Problem 119 - General Chemistry: Principles and Modern Applications

Question

The equilibria \(\mathrm{OH}^{-}+\mathrm{HClO} \longrightarrow \mathrm{H}_{2} \mathrm{O}+\mathrm{ClO}^{-}\) and \(\mathrm{ClO}^{-}+\mathrm{HNO}_{2} \longrightarrow \mathrm{HClO}+\mathrm{NO}_{2}^{-}\) both lie to the right. Which of the following is a list of acids ranked in order of decreasing strength? (a) \(\mathrm{HClO}>\mathrm{HNO}_{2}>\mathrm{H}_{2} \mathrm{O}\) (b) \(\mathrm{ClO}^{-}>\mathrm{NO}_{2}^{-}>\mathrm{OH}^{-}\) (c) \(\mathrm{NO}_{2}^{-}>\mathrm{ClO}^{-}>\mathrm{OH}\) (d) \(\mathrm{HNO}_{2}>\mathrm{HClO}>\mathrm{H}_{2} \mathrm{O}\) (e) none of these

Step-by-Step Solution

Answer

The correct answer is (d) \(\mathrm{HNO}_{2}>\mathrm{HClO}>\mathrm{H}_{2} \mathrm{O}\)

Step 1: Analyze the first equation

By looking at the first equilibrium \(\mathrm{OH}^{-}+\mathrm{HClO} \longrightarrow \mathrm{H}_{2}\mathrm{O}+\mathrm{ClO}^{-}\), since the reaction lies to the right, it means HClO is a stronger acid than H2O.

Step 2: Analyze the second equation

By analyzing the second equilibrium \(\mathrm{ClO}^{-}+\mathrm{HNO}_{2}\longrightarrow \mathrm{HClO}+\mathrm{NO}_{2}^{-}\), once again, since the reaction lies to the right, it suggests HNO2 is a stronger acid than HClO.

Step 3: Combine the results of both equations to form order

Combining the results from step 1 and step 2, the strongest acid is HNO2, then comes HClO, and finally H2O as the weakest.

Key Concepts

Acid-Base Equilibria

Understanding acid-base equilibria is essential to solving problems related to reaction directions and acid strength comparisons. An equilibrium involves a chemical reaction that can proceed in both forward and reverse directions. When we talk about acid-base equilibria, the focus is on reactions where acids donate protons ( + ions) to bases, which accept them.
In an equilibrium like \[\mathrm{OH}^{-} + \mathrm{HClO} \longrightarrow \mathrm{H}_{2}\mathrm{O} + \mathrm{ClO}^{-},\]we look for the balance between these species in the solution. The equilibrium lies to the right if the products form more readily, indicating that the reaction proceeds more significantly in that direction.
In the context of acid-base equilibria, knowing whether a reaction favors the formation of products or reactants helps in determining which acid-base pairs are stronger. This understanding allows us to rank acids on a scale of relative strength based on which side of the equilibrium is more favored. The reaction direction provides clues about the comparative strengths of acids involved.

Reaction Direction

Every chemical reaction has a preferred direction, which is where we focus our analysis for indicators of acid strength. The direction in which a reaction primarily proceeds, whether forward or reverse, tells us about the relative tendencies of the substances to form products or revert to reactants.
For example, if a reaction like\[\mathrm{OH}^{-} + \mathrm{HClO} \rightarrow \mathrm{H}_{2}\mathrm{O} + \mathrm{ClO}^{-}\]proceeds to the right, it means the products are more stable. Hence, the acid on the reactant side (HClO) is stronger than the acid on the product side (H2O) because it donates protons more effectively.
The same logic is applied in other equilibria to infer the relative strength of acids. Thus, reaction direction is a valuable empirical cue for ordering acids by strength. The ability to recognize which substances form more readily in a chemical reaction directly illuminates the hierarchy of acid strengths.

Comparing Acids

Comparing acids involves understanding their differing abilities to donate protons. Generally, an acid's strength is indicated by its tendency to release protons in solution. Strong acids dissociate more completely, yielding ions freely, while weak acids partially dissociate.
In rankings based on acid strength, consider the equilibria given:

• \(\mathrm{OH}^{-} + \mathrm{HClO} \rightarrow \mathrm{H}_{2}\mathrm{O} + \mathrm{ClO}^{-}\) suggests \(\mathrm{HClO}\) is stronger than \(\mathrm{H}_{2}\mathrm{O}\).
• \(\mathrm{ClO}^{-} + \mathrm{HNO}_{2} \rightarrow \mathrm{HClO} + \mathrm{NO}_{2}^{-}\) implies \(\mathrm{HNO}_{2}\) is stronger than \(\mathrm{HClO}\).

By comparing these reactions and ranking the acids based on which side the reactions favor, we conclude that \(\mathrm{HNO}_{2}\) is the strongest, followed by \(\mathrm{HClO}\) and \(\mathrm{H}_{2}\mathrm{O}\) as the weakest.
Understanding acid strength helps in predicting the outcomes of reactions and the structure of chemical products. This skill allows students to not only solve similar problems but also deepen their grasp of acidic and basic behavior in chemical systems.