Step 1: Understanding the Concept:
Mesityl oxide is the common name for an $\alpha, \beta$-unsaturated ketone formed by the aldol condensation of two acetone molecules followed by dehydration.
Step 2: Detailed Explanation:
1. Structure Calculation: Two molecules of acetone ($CH_3COCH_3$) condense to form 4-hydroxy-4-methylpentan-2-one, which dehydrates to form mesityl oxide:
\[ (CH_3)_2C=CH-CO-CH_3 \]
2. Numbering the Chain: Select the longest chain containing both the ketone group and the double bond. The ketone ($C=O$) has priority over the alkene ($C=C$).
- $C_1$: $CH_3$ group at the end near the ketone.
- $C_2$: Carbonyl carbon ($C=O$).
- $C_3$: Carbon of the double bond.
- $C_4$: Carbon of the double bond with a methyl substituent.
- $C_5$: Terminal $CH_3$ group.
3. Name Assembly: The parent is pentane. With the suffix -one and -ene, it becomes pent-3-en-2-one. There is a methyl group at position 4.
Result: 4-Methylpent-3-en-2-one.
Step 3: Final Answer:
The IUPAC name is 4-Methylpent-3-en-2-one.