To determine the correct answer to the question, let's identify the roles of each species involved in the reaction:
[tex]\[ HNO_2 + H_2O \rightleftharpoons H_3O^+ + NO_2^- \][/tex]
Firstly, we need to understand that this reaction represents an acid-base equilibrium. Here’s a detailed step-by-step solution:
1. Identify the Acids and Bases:
- [tex]\( HNO_2 \)[/tex] is a weak acid.
- [tex]\( H_2O \)[/tex] (water) can act as either an acid or a base depending on the context, but in this reaction, it acts as a base, accepting a proton (H+).
2. Determine the Products:
- When [tex]\( HNO_2 \)[/tex] donates a proton (H+), it forms [tex]\( NO_2^- \)[/tex].
- When [tex]\( H_2O \)[/tex] accepts a proton, it forms [tex]\( H_3O^+ \)[/tex].
3. Define Conjugate Acid-Base Pairs:
- A conjugate base is formed when an acid loses a proton.
- A conjugate acid is formed when a base gains a proton.
Let’s analyze each reactant and product:
- [tex]\( HNO_2 \)[/tex] and [tex]\( NO_2^- \)[/tex]:
- [tex]\( HNO_2 \)[/tex] acts as an acid because it donates a proton.
- [tex]\( NO_2^- \)[/tex] is what remains of [tex]\( HNO_2 \)[/tex] after it loses a proton, making [tex]\( NO_2^- \)[/tex] the conjugate base of [tex]\( HNO_2 \)[/tex].
- [tex]\( H_2O \)[/tex] and [tex]\( H_3O^+ \)[/tex]:
- [tex]\( H_2O \)[/tex] acts as a base because it accepts a proton.
- [tex]\( H_3O^+ \)[/tex] is formed when [tex]\( H_2O \)[/tex] gains a proton, making [tex]\( H_3O^+ \)[/tex] the conjugate acid of [tex]\( H_2O \)[/tex].
4. Answer Choices Analysis:
- [tex]\( NO_2^- \)[/tex] as the conjugate base of [tex]\( HNO_2 \)[/tex]: This is correct since [tex]\( NO_2^- \)[/tex] is what [tex]\( HNO_2 \)[/tex] becomes after donating a proton.
- [tex]\( NO_2^- \)[/tex] as the conjugate base of [tex]\( H_2O \)[/tex]: Incorrect, since [tex]\( H_2O \)[/tex] forms [tex]\( H_3O^+ \)[/tex], not [tex]\( NO_2^- \)[/tex].
- [tex]\( NO_2^- \)[/tex] as the conjugate acid of [tex]\( HNO_2 \)[/tex]: Incorrect, since [tex]\( NO_2^- \)[/tex] cannot be an acid in this context.
- [tex]\( NO_2^- \)[/tex] as the conjugate base of [tex]\( H_3O^+ \)[/tex]: Incorrect, since [tex]\( H_3O^+ \)[/tex] forms [tex]\( H_2O \)[/tex], not [tex]\( NO_2^- \)[/tex].
Thus, the correct answer is:
[tex]\[ NO_2^- \text{ is the conjugate base of } HNO_2. \][/tex]
