Step 1: Understand the nature of nitric acid as an oxidizing agent.
Nitric acid (HNO\(_3\)) is a strong oxidizing agent. The specific reduction product of nitrogen in nitric acid depends significantly on its concentration and the reactivity of the metal it reacts with. Generally, as the concentration of nitric acid decreases, the oxidation state of the nitrogen in the reduction product tends to be in a lower oxidation state.
Step 2: Determine the product with dilute nitric acid for zinc.
Zinc (Zn) is a moderately reactive metal.
When zinc reacts with dilute nitric acid, especially under conditions that could be considered \textit{very dilute} (as "dilute" is sometimes broadly used in multiple-choice questions to cover very dilute cases), the nitric acid is reduced to nitrous oxide (N\(_2\)O), which is a colorless gas. In some contexts, moderately dilute acid might yield NO, but for active metals like zinc, N\(_2\)O (from very dilute acid) or even ammonium nitrate (from extremely dilute acid, which then converts to N\(_2\)O or NH\(_3\)) are often the expected products. Given the options, N\(_2\)O is the most common reduction product when zinc reacts with \textit{dilute} (or very dilute) nitric acid.
The balanced chemical equation for the reaction of zinc with very dilute nitric acid producing N\(_2\)O is:
$4\text{Zn} + 10\text{HNO}_3 (\text{very dilute}) \rightarrow 4\text{Zn}(\text{NO}_3)_2 + \text{N}_2\text{O} + 5\text{H}_2\text{O}$
Step 3: Determine the product with concentrated nitric acid for zinc.
When zinc reacts with concentrated nitric acid, the nitric acid is primarily reduced to nitrogen dioxide (NO\(_2\)), which is a reddish-brown gas. This is a consistent product for most metals reacting with concentrated nitric acid.
The balanced chemical equation for the reaction of zinc with concentrated nitric acid producing NO\(_2\) is:
$\text{Zn} + 4\text{HNO}_3 (\text{conc.}) \rightarrow \text{Zn}(\text{NO}_3)_2 + 2\text{NO}_2 + 2\text{H}_2\text{O}$
Step 4: Combine the products respectively.
The question asks for the products from dilute and concentrated nitric acid, \textit{respectively}.
Product from dilute HNO\(_3\): N\(_2\)O
Product from concentrated HNO\(_3\): NO\(_2\)
Thus, the pair of products is N\(_2\)O and NO\(_2\).
Step 5: Compare with the given options.
Option (A) matches our derived products: N\(_2\)O and NO\(_2\).