See image — Isomerism and Stereochemistry Chemistry Question

💡 Solution & Explanation

Step 1 - Identify the structure: The compound shown is 2,3,5,6-tetrabromoheptane (or an equivalent symmetric tetrabromide), which contains 4 stereocenters. The structure has a pseudo-symmetry: the molecule is of the form CH3-CHBr-CHBr-CH2-CHBr-CHBr-CH3, making it a symmetric molecule with 4 stereocenters. Step 2 - Apply the 2^n rule as the maximum: With 4 stereocenters, the theoretical maximum is 2^4 = 16 stereoisomers. Step 3 - Account for internal symmetry (meso forms): Because the molecule has a plane of symmetry (it is symmetric about the central CH2), pairs of configurations that are mirror images of each other through the center of the molecule may give meso compounds, reducing the actual count below 16. Step 4 - Count actual stereoisomers: For a molecule of type A-B-CH2-B-A (where A = CHBr-CH3 unit and B = CHBr), the two halves are identical. Label the four stereocenters as C2, C3, C5, C6. The pairs (C2,C6) and (C3,C5) are related by the molecular symmetry axis. For each half (C2,C3) there are 4 combinations: (R,R), (S,S), (R,S), (S,R). The full molecule combines two halves: - (R,R)+(R,R), (S,S)+(S,S): these are enantiomers of each other — 2 stereoisomers - (R,R)+(S,S) and (S,S)+(R,R): these are the same compound (meso) — 1 stereoisomer - (R,S)+(R,S), (S,R)+(S,R), (R,S)+(S,R), (S,R)+(R,S): analyzing these for meso/enantiomer relationships gives additional stereoisomers Step 5 - Systematic count: The number of distinct stereoisomers for a symmetric molecule with 4 stereocenters arranged symmetrically is calculated as: total = 2^(n-1) + 2^(n/2-1) = 2^3 + 2^1 = 8 + 2 = 10 (using the formula for symmetric even-n case). Alternatively: enumerating all combinations of (C2,C3,C5,C6) configurations and removing duplicates due to molecular symmetry yields 10 distinct stereoisomers. Step 6 - Why other options fail: - (a) 6: Undercounts; does not account for all non-meso combinations. - (b) 8: Would be the answer if there were only 2 pairs with one meso each, but the symmetry analysis gives more. - (d) 16: This is 2^4, ignoring all meso/symmetry reductions. The maximum number of stereoisomers is 10. Therefore, the correct answer is C.