Isomerism and StereochemistryhardNUMERICAL

What is the total number of mathematically predicted "meso" isomers possible for a perfectly symmetrIsomerism and Stereochemistry Chemistry Question

Question

What is the total number of mathematically predicted "meso" isomers possible for a perfectly symmetrical organic molecule possessing exactly $4$ chiral stereocenters?

Answer: 2

💡 Solution & Explanation

For a highly symmetrical molecule possessing an even number of chiral centers ($n$), the formula to calculate the exact number of optically inactive "meso" compounds (which possess an internal plane or center of symmetry) is $2^{(n/2 - 1)}$. Given $n=4$, the calculation is $2^{(4/2 - 1)} = 2^{(2 - 1)} = 2^1 = 2$.

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