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) $\left[\mathrm{Al}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{3+}+\mathrm{H}_{2} \mathrm{O} \longrightarrow\left[\mathrm{Al}\left(\mathrm{H}_{2} \mathrm{O}\right)_{5} \mathrm{OH}\right]^{2+}+\mathrm{H}_{3} \mathrm{O}^{+}$

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) \(\mathrm{NH}_{3}+\mathrm{BF}_{3} \longrightarrow \mathrm{H}_{3}\mathrm{NBF}_{3}\)

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) \(\left[\mathrm{Al}\left(\mathrm{H}_{2}\mathrm{O}\right)_{6}\right]^{3+}+\mathrm{H}_{2} \mathrm{O} \longrightarrow\left[\mathrm{Al}\left(\mathrm{H}_{2} \mathrm{O}\right)_{5}\mathrm{OH}\right]^{2+}+\mathrm{H}_{3} \mathrm{O}^{+}\)

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.