (R), the enantiomer would be (S)-4-bromo-trans-2-hexene... actually no. The enantiomer inverts ALL stereocenters: R→S AND cis→trans. So (a) changes only R→S but keeps cis, making (a) a diastereomer. Hmm, but let me reconsider more carefully. Actually: The enantiomer of (R)-4-bromo-cis-2-hexene is (S)-4-bromo-trans-2-hexene because full mirror image inverts both the chiral center (R→S) and the geometric isomerism (cis→trans) when the substituents on the double bond are not symmetric. Wait — cis/trans geometry is not inverted by mirror imaging in general; mirror image of a cis alkene is still cis (geometric isomerism is not a stereocenter in the same sense). So the enantiomer of (R)-4-bromo-cis-2-hexene is (S)-4-bromo-cis-2-hexene (option a), since the mirror image only inverts the chiral center configuration, and cis geometry is retained. Therefore option (a) is the enantiomer, not a diastereomer. Step 4: Option (c) (R)-4-bromo-trans-2-hexene: Same constitution as the target, same chiral center configuration (R), but different double bond geometry (trans vs cis). These are stereoisomers that differ at one stereoelement (the double bond geometry) but are identical at the other (R configuration). They are NOT mirror images of each other. Hence they are diastereomers. Step 5: Options (b) and (d) involve 5-bromo-2-hexene, which is a different constitutional isomer (bromine at C5 instead of C4), so these are constitutional isomers, not stereoisomers, and cannot be diastereomers. Step 6: Conclusion. The diastereomer of (R)-4-bromo-cis-2-hexene is (R)-4-bromo-trans-2-hexene, which is option (c). It has the same molecular connectivity and the same R configuration at C4, but differs in the double bond geometry (trans instead of cis), making it a diastereomer. Therefore, the correct answer is C.