Problem 68 - Chemistry Matter and Change

Question

Oxygen Production The Russian Space Agency uses potassium superoxide \(\left(\mathrm{KO}_{2}\right)\) for the chemical oxygen generators in their space suits. $$4 \mathrm{KO}_{2}+2 \mathrm{H}_{2} \mathrm{O}+4 \mathrm{CO}_{2} \rightarrow 4 \mathrm{KHCO}_{3}+3 \mathrm{O}_{2}$$

Step-by-Step Solution

Answer

To find the mass of reactants needed and products formed in the reaction, use the balanced chemical equation: \(4 \mathrm{KO}_{2}+2 \mathrm{H}_{2} \mathrm{O}+4 \mathrm{CO}_{2} \rightarrow 4 \mathrm{KHCO}_{3}+3 \mathrm{O}_{2}\). Calculate the molar masses of each substance, and then use stoichiometry to determine the mass relationships between reactants and products. For example, the mass of oxygen (O₂) produced can be calculated as (3/4) * m(KO₂) * M(O₂) / M(KO₂), where m(KO₂) is the mass of potassium superoxide used.

Step 1: Understand the Balanced Chemical Equation

We are given the following balanced chemical equation: \[4 \mathrm{KO}_{2}+2 \mathrm{H}_{2} \mathrm{O}+4 \mathrm{CO}_{2} \rightarrow 4 \mathrm{KHCO}_{3}+3 \mathrm{O}_{2}\] This balanced chemical equation tells us that 4 moles of potassium superoxide reacts with 2 moles of water and 4 moles of carbon dioxide to produce 4 moles of potassium bicarbonate and 3 moles of oxygen.

Step 2: Calculate the Molar Mass of the Reactants and Products

To calculate the moles of each substance involved in the balanced equation, we need to know the molar mass of each substance. Using the provided periodic table or any other reference, calculate the molar masses. Potassium superoxide (KO₂): K = 39.10 g/mol, O₂ = 2*16.00 g/mol; M(KO₂) = 39.10 + 32.00 = 71.10 g/mol Water (H₂O): H₂ = 2*1.01 g/mol, O = 16.00 g/mol; M(H₂O) = 2*1.01 + 16.00 = 18.02 g/mol Carbon dioxide (CO₂): C = 12.01 g/mol, O₂ = 2*16.00 g/mol; M(CO₂) = 12.01 + 32.00 = 44.01 g/mol Potassium bicarbonate (KHCO₃): K = 39.10 g/mol, H = 1.01 g/mol, C = 12.01 g/mol, O₃ = 3*16.00 g/mol; M(KHCO₃) = 39.10 + 1.01 + 12.01 + 3 * 16.00 = 100.12 g/mol Oxygen (O₂): M(O₂) = 2 * 16.00 = 32.00 g/mol

Step 3: Determine the Mass of Reactants and Products

Using the stoichiometry of the balanced chemical equation and the molar masses calculated in the previous step, we can now determine the mass of reactants and products. For a given mass of the potassium superoxide (m(KO₂)): Mass of water (m(H₂O)) = (2/4) * m(KO₂) * M(H₂O) / M(KO₂) Mass of carbon dioxide (m(CO₂)) = (4/4) * m(KO₂) * M(CO₂) / M(KO₂) Mass of potassium bicarbonate (m(KHCO₃)) = (4/4) * m(KO₂) * M(KHCO₃) / M(KO₂) Mass of oxygen (m(O₂)) = (3/4) * m(KO₂) * M(O₂) / M(KO₂) Through these equations, we can find out the mass of reactants needed and products formed, depending on the application. For oxygen production, knowing the desired amount of oxygen produced will allow us to calculate the amounts of potassium superoxide, water, and carbon dioxide necessary for the process.

Key Concepts

Chemical Equation

A chemical equation is a symbolic representation of a chemical reaction. It shows the reactants (substances that start a reaction) and the products (substances formed by the reaction). In a balanced chemical equation, like the one provided in the exercise, the number of atoms for each element is equal on both sides of the equation. This is essential for complying with the law of conservation of mass.

In the equation provided, 4 moles of potassium superoxide (\(4 \mathrm{KO}_{2}\)), 2 moles of water (\(2 \mathrm{H}_{2} \mathrm{O}\)), and 4 moles of carbon dioxide (\(4 \mathrm{CO}_{2}\)) react to produce 4 moles of potassium bicarbonate (\(4 \mathrm{KHCO}_{3}\)) and 3 moles of oxygen (\(3 \mathrm{O}_{2}\)). A balanced chemical equation like this not only tells us which molecules and how many are involved, but also maintains parity between atoms across reactants and products.

Understanding chemical equations is crucial for knowing the proportions of elements and compounds in a reaction, allowing us to predict the amounts of each substance used or produced.

Stoichiometry

Stoichiometry is the calculation of reactants and products in chemical reactions. It enables us to interpret the chemical equation quantitatively, which means assessing how much reactant is needed, or how much product is formed. In essence, stoichiometry is the bridge between the unbalanced desires of nature and our calculated manipulations in a lab.

To perform stoichiometric calculations, we use the coefficients from the balanced chemical equation. In this case, the coefficient '4' before \(\text{KO}_2\) indicates that 4 moles of this reactant are involved in the reaction. Each coefficient represents the molar ratio between substances.

Using stoichiometry, you could determine the masses of the reactants needed to produce a certain amount of a product. It is essential for understanding how chemical reactions occur, ensuring that all reactants are used efficiently, and predicting the outcome of reactions.

Molar Mass

The molar mass is the mass of one mole of a substance and is expressed in grams per mole (\(\text{g/mol}\)). By knowing the molar masses of each component in a reaction, you’re able to convert between grams of a substance and moles, which is crucial for stoichiometry.

Let's take potassium superoxide (\(\text{KO}_2\)) as an example:

• Potassium (K) has a molar mass of 39.10 g/mol.
• Oxygen (O) is about 16.00 g/mol, and there are two oxygen atoms, totaling to 32.00 g/mol.
• The molar mass of potassium superoxide (\(\text{KO}_2\)) is therefore \(39.10 + 32.00 = 71.10\text{ g/mol}\).

Calculating the molar mass of each reactant and product is a necessary step. It helps to figure out how much of each substance is needed to fulfill the stoichiometry of the balanced equation.

Potassium Superoxide

Potassium superoxide (\(\text{KO}_2\)) is an important compound used for generating oxygen. This makes it very valuable, especially in environments where oxygen is limited, such as in spacecraft.

Potassium superoxide is known for its ability to produce oxygen through a reaction with water and carbon dioxide. The process absorbs \(\text{CO}_2\), reduces it to bicarbonate, and releases \(\text{O}_2\), making it ideal for enclosed environments.

This compound not only helps in providing breathable air but also assists in removing carbon dioxide efficiently. Therefore, understanding the chemical interactions of potassium superoxide is critical for ensuring safety and sustainability in life-support systems, particularly for astronauts.