Consider the following equation: $$ 4 \mathrm{NH}_{3}(g)+5 \mathrm{O}_{2}(g) \longrightarrow 4 \mathrm{NO}(g)+6 \mathrm{H}_{2} \mathrm{O}(g) $$ (a) How many liters of oxygen are required to react with \(2.5 \mathrm{~L}\) \(\mathrm{NH}_{3}\) ? Both gases are at STP. (b) How many grams of water vapor can be produced from \(25 \mathrm{~L}\) \(\mathrm{NH}_{3}\) if both gases are at STP? (c) How many liters of NO can be produced when \(25 \mathrm{~L}\) \(\mathrm{O}_{2}\) are reacted with \(25 \mathrm{~L} \mathrm{} \mathrm{NH}_{3}\) ? All gases are at the same temperature and pressure.

One of the most crucial skills in stoichiometry chemistry is chemical equation balancing. This involves ensuring that the same number of each type of atom appears on both sides of a chemical equation. It reflects the conservation of mass, meaning matter is neither created nor destroyed during a chemical reaction.

Let's take the equation from the exercise as an example:

• On the left side of the equation (reactants), there are 4 nitrogen (N) atoms, 12 hydrogen (H) atoms, and 10 oxygen (O) atoms.
• On the right side of the equation (products), there are also 4 nitrogen (N) atoms, 12 hydrogen (H) atoms, and 10 oxygen (O) atoms.

Observing this balance achieved in the equation is crucial because it allows us to establish the ratios of reactants to products—these ratios inform how we calculate quantities in chemical reactions, like those seen in the homework problem.

Understanding the mole concept is essential in stoichiometry, as it relates to counting particles (like atoms or molecules) when weighing and measuring chemical substances.

The mole is a standard unit of measurement in chemistry defined as the amount of substance containing as many entities (atoms, molecules, etc.) as there are atoms in 12 grams of carbon-12. This number is Avogadro's number, approximately \(6.022 \times 10^{23}\). A notable point to remember is that at standard temperature and pressure (STP), one mole of any gas occupies 22.4 liters, making calculations involving gases more straightforward. This concept was directly applied in the textbook solutions to convert liters of gas into moles, and thereafter into grams for water in the provided problem.

In chemistry, Standard Temperature and Pressure (STP) refers to a set condition of 0°C (273.15 K) and 1 atmosphere (atm) of pressure. This is an important assumption used in gas law calculations because it provides a common reference. At STP, one mole of any ideal gas occupies 22.4 liters, which is a cornerstone of solving gas-related stoichiometry problems.

When the problem states that the gases are at STP, it ensures a uniform standard for comparison. In the textbook exercise, being at STP allows us to directly use the 22.4 liters per mole volume to calculate the amount of reactants and products, demonstrated in steps 2, 3, and 4 of the problem solution.

The volume ratios of gases in a chemical reaction are derived from the coefficients in a balanced chemical equation. This stems from Avogadro's law, which states that equal volumes of different gases, at the same temperature and pressure, contain the same number of particles.

For the equation in the exercise, the stoichiometric coefficients tell us the volume ratio directly: 5 volumes of \(O_2\) react with 4 volumes of \(NH_3\). These ratios are used in calculations for determining the amounts of reactants or products at STP. Understanding this makes it much easier to calculate how reacting volumes of gas will produce given volumes of products, as shown in the homework problem's step-by-step solution.