Balance each chemical equation. (a) \(\mathrm{Na}_{2} \mathrm{~S}(a q)+\mathrm{Cu}\left(\mathrm{NO}_{3}\right)_{2}(a q) \longrightarrow \mathrm{NaNO}_{3}(a q)+\mathrm{CuS}(s)\) (b) \(\mathrm{HCl}(a q)+\mathrm{O}_{2}(g) \longrightarrow \mathrm{H}_{2} \mathrm{O}(l)+\mathrm{Cl}_{2}(g)\) (c) \(\mathrm{H}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow \mathrm{H}_{2} \mathrm{O}(l)\) (d) \(\mathrm{FeS}(s)+\mathrm{HCl}(a q) \longrightarrow \mathrm{FeCl}_{2}(a q)+\mathrm{H}_{2} \mathrm{~S}(g)\)

At the heart of chemistry lies stoichiometry, a branch of chemical science focused on quantitatively analyzing the proportions and amounts of substances involved in chemical reactions. It's the arithmetic behind chemistry, allowing scientists and students to calculate the amounts of reactants needed or products formed in a chemical equation.

Stoichiometry is grounded in the balancing of chemical equations, as it uses the coefficients in a balanced equation to perform calculations. For instance, the coefficient numbers indicate the ratio in which reactants combine and products form. When balancing the chemical equation for the reaction of sodium sulfide with copper(II) nitrate, we adjusted coefficients to adhere to these ratios, ensuring the atoms on both sides of the equation correspond and the mass remains consistent throughout the reaction.

In educational terms, think of stoichiometry like a recipe. Just as you need a specified amount of each ingredient to bake a cake, a chemical reaction requires precise amounts of each reactant to proceed as expected and yield the desired product. If we have too much or too little of one component, the reaction won't go to completion, or there will be leftover reactants.

A chemical reaction is a process where substances, known as reactants, transform into different substances called products. This transformation involves breaking and forming chemical bonds, leading to changes in the composition and properties of the involved substances. Reactions can vary greatly in terms of their complexity and the types of changes they involve.

For example, when hydrogen reacts with oxygen, the result is water – a simple yet fundamental reaction critical to life on Earth. As per the provided exercise, balancing the chemical reaction of hydrogen and oxygen (equation c), ensures that we respect the stoichiometry and the ratios in which these gases react. The balanced equation, which obeys the law of conservation of mass, tells us that two molecules of hydrogen gas react with one molecule of oxygen gas to form two molecules of water.

Understanding chemical reactions is crucial for students as it helps them grasp the concept of how different substances interact with each other, the energy changes that occur during these reactions, and the practical outcomes, such as the formation of new materials or the release of energy.

The law of conservation of mass is a fundamental principle in chemistry stating that mass in an isolated system is neither created nor destroyed by chemical reactions or physical transformations. According to this law, the mass of the reactants in a chemical reaction must equal the mass of the products.

When students balance chemical equations, they are essentially applying the law of conservation of mass. Take for instance, equation d from the exercise, where iron sulfide reacts with hydrochloric acid to produce iron chloride and hydrogen sulfide. Even though the substances change form during the reaction, if we tally the mass of iron, sulfur, chlorine, and hydrogen atoms before and after, they remain constant.

It's vital to recognize that while atoms rearrange during chemical reactions, the same number of each type of atom must be present throughout. This concept assures students that atoms don't vanish or materialize from nowhere; they simply shift from one form to another, anchoring the notion of chemical reactions to a tangible and measurable foundation. Ensuring the balance of equations makes these invisible atomic transactions visible, highlighting the timeless principle that mass is always conserved.