Write a balanced chemical equation for (a) the reaction hetween sodium hydride and water, \((b)\) the formation of synthesis gas; (c) the hydrogenation of ethene, \(\mathrm{H}_{2} \mathrm{C}=\mathrm{CH}_{2}\), and give the cxidation number of the carbon atoms in the reactant and product; (d) the reaction of magnesium with hydrochloric acid.

Understanding the principles of balancing chemical reactions is crucial for students diving into the complexities of chemistry. To balance a chemical equation, one must ensure the number of atoms for each element is equal on both the reactant and product sides. The process typically involves adjusting coefficients—whole numbers placed in front of the chemical formulas—to achieve this balance.

For example, when balancing the reaction between sodium hydride (NaH) and water (H2O), which produces sodium hydroxide (NaOH) and hydrogen gas (H2), the correct coefficients make it possible to count an equal number of Na, H, and O atoms on both sides of the equation: \[\text{NaH} + \text{H}_2\text{O} \rightarrow \text{NaOH} + \text{H}_2\].

Practicing balancing equations helps students become familiar with conservation of mass in reactions and prepares them for more advanced chemistry topics.

Stoichiometry is the mathematical relationship between the amounts of reactants and products in a chemical reaction. It is based on the balanced chemical equations and allows chemists to predict the quantities needed or produced in a reaction. For instance, the stoichiometry of the reaction between methane (CH4) and water to form synthesis gas can be explored using the balanced equation: \[\text{CH}_4 + \text{H}_2\text{O} \rightarrow \text{CO} + 3\text{H}_2\].

This tells us that one molecule of methane reacts with one molecule of water to produce one molecule of carbon monoxide and three molecules of hydrogen gas. This can be scaled up to moles, demonstrating that stoichiometry is a vital tool for both lab work and industry to convert measurements and ensure efficient chemical processes.

The ability to determine the oxidation state of an element in a compound is a significant aspect of understanding chemical reactions. Oxidation states indicate the degree of oxidation or reduction of an element, which helps predict how it can combine with other elements. This concept is illustrated in the hydrogenation of ethene (H2C=CH2), where the oxidation state of carbon changes as it reacts.

The carbons in ethene have an oxidation state of -2, which reflect the sharing of electrons in the double bond. After hydrogenation, the resulting ethane (H3C-CH3) has carbon atoms with an oxidation state of -3, signifying each carbon has gained an electron from the added hydrogen. Recognizing these changes is key in redox reactions and is applicable in electrochemistry, metallurgy, and organic synthesis.

Synthesis gas, commonly known as syngas, is a valuable fuel and industrial feedstock composed primarily of hydrogen and carbon monoxide. It's produced from a variety of carbon-based materials, including natural gas, coal, and biomass. The formation of syngas can be represented by the reaction: \[\text{CH}_4 + \text{H}_2\text{O} \rightarrow \text{CO} + 3\text{H}_2\].

Here, methane (a constituent of natural gas) reacts with steam to produce syngas. This process, known as steam reforming, is endothermic and widely used in industry. Syngas is a key intermediary in the production of synthetic fuels, ammonia for fertilizers, methanol, and other chemicals, making its formation process critical to a multitude of chemical production pathways.