Write a balanced chemical equation for (a) the hydrogenation of ethyne (acetylene, \(\left.\mathrm{C}_{2} \mathrm{H}_{2}\right)\) to ethene \(\left(\mathrm{C}_{2} \mathrm{H}_{4}\right)\) by hydrogen (give the axidation rumber of the carbon atoms in the reactant and product); (b) the shift reaction (sometimes called the water gas shift reaction, WGSR); (c) the reaction of barium hydride with water.

The hydrogenation of ethyne, also known as acetylene, is a commonly studied reaction in organic chemistry. This process involves adding hydrogen (\textbf{H\(_2\)}) to ethyne (\textbf{C\(_2\)H\(_2\)}) to form ethene (\textbf{C\(_2\)H\(_4\)}). In this reaction, the triple bond between the carbon atoms in ethyne is partially broken, and becomes a double bond in ethene, allowing for the addition of two hydrogen atoms.

Understanding the simplicity of this balanced equation explains a fundamental reaction in the chemistry of alkenes. The equation is already balanced, with equimolar amounts of ethyne and hydrogen reacting to form ethene. It's crucial to realise that, in this reaction, there is no change in oxidation state for the carbon atoms; they remain at an oxidation number of -1 before and after the reaction.

Learning how to balance such equations is foundational in chemistry education, as it paves the way for understanding more complex reactions involving alkenes and their derivatives.

The water gas shift reaction (WGSR) is an essential industrial process used in hydrogen production and carbon monoxide removal. In this reaction, carbon monoxide (CO) reacts with water (H\(_2\)O) to yield carbon dioxide (CO\(_2\)) and hydrogen gas (H\(_2\)).

One of the interesting aspects of the WGSR is that it is already balanced as written: \[\text{CO} + \text{H}_2\text{O} \rightarrow \text{CO}_2 + \text{H}_2\]. Here, each reactant and product has one carbon atom and two oxygen and hydrogen atoms, demonstrating the law of conservation of mass. Not only is it a critical concept for energy production and synthesis gas manipulation, but it also serves as a straightforward example for students learning to balance chemical equations.

Reacting barium hydride (BaH\(_2\)) with water is a typical reaction involving a metal hydride and representing a synthesis type of reaction. When BaH\(_2\) comes into contact with water, it forms barium hydroxide (Ba(OH)\(_2\)) and hydrogen gas (H\(_2\)). This reaction is important in illustrating the reactivity of hydrides and the production of hydrogen gas, which is of interest in energy applications.

The balanced equation is \[\text{BaH}_2 + 2\text{H}_2\text{O} \rightarrow \text{Ba(OH)}_2 + 2\text{H}_2\], showing the stoichiometry that two water molecules are necessary to yield one molecule of barium hydroxide and two molecules of hydrogen gas. It's a perfect example to demonstrate to students the art of balancing multi-element reactions, as water provides both the oxygen and additional hydrogen to the products.

Oxidation numbers are a fundamental concept in chemistry that indicate the degree of oxidation or reduction of an atom within a molecule. The oxidation number can be thought of as the hypothetical charge an atom would have if all bonds were ionic.

In our previous reactions example, for instance, the oxidation number of carbon in both ethyne and ethene is -1. This means that there is no change in the oxidation states of the carbon atoms during the hydrogenation of ethyne, which is a key point for students to understand. Mastering the assignment of oxidation numbers helps students predict the feasibility of redox reactions and other chemical processes.

Balancing chemical equations is an essential skill in chemistry that ensures the law of conservation of mass is upheld in a chemical reaction. It involves making sure the number of atoms for each element is equal on both sides of the reaction.

When working on this skill, students learn to systematically approach an equation and add coefficients to balance the atoms. For example, in the reaction of barium hydride with water, understanding the need for two water molecules to balance the hydrogen and oxygen atoms is crucial. Practice in chemical reaction balancing develops a strong foundation for students, as it is not only pivotal for academic success in chemistry, but also for practical laboratory work and a deeper understanding of chemical processes.