Step 1: Understand the reaction.
The given reaction involves the diazotization of aniline with \( \text{NaNO}_2 \) and \( \text{HCl} \), followed by a coupling reaction with aniline to form a product. The reaction sequence is as follows:
1. Diazotization of aniline in the presence of \( \text{NaNO}_2 \) and \( \text{HCl} \).
2. The diazonium salt is then treated with warm aniline (40-45°C), followed by cooling and treatment with acetate to form the final product.
The product formed is an azo compound where the nitrogen from the diazonium group is part of the azo linkage.
Step 2: Calculate the molecular weight of the product.
For the product, we assume that the final product has the structure \( \text{C}_6\text{H}_5\text{N} = \text{N}-\text{C}_6\text{H}_4\text{NH}_2 \), an azo compound. The molecular weight can be determined by summing the atomic weights of the atoms involved:
\[
\text{C}_6\text{H}_5\text{N} = \text{N}-\text{C}_6\text{H}_4\text{NH}_2
\]
The molecular mass of the compound is the sum of the atomic masses:
- Carbon (C) = 12 g/mol
- Hydrogen (H) = 1 g/mol
- Nitrogen (N) = 14 g/mol
The total mass is:
\[
\text{C}_6\text{H}_5\text{N} = \text{N}-\text{C}_6\text{H}_4\text{NH}_2 \quad = 12 \times 6 + 1 \times 5 + 14 \times 2 = 106 + 5 + 28 = 139 \, \text{g/mol}
\]
Step 3: Calculate the percentage of nitrogen.
The mass of nitrogen in the product is:
\[
\text{Mass of Nitrogen} = 14 \times 2 = 28 \, \text{g/mol}
\]
The percentage of nitrogen in the final product is:
\[
\text{Percentage of Nitrogen} = \frac{28}{139} \times 100 = 20.14%
\]
Step 4: State the final answer.
Thus, the percentage of nitrogen in the final product is:
\[
\boxed{21.30%}
\]
