Write a chemical equation to represent (a) the reduction of silica to elemental silicon by aluminum; (b) the preparation of potassium metasilicate by the high-temperature fusion of silica and potassium carbonate; (c) the reaction of \(\mathrm{Al}_{4} \mathrm{C}_{3}\) with water to produce methane.

The reduction of silica involves converting silica (SiO2), which is silicon dioxide, into pure elemental silicon (Si) with the aid of a reducing agent, which in this case is aluminum (Al). This process is commonly employed in metallurgy and the chemical industry. The chemical transformation can be expressed by writing a balanced chemical equation:
\[SiO_2 + 2Al \rightarrow Si + Al_2O_3\]
In this reaction, aluminum donates electrons to SiO2, reducing it to silicon. Consequently, the aluminum is oxidized, forming aluminum oxide (Al2O3). This type of reaction is crucial in the field of materials science, particularly in the production of silicon for electronic devices and semiconductors, as silicon is a fundamental material in these technologies. To fully understand this process, it's essential to grasp the principles of redox reactions, where one substance is reduced and another oxidized, maintaining the conservation of electrons.

Potassium metasilicate (K2SiO3) can be prepared through the high-temperature fusion of silica (SiO2) and potassium carbonate (K2CO3). This chemical process is central to various industrial applications, including the manufacture of cleaning agents and detergents. The balanced chemical equation for this preparation is:
\[SiO_2 + K_2CO_3 \rightarrow K_2SiO_3 + CO_2\]
Here, under high temperatures, silica reacts with potassium carbonate to form potassium metasilicate and carbon dioxide gas. This preparation is a prime example of a solid-state reaction, a type of reaction where the reactants and the products are in solid forms. Understanding this reaction requires familiarity with the behaviors of ionic compounds when subjected to heat, as well as the effect of temperature on the reactivity of chemical species.

Aluminum carbide (Al4C3), when introduced to water (H2O), undergoes a hydrolysis reaction, producing methane (CH4) and aluminum hydroxide (Al(OH)3). The equation representing this reaction is:
\[Al_4C_3 + 12H_2O \rightarrow 4Al(OH)_3 + 3CH_4\]
This reaction is exothermic, releasing energy in the form of heat. It serves as an interesting example of how certain compounds react with water to release gases. Aluminum carbide's reaction with water also has implications in the field of waste management and recycling, as it provides a method of generating hydrocarbons from metal wastes. To appreciate the intricacies of this process, one should have a solid foundation in hydrolysis reactions and the properties of carbides, particularly their reactivity with water and the formation of hydroxides and hydrocarbons.