Problem:
Structure (1) is more stable than structure (2).
My teacher stated that Structure (1) is more stable than Structure (2). I find this confusing. How can Structure (1) be more stable when Structure (2) has more methyl groups, resulting in a greater +I effect, which in turn enhances carbocation stability?
Question: Which structure is more stable above? If (1), how?
The first structure is indeed more stable than the second one. The reason being the phenomenon of Hyperconjugation, in which a hydrogen atom bonded to an $\text{sp}^3$ carbon atom, which is in conjugation to an $\text{sp}^2$ carbon is lost as $H^+$ and the electron pair that previously were involved between the bonding of hydrogen and carbon atoms are transferred though Resonance to the electron deficient $\text{sp}^2$ carbon.
In the first structure, number of $\alpha-\text{H}$ (number of hydrogen that can potentially be involved in hyperconjugation) is 3, however in second, it's only 1 in the $sp^3$ carbon in conjugation with the carbocation. The stability due to hyperconjugation is directly proportional to the number of $\alpha-\text{H}$.
As per the inductive effect is concerned, it's the least effective electronic effect, moreover, it even diminishes almost completely after 6 carbon atoms.
Always remember the AERHI rule, that stands for "Aromaticity, Electromeric, Resonance, Hyperconjugation, Inductive effect", it gives the general order of dominance of these effects, inductive effect being the lowest and aromaticity being the most dominant factor.
When a group is attached to the ortho or para position w.r.t the carbocation, we look at the hyperconjugation effect.
When a group is attached to the meta position w.r.t the carbocation, we consider the inductive effect.
In this case, both the groups are attached to the meta position, hence we check the hyperconjugation effect. In Structure (1), there are $3$ $\alpha$-H, whereas in Structure (2), there is only $1$ $\alpha$-H.
Hence Structure (1) is more stable than Structure (2).
