Problem 62 - Chemistry: The Central Science in SI Units, Global Edition

Question

The reaction between potassium superoxide, \(\mathrm{KO}_{2}\), and \(\mathrm{CO}_{2}\), $$ 4 \mathrm{KO}_{2}+2 \mathrm{CO}_{2} \longrightarrow 2 \mathrm{~K}_{2} \mathrm{CO}_{3}+3 \mathrm{O}_{2} $$ is used as a source of \(\mathrm{O}_{2}\) and absorber of \(\mathrm{CO}_{2}\) in selfcontained breathing equipment used by rescue workers. (a) How many moles of \(\mathrm{O}_{2}\) are produced when \(0.400 \mathrm{~mol}\) of \(\mathrm{KO}_{2}\) reacts in this fashion? (b) How many grams of \(\mathrm{KO}_{2}\) are needed to form \(7.50 \mathrm{~g}\) of \(\mathrm{O}_{2}\) ? (c) How many grams of \(\mathrm{CO}_{2}\) are used when \(7.50 \mathrm{~g}\) of \(\mathrm{O}_{2}\) are produced?

Step-by-Step Solution

Answer

moles of O₂ = 0.300 mol. Thus, 0.300 moles of O₂ are produced when 0.400 moles of KO₂ react.

Step 1: Identify given information

List all given data and unknowns.

Step 2: Determine relevant principles

Identify applicable chemical laws.

Step 3: Set up and solve

Apply equations and solve.

Step 4: State the answer

The answer is: moles of O₂ = 0.300 mol. Thus, 0.300 moles of O₂ are produced when 0.400 moles of KO₂ react.

Key Concepts

Chemical Equations

Chemical equations are vital in chemistry as they describe what happens in a chemical reaction. These equations consist of chemical formulas that represent the substances involved in the process. The substances present before the reaction are called reactants, while those formed as a result of the reaction are called products. For example, in the equation: \[4 \mathrm{KO}_{2} + 2 \mathrm{CO}_{2} \rightarrow 2 \mathrm{K}_{2}\mathrm{CO}_{3} + 3 \mathrm{O}_{2}\] - **Reactants**: Potassium superoxide \(\mathrm{KO}_{2}\) and carbon dioxide \(\mathrm{CO}_{2}\) - **Products**: Potassium carbonate \(\mathrm{K}_{2}\mathrm{CO}_{3}\) and oxygen \(\mathrm{O}_{2}\)Each chemical formula indicates the elements that make up the compounds and the number of atoms of each element involved, using subscripts. These equations also help us understand the kinds of interactions between molecules and how new compounds are formed.

Mole Calculations

Mole calculations allow us to translate the quantities represented in a chemical equation into real-world amounts that can be measured or observed. A mole is a unit that chemists use to measure the amount of a substance. One mole contains Avogadro's number (approximately \(6.022 \times 10^{23}\)) of particles. This could be atoms, molecules, ions, or electrons.In the given exercise, we use mole calculations to determine both how many moles of oxygen \(\mathrm{O}_{2}\) are produced and how many grams of a substance are needed or produced:- **From moles of \(\mathrm{KO}_{2}\) to moles of \(\mathrm{O}_{2}\)**: Since \(4\) moles of \(\mathrm{KO}_{2}\) produce \(3\) moles of \(\mathrm{O}_{2}\), a conversion factor is used: \[\text{moles of } \mathrm{O}_{2} = 0.400 \text{ mol } \mathrm{KO}_{2} \times \left(\frac{3 \text{ moles of } \mathrm{O}_{2}}{4 \text{ moles of } \mathrm{KO}_{2}}\right)\] - **Converting moles to grams**: The molar mass of a substance (in grams per mole) is used to convert between moles and grams. For example, to find how many grams of \(\mathrm{KO}_{2}\) are needed, the equation involves using the molar mass of \(\mathrm{KO}_{2}\). These conversions are crucial when dealing with chemical reactions because lab measurements are typically in grams rather than moles.

Balancing Reactions

Balancing reactions is an essential step in understanding chemical equations. The law of conservation of mass states that matter cannot be created or destroyed in an isolated system. Thus, the number of each type of atom must be the same in both the reactants and products. In the chemical equation provided, notice:- Reactants: \(4\) molecules of \(\mathrm{KO}_{2}\) and \(2\) molecules of \(\mathrm{CO}_{2}\) - Products: \(2\) molecules of \(\mathrm{K}_{2}\mathrm{CO}_{3}\) and \(3\) molecules of \(\mathrm{O}_{2}\)To balance the equation, coefficients (such as \(4, 2, 2, \text{and} 3\)) are placed before the chemical formulas. These coefficients ensure that:- The total number of each type of atom on the reactant side equals the total on the product side.- Potassium \((\mathrm{K})\), carbon \((\mathrm{C})\), and oxygen \((\mathrm{O})\) atoms are equally represented on both sides of the reaction. Balancing reactions correctly is critical to performing accurate stoichiometry calculations. A balanced equation ensures that the proportions of substances used and produced in the experiment match the theoretical expectations derived from the equation.