Step 1: Understanding the Question:
The question asks us to identify a chemical example of a symmetrical tertiary amine from the provided options.
Step 2: Key Formula or Approach:
Amines are classified structurally based on the number of alkyl or aryl groups attached directly to the central nitrogen atom:
• Tertiary amine ($\mathrm{3^\circ}$): The nitrogen atom is bonded to three alkyl or aryl substituents ($\mathrm{R_3N}$).
• Symmetrical (Simple) amine: A tertiary or secondary amine where all the attached alkyl or aryl groups are identical.
Step 3: Detailed Explanation:
Let's analyze the structural properties of each option:
• Trimethylamine: Its chemical formula is $\mathrm{N(CH_3)_3}$. The nitrogen is bonded to three methyl groups. Since it has three groups, it is a tertiary amine. Since all three methyl groups are completely identical, it is classified as a symmetrical tertiary amine.
• Dimethylamine: Formula is $\mathrm{(CH_3)_2NH}$. It contains a hydrogen atom on the nitrogen, making it a secondary ($mathrm{2^\circ}$) amine.
• Ethylmethylamine: Formula is $\mathrm{CH_3-NH-C_2H_5}$. It contains two different groups attached to a secondary amine framework.
• Diethylamine: Formula is $\mathrm{(C_2H_5)_2NH}$. This is a symmetrical secondary amine.
Thus, Trimethylamine is the only molecule that satisfies both being tertiary and perfectly symmetrical.
Step 4: Final Answer:
The example of a symmetrical tertiary amine is Trimethylamine, which corresponds to option (A).