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To solve the chain of transformations, we're dealing with the chemical properties of aluminum compounds and some general chemistry reactions.

Chain of Transformations

1. \( \text{Al(OH)}_3 \xrightarrow{t} \text{Al}_2\text{O}_3 + \text{H}_2\text{O} \)

   • Explanation: When aluminum hydroxide \( \text{Al(OH)}_3 \) is heated, it decomposes to form aluminum oxide \( \text{Al}_2\text{O}_3 \) and water. This is a typical dehydration reaction of hydroxides.

2. \( \text{Al}_2\text{O}_3 + 2 \text{NaOH} \xrightarrow{\text{fusion}} 2 \text{NaAlO}_2 + \text{H}_2\text{O} \)

   • Explanation: Aluminum oxide reacts with sodium hydroxide when melted together to form sodium aluminate \( \text{NaAlO}_2 \) and water. This is an example of aluminum oxide acting as an acid (acidic oxide) in a reaction with a base.

3. \( \text{NaAlO}_2 + 4 \text{HCl} \rightarrow \text{AlCl}_3 + \text{NaCl} + 2 \text{H}_2\text{O} \)

   • Explanation: Sodium aluminate reacts with hydrochloric acid to form aluminum chloride \( \text{AlCl}_3 \), sodium chloride \( \text{NaCl} \), and water. Here, the aluminate ion is neutralized by the acid.

4. \( \text{AlCl}_3 + 3 \text{LiOH} \rightarrow \text{Al(OH)}_3 + 3 \text{LiCl} \)

   • Explanation: Aluminum chloride reacts with lithium hydroxide, leading to the formation of aluminum hydroxide and lithium chloride. This is a double displacement reaction where the \(\text{Cl}^-\) and \(\text{OH}^-\) ions trade partners.

Summary of Process

1. Dehydration: \(\text{Al(OH)}_3\) is heated to form \(\text{Al}_2\text{O}_3\).
2. Fusion with Base: \(\text{Al}_2\text{O}_3\) reacts with \(\text{NaOH}\) to produce \(\text{NaAlO}_2\).
3. Acid Neutralization: \(\text{NaAlO}_2\) is treated with \(\text{HCl}\) to yield \(\text{AlCl}_3\).
4. Regeneration of Hydroxide: \(\text{AlCl}_3\) reacts with \(\text{LiOH}\) to form \(\text{Al(OH)}_3\).

This series of reactions demonstrates the characteristics of aluminum compounds as both an acid and a base (amphoteric behavior), as well as the typical interaction of metal hydroxides, oxides, and halides with acids and bases.