Problem 99 - General Chemistry: Principles and Modern Applications

Question

The following four equilibria lie to the right: \(\mathrm{N}_{2} \mathrm{H}_{5}^{+}+\) \(\mathrm{CH}_{3} \mathrm{NH}_{2} \longrightarrow \mathrm{N}_{2} \mathrm{H}_{4}+\mathrm{CH}_{3} \mathrm{NH}_{3}^{+} ; \mathrm{H}_{2} \mathrm{SO}_{3}+\mathrm{F}^{-} \longrightarrow\) \(\mathrm{HSO}_{3}^{-}+\mathrm{HF} ; \mathrm{CH}_{3} \mathrm{NH}_{3}^{+}+\mathrm{OH}^{-} \longrightarrow \mathrm{CH}_{3} \mathrm{NH}_{2}+\) \(\mathrm{H}_{2} \mathrm{O} ;\) and \(\mathrm{HF}+\mathrm{N}_{2} \mathrm{H}_{4} \longrightarrow \mathrm{F}^{-}+\mathrm{N}_{2} \mathrm{H}_{5}^{+}\) (a) Rank all the acids involved in order of decreasing acid strength. (b) Rank all the bases involved in order of decreasing base strength. (c) State whether each of the following two equilibria lies primarily to the right or to the left: (i) \(\mathrm{HF}+\mathrm{OH}^{-} \longrightarrow \mathrm{F}^{-}+\mathrm{H}_{2} \mathrm{O} ;\) (ii) \(\mathrm{CH}_{3} \mathrm{NH}_{3}^{+}+\) \(\mathrm{HSO}_{3}^{-} \longrightarrow \mathrm{CH}_{3} \mathrm{NH}_{2}+\mathrm{H}_{2} \mathrm{SO}_{3}\).

Step-by-Step Solution

Answer

a) Acids from strongest to weakest: \( \mathrm{N}_{2} \mathrm{H}_{5}^{+} \), \( \mathrm{H}_{2} \mathrm{SO}_{3} \), \( \mathrm{CH}_{3} \mathrm{NH}_{3}^{+} \), \( \mathrm{HF} \). b) Bases from strongest to weakest: \( \mathrm{CH}_{3} \mathrm{NH}_{2} \), \( \mathrm{F}^{-} \), \( \mathrm{OH}^{-} \), \( \mathrm{N}_{2} \mathrm{H}_{4} \). c) (i) The equilibrium lies to the left, (ii) the equilibrium lies to the right.

Step 1: Identifying Acids and Bases

First, identify the acids and bases on the left side of each equilibrium reaction. Acids are substances that donate protons (H+), while bases accept protons.

Step 2: Ranking Acids

Ranking of acids in decreasing order of strength would be \( \mathrm{N}_{2} \mathrm{H}_{5}^{+} \), \( \mathrm{H}_{2} \mathrm{SO}_{3} \), \( \mathrm{CH}_{3} \mathrm{NH}_{3}^{+} \), and \( \mathrm{HF} \). Strong acids tend to lose protons more readily, shifting the equilibrium to the right.

Step 3: Ranking Bases

Next, rank bases in decreasing order of strength as \( \mathrm{CH}_{3} \mathrm{NH}_{2} \), \( \mathrm{F}^{-} \), \( \mathrm{OH}^{-} \), and \( \mathrm{N}_{2} \mathrm{H}_{4} \). Bases with strong ability to attract protons will shift the equilibrium to the right.

Step 4: Predicting the direction of equilibrium (i)

Predict for the equilibrium \( \mathrm{HF}+\mathrm{OH}^{-} \longrightarrow \mathrm{F}^{-}+\mathrm{H}_{2} \mathrm{O} \) whether it lies to the right or left. Based on the ranking, \( \mathrm{HF} \) is a weaker acid than \( \mathrm{H}_{2} \mathrm{O} \), and \( \mathrm{OH}^{-} \) is a stronger base than \( \mathrm{F}^{-} \). Thus, this equilibrium lies to the left.

Step 5: Predicting the direction of equilibrium (ii)

Predict for the equilibrium \( \mathrm{CH}_{3} \mathrm{NH}_{3}^{+}+ \mathrm{HSO}_{3}^{-} \longrightarrow \mathrm{CH}_{3} \mathrm{NH}_{2}+\mathrm{H}_{2} \mathrm{SO}_{3} \). Here, \( \mathrm{CH}_{3} \mathrm{NH}_{3}^{+} \) is a stronger acid than \( \mathrm{H}_{2} \mathrm{SO}_{3} \), and \( \mathrm{HSO}_{3}^{-} \) is a weaker base than \( \mathrm{CH}_{3} \mathrm{NH}_{2} \). Thus, this equilibrium lies to the right.

Key Concepts

Acid and Base Strength Ranking

Understanding the strength ranking of acids and bases is crucial in chemistry, especially when it comes to predicting the behavior of chemical species in reaction environments. Acids and bases can be ranked based on their propensity to donate or accept protons, respectively.

Let's break down this concept by considering the acid strength. An acid is a substance that can donate a proton (H+ ion) to another species. The strength of an acid is gauged by how easily it can lose its proton. A strong acid will readily donate its proton, shifting the equilibrium position of a reaction to favor the formation of the conjugate base.

The exact opposite principle applies to bases. A base is a substance that can accept a proton. A strong base has a high affinity for protons and will pull the equilibrium towards itself, forming more of the conjugate acid. The strength of bases is influenced by several factors, including the stability of the resulting conjugate acid and the solvation effects in different media.

Ranking acids and bases helps us understand and predict how different substances will behave in a given reaction or solution; for instance, in a mixture of different bases, the strongest base tends to capture the available protons more effectively than its weaker counterparts.

Proton Donation and Acceptance

The concepts of proton donation and acceptance form the basis of the Brønsted-Lowry acid-base theory and are essential in the study of chemical equilibria. Proton (H+) donation and acceptance are the defining actions of acids and bases, respectively.

When an acid donates a proton, it transforms into its conjugate base, which is the acid's counterpart capable of accepting a proton. Conversely, when a base accepts a proton, it becomes its conjugate acid. This exchange of protons is not merely a one-way street; it's dynamic, reversible, and influenced by the strengths of the reacting acids and bases.

In a chemical equilibrium involving acids and bases, the direction and extent of proton exchange can be determined by comparing the relative strengths of the acids and bases. For example, a very strong acid will donate its proton so effectively that the reverse reaction (proton acceptance) is negligible, leading to a product-favored equilibrium. Meanwhile, a weak acid might be in a closely contested tussle with its base counterpart, resulting in a more balanced equilibrium.

Predicting Equilibrium Direction

Predicting the direction of a chemical equilibrium is a fundamental skill in chemistry that depends on understanding the relative strength of acids and bases involved in the reaction. Based on Le Chatelier's Principle, a reaction at equilibrium will adjust to minimize the effects of a change in conditions, such as concentration or pressure.

Using the concept of acid and base strength ranking, one can predict the direction in which a reaction will proceed. A general rule is that a reaction will favor the formation of weaker acids and bases. Therefore, if a stronger acid reacts with a stronger base, the equilibrium will typically shift towards the side with the weaker acid and weaker base.

For example, if a weak acid reacts with a strong base, the equilibrium will likely be positioned to the side of the resulting weaker conjugate acid and base. The key is always to consider the relative strengths of the reactants and the stability of the products, as this will dictate the extent to which the reaction achieves equilibrium.