How many stereoisomers are possible for the structure below?[Fill in the blank]

Question

BlackTom AI · Accepted Answer

Each substituted ring carbon bearing a single hydrogen and a substituent is a stereogenic center here, so count the chiral centers first.

Knowledge points:
- A saturated sp3 carbon attached to four different groups is a stereocenter.
- For n non-equivalent stereocenters with no internal mirror symmetry (no meso forms), the maximum number of stereoisomers is 2^n.
- Conformational differences (chair flips) do not count as distinct stereoisomers if they interconvert rapidly; only configurational stereoisomers count.

Step-by-step reasoning:
1. Identify the substituted carbons on the cyclohexane drawn: one carbon bears an OH, a second carbon bears a methyl, and a third carbon bears an isopropyl (CH(CH3)2) substituent. Each of those ring carbons is sp3 and has one hydrogen plus three different substituent groups (the two different ring fragments on either side are not identical because the pattern of substituents around the ring is asymmetric). Therefore each of these three carbons is a stereocenter.
2. Count stereocenters: n = 3.
3. Compute maximum stereoisomers: 2^n = 2^3 = 8. This gives the total number of stereoisomers assuming no internal plane of symmetry or meso compound reduces the count.
4. Check for meso/symmetry: with three stereocenters (an odd number) and the given asymmetric substitution pattern (isopropyl, methyl, and OH at non-symmetric positions), there is no internal mirror plane that would produce meso forms. Thus no reduction from the 2^3 count occurs.

Why the correct answer (d. 8) is correct:
- There are three independent stereocenters and no symmetry to make meso compounds, so all 2^3 = 8 stereoisomers are distinct.

Why the other options are incorrect:
- a. 1 and b. 2 are far too few because multiple stereocenters exist; they ignore the multiplicative effect of independent chiral centers.
- c. 4 would be correct only if there were two stereocenters (2^2 = 4) or if meso symmetry reduced the count; neither condition applies here.

Conclusion: The structure has three stereocenters and therefore 2^3 = 8 stereoisomers, confirming answer d. 8.

How many stereoisomers are possible for the structure below?[Fill in the blank]单项选择题

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