Identify the more stable carbocation in each pair.
(a)

Verified step by step guidance

1. Step 1: Analyze the structure of the first carbocation. It is a secondary carbocation attached to a cyclohexane ring. Secondary carbocations are moderately stable due to the inductive effect of adjacent alkyl groups, which can donate electron density to stabilize the positive charge.
2. Step 2: Analyze the structure of the second carbocation. It is a benzylic carbocation, where the positive charge is adjacent to a benzene ring. Benzylic carbocations are highly stable due to resonance stabilization. The positive charge can delocalize over the aromatic ring, spreading the charge across multiple atoms.
3. Step 3: Compare the stability of the two carbocations. Resonance stabilization in the benzylic carbocation provides significantly more stability than the inductive effect in the secondary carbocation.
4. Step 4: Recall the general rule: carbocations stabilized by resonance are more stable than those stabilized by inductive effects alone. This makes the benzylic carbocation the more stable option.
5. Step 5: Conclude that the benzylic carbocation is more stable due to resonance stabilization, which allows the positive charge to be delocalized over the aromatic ring.

Key Concepts

Carbocation Stability

Carbocations are positively charged carbon species that can vary in stability based on their structure. Stability increases with the degree of substitution; tertiary (3°) carbocations are more stable than secondary (2°), which are more stable than primary (1°). This is due to hyperconjugation and the inductive effect from surrounding alkyl groups that help to disperse the positive charge.

Hyperconjugation

Hyperconjugation is a stabilizing interaction that occurs when the electrons in a sigma bond (usually C-H or C-C) interact with an adjacent empty p-orbital or a positively charged carbon. This delocalization of electrons helps to stabilize the carbocation by spreading out the positive charge over a larger area, making the carbocation less reactive and more stable.

Inductive Effect

The inductive effect refers to the electron-withdrawing or electron-donating effects transmitted through sigma bonds in a molecule. Alkyl groups are electron-donating, which can stabilize a carbocation by reducing the positive charge's density. The greater the number of alkyl groups attached to the carbocation, the more stable it becomes due to this inductive effect.