Write balanced chemical equations for the reactions used to prepare each of the following compounds from the given starting material(s). In some cases, additional reactants may be required. (a) solid ammonium nitrate from gaseous molecular nitrogen via a two-step process (first reduce the nitrogen to ammonia, then neutralize the ammonia with an appropriate acid) (b) gaseous hydrogen bromide from liquid molecular bromine via a one-step redox reaction (c) gaseous \(\mathrm{H}_{2} \mathrm{S}\) from solid \(\mathrm{Zn}\) and \(\mathrm{S}\) via a two-step process (first a redox reaction between the starting materials, then reaction of the product with a strong acid)

The Haber process is a large-scale method to synthesize ammonia (\text{NH}_3) from nitrogen (\text{N}_2) and hydrogen (\text{H}_2) gases. It's a critical industrial reaction because ammonia is essential for producing fertilizers and various chemicals. Under high temperature (approximately 500 °C) and pressure (around 200 atmospheres), and in the presence of an iron-based catalyst, nitrogen and hydrogen react to form ammonia. The balanced equation representing this exothermic reaction is:
\[\begin{equation} \text{N}_{2}(g) + 3\text{H}_{2}(g) \rightarrow 2\text{NH}_{3}(g) \ \end{equation}\]
This process is named after Fritz Haber, who, with the help of Carl Bosch, developed and commercialized the procedure in the early 20th century. Despite its environmental impact due to high energy consumption, the Haber process remains the cornerstone of nitrogen-based fertilizer production today.

Ammonia synthesis, often associated with the Haber process, is vital for various industrial applications, especially for fertilizers and other nitrogen compounds. The synthesis reflects the bonding of pure nitrogen and hydrogen gases to form ammonia in a reversible reaction. An excellent example of this is the production of solid ammonium nitrate, useful as a fertilizer, which starts with ammonia synthesis and is followed by an acid-base neutralization step. Here's the initial part of the synthesis equation once more:
\[\begin{equation} \text{N}_{2}(g) + 3\text{H}_{2}(g) \rightarrow 2\text{NH}_{3}(g) \ \end{equation}\]
After its generation, the produced ammonia can be further processed into various compounds, such as the mentioned ammonium nitrate, by reacting it with other chemicals.

Acid-base neutralization is a chemical reaction wherein an acid and a base react to form water and a salt. It's one of the most fundamental chemical processes and is commonly used in various applications, including the manufacturing of fertilizers and household cleaning products. The reaction between ammonia gas and nitric acid to produce solid ammonium nitrate is an example of an acid-base neutralization, which can be represented by the following balanced chemical equation:
\[\begin{equation} \text{NH}_{3}(g) + \text{HNO}_3(aq) \rightarrow \text{NH}_4\text{NO}_3(s) \ \end{equation}\]
The usability of ammonium nitrate as a nutrient-rich fertilizer arises from its ability to provide both nitrogen and hydrogen to plants, showcasing the agricultural importance of acid-base neutralization reactions.

Redox reactions (or oxidation-reduction reactions) involve the transfer of electrons between two species. These reactions are integral to many processes such as photosynthesis, respiration, battery operation, and in many industrial and laboratory syntheses. A classic example of a redox reaction is the formation of hydrogen bromide (\text{HBr}) gas from hydrogen (\text{H}_2) and bromine (\text{Br}_2) molecules. The gaseous hydrogen is oxidized as it loses electrons, and the liquid bromine is reduced as it gains electrons, which is shown in the balanced equation:
\[\begin{equation} \text{H}_2(g) + \text{Br}_2(l) \rightarrow 2\text{HBr}(g) \ \end{equation}\]
Moreover, the production of \text{H}_2\text{S} from zinc and sulfur also involves a redox reaction in the first of its two-step process. With electrons being transferred from zinc to sulfur to form zinc sulfide (\text{ZnS}), this step precedes the acid reaction that releases \text{H}_2\text{S} gas.

Various methods exist for preparing gases in the laboratory and industry, depending on the specific gas and intended use. These methods may utilize chemical reactions, such as synthesis, displacement, or decomposition. Producing \text{H}_2\text{S} gas exemplifies a two-step gas preparation method. Initially, a redox reaction between zinc and sulfur forms zinc sulfide:
\[\begin{equation} \text{Zn}(s) + \text{S}(s) \rightarrow \text{ZnS}(s) \ \end{equation}\]
The subsequent reaction of zinc sulfide with hydrochloric acid liberates \text{H}_2\text{S} gas:
\[\begin{equation} \text{ZnS}(s) + 2\text{HCl}(aq) \rightarrow \text{ZnCl}_2(aq) + \text{H}_2\text{S}(g) \ \end{equation}\]
This two-step method underscores the importance of understanding the reactivity of different materials and the right conditions (such as temperature, pressure, and catalysts) necessary to achieve the desired gas efficiently and safely.