HydrocarbonshardNUMERICAL

Consider the smallest possible completely conjugated, monocyclic planar carbocation that obeys HuckeHydrocarbons Chemistry Question

Question

Consider the smallest possible completely conjugated, monocyclic planar carbocation that obeys Huckel's rule and exhibits true aromaticity. Let $X$ be the number of carbon atoms in this ring, and $Y$ be the number of $\pi$ electrons it contains. What is the value of $X + Y$?

Answer: 5

💡 Solution & Explanation

The smallest aromatic ring corresponds to Huckel's integer $n=0$, yielding $4(0)+2 = 2$ $\pi$ electrons ($Y=2$). To have a completely conjugated monocyclic ring holding 2 $\pi$ electrons and a formal charge allowing cyclic delocalization, a minimum of 3 carbon atoms ($X=3$) is required (forming the cyclopropenyl cation, $C_3H_3^+$). The sum is $X + Y = 3 + 2 = 5$.

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