Explain each of the following statements: (a) An aqueous solution of \(\mathrm{AlCl}_{3}\) is acidic. (b) \(\mathrm{Al}(\mathrm{OH})_{3}\) is soluble in \(\mathrm{NaOH}\) solutions but not in \(\mathrm{NH}_{3}\) solution.

Amphoteric substances are fascinating because they can behave as both an acid and a base, depending on the chemical environment they're in. This dual-acting nature of amphoterism is characterized by a substance's ability to react with both acidic and basic species. Aluminium hydroxide, Al(OH)_3, is a classic example of an amphoteric compound. In the context of our AlCl_3 solution, the aluminium ions interact with water to form Al(OH)_3, which can subsequently react with a strong base such as sodium hydroxide (NaOH). The reaction produces a soluble complex, [Al(OH)_4]-, thus illustrating its basic behavior.

However, its acidic characteristic comes forward when we consider that it does not react with ammonia (NH_3), a weak base. This is because ammonia doesn't provide sufficient hydroxide ions to stabilize the aluminium in solution. Understanding the amphoteric nature of substances is pivotal as it explains the diverse chemical behavior and solubility of compounds in various solutions.

Solubility in solutions is a measure of how well a substance can dissolve in a solvent, and it's critical to predicting how substances will behave in different environments. The solubility can change dramatically with variables like temperature, pressure, and pH levels. When it comes to Al(OH)_3, its solubility in a NaOH solution can be attributed to the formation of the soluble [Al(OH)_4]- complex. This occurs due to the availability of excess hydroxide ions from the NaOH, which facilitates the dissolution of Al(OH)_3.

On the flip side, the solubility of Al(OH)_3 in ammonia is limited due to the lack of sufficient hydroxide ions to form a soluble complex. Instead, Al(OH)_3 remains largely undissolved, showcasing how solubility is heavily influenced by the chemical composition of the solute and solvent, as well as their interactions.

Understanding chemical reactions with acids and bases is fundamental in chemistry, as it allows us to predict the behavior of substances and understand their properties. Acids and bases interact with each other to neutralize and form water and salts, and these reactions are governed by principles of acid-base chemistry. In the case of AlCl_3 in water, the aluminium chloride reacts with water, a reaction that showcases the acidic properties of AlCl_3. It forms HCl, a strong acid, and Al(OH)_3, which further demonstrates acid-base reactions as it can subsequently behave as a base when reacting with a strong base like NaOH.

The reactions of acids and bases are at play in everyday life, from the digestion in our stomach to the formation of soap. In a learning context, when a student grasps the principles behind these reactions, such as how AlCl_3 leads to an acidic solution, it paves the way for a deeper understanding of both the theoretical and practical aspects of acidity, pH, and the intriguing nature of amphoteric compounds.