Isomerism and StereochemistryhardMCQ SINGLE⭐ Must-Do

For highly symmetrical organic molecules containing an ODD number ('') of chiral centers, what is thIsomerism and Stereochemistry Chemistry Question

Question

For highly symmetrical organic molecules containing an ODD number ('$n$') of chiral centers, what is the heavily simplified mathematical formula used to determine the TOTAL overall number of stereoisomers (active + meso) for such a molecule?

Answer: B

💡 Solution & Explanation

Symmetrical molecules with odd chiral centers feature a central pseudo-chiral carbon that can generate meso forms. The formula for active isomers is $2^{n-1} - 2^{(n-1)/2}$, and for meso is $2^{(n-1)/2}$. When summed to find the total stereoisomers, the subtractive and additive meso terms cancel perfectly, leaving the simplified Total formula as exactly $2^{n-1}$.

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