In the laboratory preparation of oxygen gas, the following reaction is carried out: \(2 \mathrm{KClO}_{3}(s) \rightarrow 2 \mathrm{KCl}(s)+3 \mathrm{O}_{2}(g)\) (a) How many moles of oxygen gas can be produced from the decomposition of \(500.0 \mathrm{~g}\) of \(\mathrm{KClO}_{3} ?\) (b) What volume in liters would the oxygen gas produced in part (a) occupy at \(24.0{ }^{\circ} \mathrm{C}\) and \(750.0 \mathrm{~mm} \mathrm{Hg} ?\) (c) What volume in liters would this gas occupy at STP?

Stoichiometry is an area of chemistry that involves calculating the amounts of reactants and products in chemical reactions. It is based on the conservation of mass where the total mass of the reactants equals the total mass of the products. To perform stoichiometric calculations, we first need to understand the balanced chemical equation, which shows the ratio in which substances react and are produced.

In the given exercise, the balanced reaction is:
\[2 \mathrm{KClO}_{3}(s) \rightarrow 2 \mathrm{KCl}(s) + 3 \mathrm{O}_{2}(g)\]
This equation tells us that two moles of potassium chlorate (\(\mathrm{KClO}_{3}\)) decompose to produce two moles of potassium chloride (\(\mathrm{KCl}\)) and three moles of oxygen gas (\(\mathrm{O}_{2}\)). The stoichiometric calculation involves using this ratio to determine the amount of oxygen produced from a given amount of potassium chlorate.

Stoichiometry is crucial for ensuring reactions are conducted efficiently and safely, with the correct proportions of substances. It's a fundamental concept in chemistry that helps in predicting the yields of products in various industrial and laboratory settings.

The mole concept is a fundamental principle in chemistry that relates the mass of a substance to the number of particles it contains. One mole is defined as the amount of a substance that contains as many particles (atoms, ions, or molecules) as there are atoms in 12 grams of carbon-12. This number is known as Avogadro's number, approximately \(6.022 \times 10^{23}\) entities per mole.

In practice, the mole concept enables chemists to count particles by weighing them. The molecular or molar mass expressed in grams per mole is numerically equivalent to the atomic or molecular weight of the substance. For example, in our exercise, the molar mass of potassium chlorate (\(\mathrm{KClO}_{3}\)) is calculated by adding the atomic masses of potassium (K), chlorine (Cl), and oxygen (O).

The exercise demonstrates how to convert grams of potassium chlorate to moles. This conversion is crucial because chemical reactions are based on the moles of substances, not their mass. Understanding the mole concept allows students to bridge the gap between the macroscopic mass of compounds and the microscopic number of atoms or molecules involved in chemical reactions.

The Ideal Gas Law is an equation of state for a hypothetical ideal gas. It provides a relationship between the pressure (P), volume (V), moles (n), and temperature (T) of a gas, and is expressed as:
\[PV = nRT\],
where R is the ideal, or universal, gas constant. In the context of the exercise, once the moles of oxygen gas are determined through stoichiometry, the Ideal Gas Law can be used to calculate the volume that the gas will occupy under specific temperature and pressure conditions.

For instance, the exercise requires calculating the volume of oxygen at two different sets of conditions: one at 24.0°C and 750.0 mm Hg, and one at standard temperature and pressure (STP). The ability to use the Ideal Gas Law in this manner is valuable for predicting the behavior of gases in real-world scenarios, such as engineering processes, environmental science, and even respiratory physiology. While real gases do not perfectly obey the Ideal Gas Law, it remains a close approximation for many gases under a range of conditions. The Ideal Gas Law is a pivotal piece of knowledge for anyone studying chemistry or related fields.

Standard Temperature and Pressure (STP) is a set of conditions commonly used as a reference point in chemistry to report the properties of substances, including gases. STP is defined as a temperature of 0°C (273.15 K) and a pressure of 1 atmosphere (atm).

When comparing the volume of gases, it's essential to use a common set of conditions for accurate comparison, and STP serves as this standard. In the exercise, the final step involves recalculating the volume of oxygen gas at STP after finding its volume at another temperature and pressure. This highlights the variation in gas volume with changing conditions, and why STP is a useful benchmark.

Understanding STP allows students and scientists to predict how gases will behave in standard lab conditions. It also facilitates the comparison of various gases and their properties and is used in various scientific tables and reference materials. When dealing with gases, remembering the conditions of STP can greatly aid in the clarity and accuracy of scientific communication and data analysis.