Problem 12 - Chemistry: The Central Science in SI Units, Global Edition

Question

For each of these reactions, identify the acid and base among the reactants, and state if the acids and bases are Lewis, Arrhenius, and/or Brønsted-Lowry: (a) \(\mathrm{PCl}_{4}^{+}+\mathrm{Cl}^{-} \longrightarrow \mathrm{PCl}_{5}\) (b) \(\mathrm{NH}_{3}+\mathrm{BF}_{3} \longrightarrow \mathrm{H}_{3} \mathrm{NBF}_{3}\) (c) \(\left[\mathrm{Al}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{3+}+\mathrm{H}_{2} \mathrm{O} \longrightarrow\left[\mathrm{Al}\left(\mathrm{H}_{2} \mathrm{O}\right)_{5} \mathrm{OH}\right]^{2+}+\mathrm{H}_{3} \mathrm{O}^{+}\)

Step-by-Step Solution

Answer

(a) \(\mathrm{PCl}_{4}^{+}\) is a Lewis Acid, and \(\mathrm{Cl}^{-}\) is a Lewis Base. Neither Arrhenius nor Brønsted-Lowry definitions apply. (b) \(\mathrm{NH}_{3}\) is a Lewis Base, and \(\mathrm{BF}_{3}\) is a Lewis Acid. Neither Arrhenius nor Brønsted-Lowry definitions apply. (c) \(\left[\mathrm{Al}\left(\mathrm{H}_{2}\mathrm{O}\right)_{6}\right]^{3+}\) is a Brønsted-Lowry and Lewis Acid, and \(\mathrm{H}_{2} \mathrm{O}\) is a Brønsted-Lowry and Lewis Base. The Arrhenius definition does not apply.

Step 1: Identify Acid and Base.reactants

As per the Lewis definition, \(\mathrm{PCl}_{4}^{+}\) is an electron-pair acceptor, making it a Lewis Acid. \(\mathrm{Cl}^{-}\) is an electron-pair donor, making it a Lewis Base. For this reaction, we don't have any protons (H+) or hydroxide ions (OH-), so the Arrhenius and Brønsted-Lowry definitions are not applicable. #Step 2: Classify reaction (b)# (b) \(\mathrm{NH}_{3}+\mathrm{BF}_{3} \longrightarrow \mathrm{H}_{3}\mathrm{NBF}_{3}\)

Step 2: Identify Acid and Base.reactants

The \(\mathrm{NH}_{3}\) can donate an electron pair, so it is a Lewis Base, and \(\mathrm{BF}_{3}\) is an electron-pair acceptor, making it a Lewis Acid. As in the previous case, there are no H+ or OH- ions involved in this reaction, so the Arrhenius and Brønsted-Lowry definitions are not applicable. #Step 3: Classify reaction (c)# (c) \(\left[\mathrm{Al}\left(\mathrm{H}_{2}\mathrm{O}\right)_{6}\right]^{3+}+\mathrm{H}_{2} \mathrm{O} \longrightarrow\left[\mathrm{Al}\left(\mathrm{H}_{2} \mathrm{O}\right)_{5}\mathrm{OH}\right]^{2+}+\mathrm{H}_{3} \mathrm{O}^{+}\)

Step 3: Identify Acid and Base.reactants

In this reaction, \(\left[\mathrm{Al}\left(\mathrm{H}_{2}\mathrm{O}\right)_{6}\right]^{3+}\) can donate an H+ ion to the water molecule, making it a Brønsted-Lowry Acid. The water molecule \(\mathrm{H}_{2} \mathrm{O}\) accepts the proton (H+) from the complex ion, making it a Brønsted-Lowry Base. Moreover, water transfers an electron pair to the aluminum complex ion, so it also acts as a Lewis Base. The \(\left[\mathrm{Al}\left(\mathrm{H}_{2}\mathrm{O}\right)_{6}\right]^{3+}\) can accept an electron pair, making it a Lewis Acid. This reaction does not involve the production of H+ or OH- ions, so the Arrhenius definition does not apply here. In conclusion, we have classified the acids and bases for each reaction using the Lewis, Arrhenius, or Brønsted-Lowry definitions when applicable.

Key Concepts

Lewis Acids and Bases

Lewis acids and bases focus on the transfer of electron pairs. In a Lewis acid-base reaction, the acid is an electron pair acceptor, while the base is an electron pair donor. Let's break it down further, using an example for clarity.

The reaction between \[\mathrm{NH}_{3} + \mathrm{BF}_{3} \longrightarrow \mathrm{H}_{3}\mathrm{NBF}_{3}\]can be explained by Lewis theory. Here, \(\mathrm{BF}_{3}\) accepts an electron pair from \(\mathrm{NH}_{3}\), making \(\mathrm{BF}_{3}\) the Lewis acid and \(\mathrm{NH}_{3}\) the Lewis base. Notice that there's no exchange of protons (H\(^+\)) like in other theories. Instead, it's all about the electron pairs.

• Lewis Acid: Electron pair acceptor
• Lewis Base: Electron pair donor

When examining any reaction, look for entities that gain or lose electron pairs to identify the Lewis acid and base.

Brønsted-Lowry Acids and Bases

The Brønsted-Lowry acid-base theory introduces the concept of proton exchange. This theory is applicable in reactions where protons (H\(^+\)) are transferred from one species to another.

Consider the reaction involving\[\left[\mathrm{Al}\left(\mathrm{H}_{2}\mathrm{O}\right)_{6}\right]^{3+} + \mathrm{H}_{2} \mathrm{O} \longrightarrow \left[\mathrm{Al}\left(\mathrm{H}_{2} \mathrm{O}\right)_{5}\mathrm{OH}\right]^{2+} + \mathrm{H}_{3} \mathrm{O}^{+}\]Here, \(\left[\mathrm{Al}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{3+}\) donates a proton to water, making it a Brønsted-Lowry acid. Water, on the other hand, receives a proton, acting as a Brønsted-Lowry base. The beauty of this concept is in its focus on proton transfer, which is central in many chemical reactions.

• Brønsted-Lowry Acid: Proton donor
• Brønsted-Lowry Base: Proton acceptor

Look for the movement of protons to determine these roles in a reaction.

Arrhenius Acid-Base Theory

Arrhenius acid-base theory is one of the earliest acid-base theories. It is important to understand for a foundational grasp of acid-base chemistry.

An Arrhenius acid increases the concentration of hydrogen ions (H\(^+\)) in an aqueous solution, while an Arrhenius base increases hydroxide ions (OH\(^-\)). This theory is more limited compared to Lewis and Brønsted-Lowry because it strictly applies to substances in water.

• Arrhenius Acid: Raises H\(^+\) concentration in water
• Arrhenius Base: Raises OH\(^-\) concentration in water

In the exercises provided, the Arrhenius theory does not apply as there are no resulting H\(^+\) or OH\(^-\) ions produced directly in water. Despite its limitations, this theory offers a straightforward approach to understanding basic reactions in aqueous solutions.