Predict the product in the following reactions:
(i) `H_(5)C_(6)-overset(OH)overset(|)underset(H)underset(|)(C)-overset(OH)overset(|)underset(H)underset(|)(C)-CH_(3)overset(H_(2)SO_(4))rarr` (ii) `H_(3)C-overset(OH)overset(|)underset(CH_(3))underset(|)(C)-underset(H)underset(|)overset(OH)overset(|)(C)-Hoverset(H_(2)SO_(4))rarr`
(iii) `H_(5)C_(6)-overset(OH)overset(|)underset(C_(6)H_(5))underset(|)(C)-underset(CH_(3))underset(|)overset(OH)overset(|)(C)-CH_(3)overset(H_(2)SO_(4))rarr`

Explanation

To predict the products of the given reactions, we will analyze each reaction step by step, focusing on the mechanism involved, particularly the rearrangement processes that occur due to the presence of sulfuric acid (H₂SO₄).

### Reaction (i):
1. **Identify the structure**: The starting compound is a diol (two hydroxyl groups) with a methyl group and a phenyl group.
2. **Protonation of hydroxyl groups**: The hydroxyl groups (OH) will be protonated by H₂SO₄, forming a better leaving group (H₂O).
3. **Formation of carbocation**: The protonation leads to the departure of water, generating a carbocation. The stability of the carbocation is crucial; the phenyl group stabilizes the carbocation via resonance more than the methyl group.
4. **Rearrangement**: A hydride shift occurs from the methyl group to the carbocation, resulting in a more stable carbocation.
5. **Nucleophilic attack**: The lone pair on the oxygen of the remaining hydroxyl group attacks the carbocation, leading to the formation of a ketone.
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