Which nitrogen derivative forms an aqueous solution with a pH less than 7, and why?

• A. N$_2$O (Nitrous oxide): This is a neutral oxide. It does not react with water to form an acid or a base. An aqueous solution of N$_2$O would have a pH of approximately 7.
• B. NO (Nitric oxide): This is also a neutral oxide. It does not react with water to form an acid or a base. An aqueous solution of NO would have a pH of approximately 7.
• C. NO$_2$ (Nitrogen dioxide): This is an acidic oxide. When nitrogen dioxide dissolves in water, it reacts to form nitric acid (HNO$_3$) and nitrous acid (HNO$_2$). The reaction is: $$2\text{NO}_2(g) + \text{H}_2\text{O}(l) \to \text{HNO}_3(aq) + \text{HNO}_2(aq)$$ Since both HNO$_3$ and HNO$_2$ are acids, the resulting aqueous solution will be acidic, meaning its pH will be less than 7.
• D. NaNO$_3$ (Sodium nitrate): This is a salt formed from a strong base (NaOH) and a strong acid (HNO$_3$). When dissolved in water, it dissociates into Na$^+$ and NO$_3^-$ ions. Neither of these ions undergoes significant hydrolysis. Therefore, an aqueous solution of NaNO$_3$ is neutral, with a pH of approximately 7.

Based on the analysis, NO$_2$ reacts with water to produce acids, resulting in a solution with a pH less than 7.

The final answer is $\boxed{\text{C}}$