Step 1: Concept
In an acid-base reaction, the conjugate base of an acid is the species formed when the acid donates a proton (H$^+$), and the conjugate acid of a base is the species formed when the base accepts a proton. For example, if $\text{NH}_3 + \text{H}^+ \rightarrow \text{NH}_4^+$, then $\text{NH}_4^+$ is the conjugate acid of $\text{NH}_3$.
Step 2: Meaning
A conjugate acid-base pair consists of a substance and its reaction product after it has gained or lost a proton. The key to identifying such pairs lies in recognizing which molecule can donate a proton (acid) and which can accept one (base).
Step 3: Analysis
Let's analyze each option:
Option A: $\text{NH}_4^+$ and $\text{NH}_3$
- $\text{NH}_4^+$ is formed when $\text{NH}_3$ donates a proton. Therefore, $\text{NH}_3$ acts as the base (accepts H$^+$) and $\text{NH}_4^+$ acts as its conjugate acid.
Option B: $\text{HCl}$ and $\text{NaOH}$
- These are not a conjugate pair because they do not directly form each other by proton transfer. Instead, $\text{HCl}$ is an acid that can donate H$^+$ to $\text{NaOH}$ (a base), forming water and sodium chloride.
Option C: $\text{H}_2\text{SO}_4$ and $\text{SO}_4^{2-}$
- $\text{H}_2\text{SO}_4$ can donate protons to form $\text{HSO}_4^-$, but not directly to $\text{SO}_4^{2-}$ in a simple proton transfer reaction. Thus, they are not a conjugate pair.
Option D: $\text{HNO}_3$ and $\text{H}_2\text{O}$
- These do not form each other by proton transfer. $\text{HNO}_3$ is an acid that can donate H$^+$ to water, but this does not make them a conjugate pair.
Step 4: Conclusion
The only option where one species directly forms the other through a simple proton transfer reaction is Option A: $\text{NH}_4^+$ and $\text{NH}_3$.
Final Answer: (A)