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The Arrhenius definition is one of the earliest theories about acids and bases. According to this concept, an acid is a substance that increases the concentration of hydrogen ions \(H^+\) when dissolved in water, while a base increases the concentration of hydroxide ions \(OH^-\). This definition, although straightforward, requires that the reaction occurs in an aqueous environment.

For instance, in reaction (a) given in the problem, \(\mathrm{CO_2(g)} + \mathrm{LiOH(s)} \rightarrow \mathrm{LiHCO_3(s)}\), there aren't any hydrogen or hydroxide ions involved because no aqueous solution is present. Instead, it involves a solid reacting with a gas, making it not fit the Arrhenius model.

• Acid: Increases \(H^+\) in solution.
• Base: Increases \(OH^-\) in solution.
• Requires: Aqueous environment.

In reaction (b), \(\mathrm{SO_2(g)} + \mathrm{H_2O(g)} \rightleftharpoons \mathrm{H_2SO_3(g)}\), sulfur dioxide reacts with water to form sulfurous acid, which can dissociate to increase \(H^+\) concentration, making this reaction fit the Arrhenius model.

The Bronsted-Lowry Theory provides a more flexible approach to defining acids and bases, not limited to aqueous solutions. In this theory, acids are considered proton \(H^+\) donors, and bases are proton acceptors. This broader definition allows for an understanding of acid-base reactions in various contexts.

In reaction (a), \(\mathrm{CO_2(g)}\) interacting with \(\mathrm{LiOH(s)}\), no specific \(H^+\) transfer is observed so it doesn't quite fit into the Bronsted-Lowry frame as a classic acid-base reaction.

• Acid: Proton donor.
• Base: Proton acceptor.
• Not limited to water solutions.

In reaction (b), sulfur dioxide \(\mathrm{SO_2(g)}\) reacts with water \(\mathrm{H_2O}\), with water donating a proton to form \(\mathrm{H_2SO_3}\). This exemplifies the Bronsted-Lowry concept of acids and bases effectively.

The Lewis Acid-Base Theory provides an even more generalized framework compared to the previous theories. A Lewis acid is an electron pair acceptor and a Lewis base is an electron pair donor. This theory extends the concept to include a wider range of chemical reactions beyond just proton transfer.

In reaction (a), \(\mathrm{CO_2}\) serves as a Lewis acid by accepting electron pairs from \(\mathrm{OH^-}\), which acts as a Lewis base. The formation of \(\mathrm{LiHCO_3}\) showcases a clear Lewis acid-base interaction.

• Lewis Acid: Electron pair acceptor.
• Lewis Base: Electron pair donor.
• Broadest definition that includes electron transfer.

Similarly, in reaction (b), \(\mathrm{SO_2}\) accepts electron pairs from \(\mathrm{H_2O}\), forming \(\mathrm{H_2SO_3}\) and demonstrating Lewis acid-base behavior. This theory covers a diverse range of chemical processes, including those not involving protons directly.