Step 1: Understanding the Concept:
According to the Brønsted-Lowry theory of acids and bases:
- An **acid** is a proton (H\(^+\)) donor.
- A **base** is a proton (H\(^+\)) acceptor.
- A **Conjugate Acid** is the species formed when a base accepts a proton.
- A **Conjugate Base** is the species formed when an acid donates a proton.
The bicarbonate ion (HCO\(_3^-\)) is amphoteric, meaning it can act as both an acid and a base.
Step 2: Detailed Explanation:
1. **To find the Conjugate Acid of HCO\(_3^-\):**
We treat HCO\(_3^-\) as a base and add a proton (H\(^+\)) to it.
\[ \text{HCO}_3^- + \text{H}^+ \to \text{H}_2\text{CO}_3 \]
Thus, H\(_2\)CO\(_3\) (Carbonic acid) is the conjugate acid.
2. **To find the Conjugate Base of HCO\(_3^-\):**
We treat HCO\(_3^-\) as an acid and remove a proton (H\(^+\)) from it.
\[ \text{HCO}_3^- \to \text{H}^+ + \text{CO}_3^{2-} \]
Thus, CO\(_3^{2-}\) (Carbonate ion) is the conjugate base.
The question asks for the conjugate acid and conjugate base **respectively**. Therefore, the order should be (H\(_2\)CO\(_3\), CO\(_3^{2-}\)).
Step 3: Final Answer:
The conjugate acid is H\(_2\)CO\(_3\) and the conjugate base is CO\(_3^{2-}\).
Hence, the correct option is (B).