Organic Chemistry – Some Basic Principles Part 3

Concept:Stability of carbocations increases with more hyperconjugation interactions, which require $\alpha$-hydrogens (hydrogen atoms on carbon adjacent to the positively charged carbon).Explanation:In $\left(\mathrm{CH}_3\right)_3\overset{\oplus}{\mathrm{C}}$ (tert‑butyl carbocation), the positively charged carbon is bonded to three methyl groups.Each methyl group acts as an $\alpha$-carbon, and each has three $\alpha$-hydrogens.Total $\alpha$-hydrogens = $3 \times 3 = 9$, so nine hyperconjugation structures are possible.In $\overset{\oplus}{\mathrm{C}}\mathrm{H}_3$ (methyl carbocation), there is no carbon adjacent to the charged carbon; hence zero $\alpha$-hydrogens and no hyperconjugation.Therefore, $\left(\mathrm{CH}_3\right)_3\overset{\oplus}{\mathrm{C}}$ is far more stable than $\overset{\oplus}{\mathrm{C}}\mathrm{H}_3$.Statement I is true because it correctly states the presence of nine hyperconjugation interactions and the greater stability.Statement II claims that $\overset{\oplus}{\mathrm{C}}\mathrm{H}_3$ is less stable than $\left(\mathrm{CH}_3\right)_3\overset{\oplus}{\mathrm{C}}$ because only three hyperconjugation interactions occur in $\overset{\oplus}{\mathrm{C}}\mathrm{H}_3$.The first part (less stable) is correct, but the reason is wrong — $\overset{\oplus}{\mathrm{C}}\mathrm{H}_3$ has zero hyperconjugation, not three.Hence Statement II is false.Answer:Option B: Statement I is true but Statement II is false.