Problem 37 - Chemistry: An Atoms-Focused Approach

Question

Oxygen for First Responders In self-contained breathing devices used by first responders, potassium superoxide, \(\mathrm{KO}_{2}\) reacts with exhaled carbon dioxide to produce potassium carbonate and oxygen: $$4 \mathrm{KO}_{2}(s)+2 \mathrm{CO}_{2}(g) \rightarrow 2 \mathrm{K}_{2} \mathrm{CO}_{3}(s)+3 \mathrm{O}_{2}(g)$$ How much \(\mathrm{O}_{2}\) could be produced from \(85 \mathrm{g} \mathrm{KO}_{2} ?\)

Step-by-Step Solution

Answer

Answer: 28.67 grams of O2 can be produced from 85g of KO2.

Step 1: Convert the mass of KO2 to moles

To convert the mass of KO2 to moles, we will use the molar mass of KO2. The molar mass of KO2 can be calculated as follows: Molar mass of K = 39.1 g/mol Molar mass of O = 16.0 g/mol Molar mass of KO2 = 39.1 + 2 * 16.0 = 71.1 g/mol We can now calculate the moles of KO2 using the given mass: moles of KO2 = (mass of KO2) / (molar mass of KO2) = 85 g / 71.1 g/mol = 1.195 moles

Step 2: Use stoichiometry to calculate the amount of O2 produced

Using the balanced chemical equation, we can determine the mole ratio between KO2 and O2: 4 KO2 : 3 O2 This means that for every 4 moles of KO2, 3 moles of O2 are produced. We can now use this ratio to determine the moles of O2 produced from the given amount of KO2: moles of O2 = (moles of KO2) * (3 moles O2 / 4 moles KO2) = 1.195 moles * (3 moles O2 / 4 moles KO2) = 0.896 moles of O2

Step 3: Convert the moles of O2 to grams

To find the mass of O2 produced, we need to convert the moles of O2 to grams. We will use the molar mass of O2 for this conversion: Molar mass of O = 16.0 g/mol Molar mass of O2 = 2 * 16.0 = 32.0 g/mol mass of O2 = (moles of O2) * (molar mass of O2) = 0.896 moles * 32.0 g/mol = 28.67 g Thus, 28.67 grams of O2 could be produced from 85g of KO2.

Key Concepts

Chemical reactions

Chemical reactions are processes where substances change into new substances. In the context of first responders' breathing devices, potassium superoxide (KO₂) reacts with carbon dioxide (CO₂) to produce potassium carbonate (K₂CO₃) and oxygen (O₂). This reaction is critical because it generates breathable oxygen, supporting firefighters and rescuers in smoke-filled environments.
Understanding a chemical reaction involves recognizing the reactants (substances that start the reaction) and the products (new substances formed). In our case, KO₂ and CO₂ are the reactants, while K₂CO₃ and O₂ are the products.
Some key characteristics of chemical reactions include:

• Change in substances, meaning new chemical entities are formed.
• Conservation of mass, where the mass of reactants equals the mass of the products.
• Energy changes, where reactions can absorb or release energy.

Understanding these principles helps us analyze reactions, predict products, and calculate the amounts of substances involved.

Molar mass

Molar mass is a fundamental concept in stoichiometry that refers to the mass of one mole of a substance. It is essential for converting between grams and moles, allowing us to connect the mass of a substance to the number of particles or molecules it contains.
To calculate the molar mass of a compound, sum up the atomic masses of all the atoms in its chemical formula. For potassium superoxide (\(KO_2\)):

• Potassium (K) has an atomic mass of 39.1 g/mol.
• Oxygen (O) has an atomic mass of 16.0 g/mol.

Thus, the molar mass of KO₂ is \(39.1 + 2 imes 16.0 = 71.1 ext{ g/mol}\).
In stoichiometry, this concept allows us to convert a given mass to moles, facilitating calculations involving chemical reactions. By understanding and using molar mass, students can translate the quantities of actual substances they have in the lab into the theoretical quantities needed to predict chemical behavior.

Balanced chemical equation

A balanced chemical equation is essential for understanding the proportions in which substances react. It ensures that the number of atoms of each element is the same on both sides of the equation, reflecting the principle of mass conservation.
The balanced equation for the reaction of potassium superoxide and carbon dioxide to produce potassium carbonate and oxygen is:\[4 ext{ KO}_2 + 2 ext{ CO}_2 ightarrow 2 ext{ K}_2 ext{CO}_3 + 3 ext{ O}_2\]
This shows that:

• 4 moles of KO₂ react with 2 moles of CO₂.
• This results in 2 moles of K₂CO₃ and 3 moles of O₂.

Using a balanced equation, we can understand the stoichiometric ratios between the reactants and products. This is crucial for calculations such as how much oxygen can be produced from a given amount of potassium superoxide. By applying these ratios, students can predict the outcomes of reactions and formulate precise quantities of reactants needed for desired products.