Balance each of the following chemical equations: a. \(\mathrm{PbO}+\mathrm{NH}_{3} \rightarrow \mathrm{Pb}+\mathrm{N}_{2}+\mathrm{H}_{2} \mathrm{O}\) b. \(\mathrm{Mg}_{3} \mathrm{~N}_{2}+\mathrm{H}_{2} \mathrm{O} \rightarrow \mathrm{Mg}(\mathrm{OH})_{2}+\mathrm{NH}_{3}\) c. \(\mathrm{C}_{3} \mathrm{H}_{8}+\mathrm{O}_{2} \rightarrow \mathrm{CO}_{2}+\mathrm{H}_{2} \mathrm{O}\)

Stoichiometry is a pivotal concept in chemistry that involves the calculation of reactants and products in chemical reactions. It provides the quantitative relationship between the amounts of substances involved in a reaction. To understand stoichiometry, one must become proficient in balancing chemical equations, where the principle of conservation of mass dictates that the number of atoms of each element must be the same on both sides of the equation.

For example, in the exercise provided, we need to balance the equation for the reaction between lead(II) oxide (PbO) and ammonia (NH3). By using stoichiometry, we can determine the exact number of molecules of ammonia and water needed to react with a certain amount of lead(II) oxide to produce lead (Pb), nitrogen (N2), and water (H2O).

Stoichiometry is not just about balancing equations; it also allows us to predict the yield of a reaction, understand limiting reagents, and calculate the concentration of solutions. These calculations are crucial in fields such as pharmaceuticals, engineering, and environmental science. For students, grasping the principles of stoichiometry can make complex chemical problems more manageable and open up a world of practical applications.

A chemical reaction is a process that results in the transformation of one set of chemical substances to another. Chemical reactions can be represented by chemical equations, which are symbolic expressions that use chemical formulas and coefficients to depict the substances involved in the reaction.

In the textbook exercise, we see three different reactions. The first involves a redox reaction where lead(II) oxide reduces to lead, and ammonia oxidizes to nitrogen and water. The second reaction shows the hydrolysis of magnesium nitride to form magnesium hydroxide and ammonia. Finally, the third one is a combustion reaction where propane (C3H8) reacts with oxygen (O2) to form carbon dioxide (CO2) and water.

Understanding the type of reaction is crucial as it helps predict the products and the energy changes involved. For example, combustion reactions will always produce heat, which is vital information when considering safety and practicality in industrial processes. By studying chemical reactions, students learn about the conservation of mass and energy, reaction kinetics, and the factors that affect reaction rates, all of which are fundamental to both academic and real-world chemical analysis.

Molecular coefficients in chemical equations are the numbers placed in front of the chemical formulas to balance the equation in accordance with the law of conservation of mass. These coefficients represent the relative number of molecules or moles of each substance involved in the reaction.

The exercise provided an illustration of how coefficients are determined when balancing equations. In equation (a), a 2 is placed before NH3 to indicate that two molecules of ammonia are required. In equation (b), a coefficient of 3 before Mg(OH)2 and 6 before H2O signifies that three molecules of magnesium hydroxide and six molecules of water participate in the reaction. Lastly, in equation (c), coefficients of 3 for CO2 and 4 for H2O are used to show the stoichiometric amounts of these products based on one molecule of propane.

It's important for students to understand that these numbers are not arbitrary but are derived through a systematic balancing process. Mastery of determining molecular coefficients not only aids in solving homework but also prepares students for more advanced topics like chemical thermodynamics and reaction kinetics where precise measurements and ratios are indispensable.