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Balancing chemical equations is a fundamental skill in chemistry that ensures the law of conservation of mass is respected within a chemical reaction. When we balance an equation, our goal is to have the same number of each type of atom on both sides of the equation. This simulates real-world reactions, where matter is neither created nor destroyed. For example, when calcium carbide reacts with water, the unbalanced equation is:
\( \text{CaC}_2 (s) + \text{H}_2\text{O} (l) \rightarrow \text{C}_2\text{H}_2 (g) + \text{Ca(OH)}_2 (aq) \).
By observing that there are two hydrogen atoms in the reactant side and four in the product side, we can balance the equation by adding a coefficient of two in front of the water molecule:
\( \text{CaC}_2 (s) + 2\text{H}_2\text{O} (l) \rightarrow \text{C}_2\text{H}_2 (g) + \text{Ca(OH)}_2 (aq) \).
Thus, the first reaction is properly balanced with an equal number of each atom on both sides, adhering to the fundamental law.

Chemical reactions involve the transformation of one set of chemical substances to another. As evidenced by our example, calcium carbide reacting with water to produce acetylene and calcium hydroxide is a type of chemical reaction called a hydrolysis reaction. The process involves solid reactants and liquid reactants producing gaseous and aqueous products. Understanding the different states of matter and types of reactions can help students better visualize and predict products of reactions. By identifying the reactants and products, and the state of each, students can gain insights into how different substances interact at a molecular level.

Stoichiometry is the study of the quantitative relationships, or ratios, within chemical reactions. It serves as the mathematical backbone of chemistry, allowing us to predict how much product will form from given amounts of reactants. In balancing our equations, stoichiometry ensures that the mole ratios are maintained. With the balanced hydrolysis of calcium carbide, one mole of calcium carbide reacts with two moles of water, yielding one mole of acetylene gas and one mole of calcium hydroxide. In more complex reactions, stoichiometry can require balancing not just single atoms but polyatomic ions and molecules, as well as accounting for molar coefficients and ratios.

Combustion reactions are a type of chemical reaction where a fuel reacts with an oxidant, releasing energy in the form of light or heat. In the given problem, we see the combustion of acetylene gas in the second step. The general form of a combustion reaction involving hydrocarbons is the fuel reacting with oxygen to form carbon dioxide and water, releasing energy. Balancing these equations requires careful attention to the oxygen molecules due to their diatomic nature. For acetylene, the balanced combustion reaction is:
\(2 \text{C}_2\text{H}_2 (g) + 5 \text{O}_2 (g) \rightarrow 4 \text{CO}_2 (g) + 2 \text{H}_2\text{O} (g)\)
. This equation indicates that two moles of acetylene gas react with five moles of oxygen gas to produce four moles of carbon dioxide gas and two moles of water vapor.