ClO2-(aq) + HCOOH(aq) ⇄ HClO2(aq) + HCOO-(aq) Keq < 1 What are the relative strengths of the acids a — Acids and Bases Chemistry Question

STEPS:

1. Identify the Brønsted^-Lowry acids and bases on both sides of the equation:
* Reactants side: Formic acid, $\text{HCOOH}(aq)$, acts as the proton donor (acid), while the chlorite ion, $\text{ClO}_2^-(aq)$, acts as the proton acceptor (base).
* Products side: Chlorous acid, $\text{HClO}_2(aq)$, acts as the conjugate acid (capable of donating a proton in the reverse reaction), while the formate ion, $\text{HCOO}^-(aq)$, acts as the conjugate base (capable of accepting a proton in the reverse reaction).

2. Interpret the thermodynamic meaning of the equilibrium constant ($K_{\text{eq}} < 1$):
* An equilibrium constant of less than 1 ($K_{\text{eq}} < 1$) indicates that the reactants are favored at equilibrium.
* This means that under equilibrium conditions, the concentration of the reactants ($\text{ClO}_2^-$ and $\text{HCOOH}$) is significantly higher than the concentration of the products ($\text{HClO}_2$ and $\text{HCOO}^-$).

3. Apply the fundamental rule of acid-base equilibrium:
* In any Brønsted^-Lowry acid-base reaction, proton-transfer equilibria always favor the side of the reaction with the weaker acid and the weaker base.
* This occurs because stronger acids have a greater tendency to lose protons, and stronger bases have a greater tendency to attract protons, reacting highly efficiently to produce their more stable, weaker counterparts.

4. Determine the relative acid strengths:
* Since the reactants are favored at equilibrium, the reactant acid ($\text{HCOOH}$) must be the weaker acid, and the product acid ($\text{HClO}_2$) must be the stronger acid:
$$\mathbf{\text{Acid Strength: } \text{HClO}_2 > \text{HCOOH}}$$

5. Determine the relative base strengths:
* Since the reactants are favored at equilibrium, the reactant base ($\text{ClO}_2^-$) must be the weaker base, and the product conjugate base ($\text{HCOO}^-$) must be the stronger base:
$$\mathbf{\text{Base Strength: } \text{ClO}_2^- < \text{HCOO}^-}$$
* *Note: This perfectly aligns with conjugate acid-base theory, which states that a stronger acid ($\text{HClO}_2$) must conjugate to a weaker base ($\text{ClO}_2^-$), and a weaker acid ($\text{HCOOH}$) must conjugate to a stronger base ($\text{HCOO}^-$).*

6. Select the matching option:
* Combining these two relative strengths ($\text{Acid Strength: } \text{HClO}_2 > \text{HCOOH}$ and $\text{Base Strength: } \text{ClO}_2^- < \text{HCOO}^-$) identifies Option D as the correct answer.

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WHY_OTHERS_WRONG:

• Option A is incorrect: This option claims that $\text{HClO}_2$ is a weaker acid than $\text{HCOOH}$ and that $\text{ClO}_2^-$ is a weaker base than $\text{HCOO}^-$. This is a conceptual mismatch; it places the weaker acid and the stronger base on opposite sides of the equilibrium, which violates conjugate acid-base rules. Furthermore, if $\text{HCOOH}$ were the stronger acid, the forward reaction would be favored, leading to a $K_{\text{eq}} > 1$.
• Option B is incorrect: This option states that $\text{HCOOH}$ is the stronger acid and $\text{ClO}_2^-$ is the stronger base. If both reactants were the stronger species, they would react forward almost completely to establish equilibrium, resulting in a product-favored system with a $K_{\text{eq}} > 1$.
• Option C is incorrect: While this option correctly identifies that $\text{HClO}_2$ is the stronger acid, it incorrectly claims that $\text{ClO}_2^-$ is the stronger base. Because a stronger acid is always coupled with a weaker conjugate base, the stronger acid $\text{HClO}_2$ must have a weaker conjugate base than $\text{HCOOH}$ does, meaning $\text{ClO}_2^-$ must be a weaker base than $\text{HCOO}^-$.