Problem 138 - Introductory Chemistry Atoms First

Question

Potassium nitrate decomposes upon heating to form potassium oxide, nitrogen gas, and oxygen gas. If \(19.6 \mathrm{~g}\) of potassium nitrate have decomposed, how many molecules of oxygen gas have been formed?

Step-by-Step Solution

Answer

The number of oxygen gas molecules formed in the decomposition of 19.6 g of potassium nitrate is approximately \(2.92 \times 10^{23}\) molecules.

Step 1: Write the balanced chemical equation for the decomposition of potassium nitrate

The decomposition reaction of potassium nitrate is given as follows: 2 KNO₃ (s) → 2 K₂O (s) + 2 N₂ (g) + 5 O₂ (g)

Step 2: Calculate the moles of potassium nitrate (KNO₃)

Given, 19.6 g of potassium nitrate decomposes. First, calculate the molar mass of KNO₃ using the atomic masses of its constituent elements: Molar mass of KNO₃ = (1 × atomic mass of K) + (1 × atomic mass of N) + (3 × atomic mass of O) Molar mass of KNO₃ = (1 × 39.1 g/mol) + (1 × 14.0 g/mol) + (3 × 16.0 g/mol) Molar mass of KNO₃ = 39.1 + 14.0 + 48.0 Molar mass of KNO₃ = 101.1 g/mol Now, calculate the moles of KNO₃ using its given mass and molar mass: Moles of KNO₃ = Mass of KNO₃ / Molar mass of KNO₃ Moles of KNO₃ = 19.6 g / 101.1 g/mol Moles of KNO₃ = 0.194 mol

Step 3: Use stoichiometry to find moles of oxygen gas (O₂) formed

According to the balanced chemical equation, 2 moles of KNO₃ produce 5 moles of O₂. Therefore, we can set up the following proportion to find the moles of O₂ produced: (0.194 mol KNO₃)(5 mol O₂ / 2 mol KNO₃) Now, calculate the moles of O₂: Moles of O₂ = 0.194 × (5/2) Moles of O₂ = 0.485 mol

Step 4: Calculate the number of molecules of oxygen gas from moles

The number of molecules can be calculated using Avogadro's constant: Number of molecules = Moles of O₂ × (6.022 × 10²³ molecules/mol) Number of molecules = 0.485 mol × (6.022 × 10²³) Number of molecules = 2.92 × 10²³ molecules The number of oxygen gas molecules formed is approximately \(2.92 \times 10^{23}\) molecules.

Key Concepts

Chemical Equations

Chemical equations are symbolic representations of chemical reactions. They show the substances involved in a reaction and how they change. Each chemical equation must be balanced, meaning that the number of atoms for each element is the same on both sides of the equation. This balance reflects the law of conservation of mass, stating that matter cannot be created or destroyed in a chemical reaction.
To balance a chemical equation, follow these steps:

• Identify the reactants and products.
• Write the unbalanced equation.
• Count the number of atoms for each element on both sides.
• Add coefficients to balance the atoms, one element at a time.
• Double-check the balanced equation to ensure all atoms are conserved.

This is essential as it allows us to calculate the exact amount of reactants needed and products formed in a chemical reaction.

Molar Mass

Molar mass is a critical concept in chemistry that refers to the mass of one mole of a substance, usually expressed in grams per mole (g/mol). It is derived from the atomic masses of the constituent elements in a compound, as found on the periodic table.
In our example, to find the molar mass of potassium nitrate ( KNO₃ ), we add the atomic masses of potassium (K), nitrogen (N), and three oxygen (O) atoms:

• Potassium: 39.1 g/mol
• Nitrogen: 14.0 g/mol
• Oxygen: 3 × 16.0 g/mol = 48.0 g/mol
• Molar mass of KNO₃ = 39.1 + 14.0 + 48.0 = 101.1 g/mol

Molar mass helps convert between the mass of a substance and the amount in moles, which is vital for stoichiometry calculations.

Avogadro's Number

Avogadro's number, approximately 6.022 × 10²³, is a constant that indicates the number of particles (atoms, molecules, or ions) in one mole of a substance. It serves as a bridge between the atomic scale and the macroscopic scale and is crucial for stoichiometric calculations in chemistry.
Using Avogadro's number, we can calculate the number of molecules in a given amount of substance by multiplying the moles of the substance by Avogadro's constant. For example, if we have 0.485 moles of oxygen gas, the number of oxygen molecules is calculated as:

• Number of molecules = 0.485 mol × 6.022 × 10²³ molecules/mol
• Number of molecules ≈ 2.92 × 10²³

This calculation helps quantify the microscopic entities involved in chemical processes.

Potassium Nitrate Decomposition

Potassium nitrate ( KNO₃ ) is a chemical compound that decomposes upon heating into potassium oxide, nitrogen gas, and oxygen gas. This process can be described by the balanced chemical equation:

• 2 KNO₃ (s) → 2 K₂O (s) + 2 N₂ (g) + 5 O₂ (g)

This reaction indicates that when 2 moles of KNO₃ decompose, it results in 2 moles of potassium oxide, 2 moles of nitrogen gas, and 5 moles of oxygen gas. Understanding this reaction is critical due to the following reasons:

• It requires recognizing how matter is redistributed during decomposition.
• Understanding the stoichiometry of the reaction can help calculate the reactants needed and products formed.
• It's a practical example of energy-driven chemical changes and how they can produce useful substances like gases.

Potassium nitrate's decomposition is a vivid illustration of chemical transformations in action.