Problem 176 - Introductory Chemistry Atoms First

Question

Consider the following decomposition reaction in which \(47.20 \mathrm{~g}\) of some compound is decomposed into its elements.

Step-by-Step Solution

Answer

A general outline for solving decomposition reactions involves: understanding the decomposition reaction, writing the balanced chemical equation, finding the molar mass of the compound and its constituent elements, converting grams of the compound to moles, using stoichiometry to determine the moles of each element produced, converting moles of elements to grams, and verifying the conservation of mass. In this specific case, we don't have enough information to provide a complete solution, but knowing these steps will help you solve similar problems in the future.

Step 1: Understand the decomposition reaction

In a decomposition reaction, a single compound breaks down into two or more simpler substances (usually the constituent elements). These reactions typically require an input of energy in the form of heat, light, or electricity, e.g., 2H₂O → 2H₂ + O₂.

Step 2: Write the balanced chemical equation

Write the balanced chemical equation for the decomposition reaction. Make sure the number of atoms on both sides of the equation is equal. For example, if the compound AB decomposes into A and B, make sure both sides of the equation have an equal number of A and B atoms: AB → A + B.

Step 3: Find the molar mass of the compound and its constituent elements

Use a periodic table to find the molar mass of each element in the compound and the compound itself. Molar mass is the mass of one mole of the substance in grams, and it is equal to the sum of the atomic masses of the constituent elements.

Step 4: Convert grams of the compound to moles

Divide the given mass of the compound (47.20 grams) by its molar mass to find the moles of the compound. Moles = Mass / Molar Mass.

Step 5: Use stoichiometry to determine the moles of each element produced

Refer to the balanced chemical equation and use stoichiometry to determine the number of moles of each constituent element that would be produced when the compound decomposes. This will involve determining the mole ratio between the compound and each element in the reaction.

Step 6: Convert moles of elements to grams

Multiply the moles of each element by its molar mass to determine the mass of each element produced in grams. Mass = Moles × Molar Mass.

Step 7: Verify conservation of mass

The law of conservation of mass states that mass cannot be created nor destroyed in a chemical reaction. Ensure the sum of the masses of the constituent elements produced is equal to the initial mass of the compound. In this case, the sum of the masses of the elements should be equal to 47.20 grams. Remember that this is a general outline of the steps to solve a decomposition reaction problem. In this particular case, we do not have the specific compound or balanced chemical equation needed for a complete solution but understanding these steps prepares you to solve similar problems in the future.

Key Concepts

Balanced Chemical Equation

In a decomposition reaction, the compound breaks down into its simpler elements or compounds. The first step in solving a decomposition problem is writing the balanced chemical equation. Balancing means ensuring that the number of each type of atom is the same on both sides of the equation.

For example, if the compound breaks down from AB to A and B, you would represent it as:

• Left Side: AB
• Right Side: A + B

It is crucial to count the atoms of each element on both sides of the equation to ensure they are equal. This ensures that no atoms are lost or gained in the process, aligning with the principles of chemical reactions. A balanced equation is critical as it provides the foundation for determining the proportions of each substance involved in the reaction.

Molar Mass

Molar mass is a fundamental concept when dealing with chemical reactions. It refers to the mass of one mole of a substance, typically expressed in grams per mole (g/mol). Understanding molar mass is essential as it allows us to relate the mass of a substance to the number of moles.

To determine the molar mass of a compound, add up the atomic masses of the elements present, which can be found on the periodic table. For instance, for a compound like \( ext{H}_2 ext{O}\), the molar mass calculation involves:

• Hydrogen: 2 atoms x 1.01 g/mol = 2.02 g/mol
• Oxygen: 1 atom x 16.00 g/mol = 16.00 g/mol
• Total Molar Mass = 18.02 g/mol

Knowing the molar mass acts as a bridge to convert between mass (in grams) and moles in a reaction, enabling you to utilize the information from the balanced equation effectively.

Stoichiometry

Stoichiometry is the quantitative relationship between the reactants and products in a chemical reaction. It's like the recipe of a chemical equation, telling you how much of each ingredient you need and how much product you'll get.

Utilizing the balanced chemical equation, stoichiometry helps you to find out how many moles of a product are produced from a given amount of reactant and vice versa. For instance, if the equation is \( ext{2H}_2 ext{O} \rightarrow ext{2H}_2 + ext{O}_2\), it tells you:

• For every 2 moles of \( ext{H}_2 ext{O}\), 2 moles of \( ext{H}_2\) and 1 mole of \( ext{O}_2\) are produced.

This allows you to determine how much of each element is produced during the decomposition, and to predict the outcomes accurately based on initial conditions.

Conservation of Mass

The principle of the conservation of mass states that mass is neither created nor destroyed in a chemical reaction. This means the mass of the reactants will equal the mass of the products.

For decomposition reactions, after breaking down a compound into its elements, the total mass of these elements should equal the original compound's mass. This is vital for verifying your calculations.

• Initial Compound Mass = Mass of Elements Produced

Checking these masses ensures that no errors occurred during the calculations. In practice, if you started with 47.20 g of a compound, the sum of the masses of the decomposed elements should also total 47.20 g. This serves as a validation of accuracy in your stoichiometry and balance calculations.