Problem 9 - Chemistry: The Central Science in SI Units, Global Edition

Question

Write "true" or "false" for each statement. (a) We balance chemical equations as we do because energy must be conserved. (b) If the reaction \(2 \mathrm{O}_{3}(g) \rightarrow 3 \mathrm{O}_{2}(g)\) goes to completion and all \(\mathrm{O}_{3}\) is converted to \(\mathrm{O}_{2}\), then the mass of \(\mathrm{O}_{3}\) at the beginning of the reaction must be the same as the mass of \(\mathrm{O}_{2}\) at the end of the reaction. \((\mathbf{c})\) You can balance the "water-splitting" reaction \(\mathrm{H}_{2} \mathrm{O}(l) \rightarrow \mathrm{H}_{2}(g)+\mathrm{O}_{2}(g)\) by writing it this way: \(\mathrm{H}_{2} \mathrm{O}_{2}(l) \rightarrow \mathrm{H}_{2}(g)+\mathrm{O}_{2}(g)\).

Step-by-Step Solution

Answer

(a) False. (b) True. (c) False.

Step 1: Statement (a) Evaluation

We balance chemical equations as we do because energy must be conserved. This statement is false. Chemical equations are balanced in order to satisfy the law of conservation of mass, not to conserve energy. Balancing chemical equations ensures that the same number of atoms of each element are present on both sides of the equation, while the conservation of energy relates to the fact that the total initial energy equals the total final energy in a closed system.

Step 2: Statement (b) Evaluation

If the reaction \(2 \mathrm{O}_{3}(g) \rightarrow 3 \mathrm{O}_{2}(g)\) goes to completion and all \(\mathrm{O}_{3}\) is converted to \(\mathrm{O}_{2}\), then the mass of \(\mathrm{O}_{3}\) at the beginning of the reaction must be the same as the mass of \(\mathrm{O}_{2}\) at the end of the reaction. This statement is true. According to the law of conservation of mass, the total mass of reactants in a chemical reaction must be equal to the total mass of products. In this reaction, all O₃ molecules are converted to O₂, so the mass of O₃ at the initial stage must be equal to the mass of O₂ at the final stage.

Step 3: Statement (c) Evaluation

You can balance the "water-splitting" reaction \(\mathrm{H}_{2} \mathrm{O}(l) \rightarrow \mathrm{H}_{2}(g)+\mathrm{O}_{2}(g)\) by writing it this way: \(\mathrm{H}_{2} \mathrm{O}_{2}(l) \rightarrow \mathrm{H}_{2}(g)+\mathrm{O}_{2}(g)\). This statement is false. Writing the equation as \(\mathrm{H}_{2} \mathrm{O}_{2}(l) \rightarrow \mathrm{H}_{2}(g)+\mathrm{O}_{2}(g)\) introduces an incorrect chemical formula for the reactant side, which is hydrogen peroxide instead of water. The balanced form of water-splitting reaction should be \(2 \mathrm{H}_{2} \mathrm{O}(l) \rightarrow 2 \mathrm{H}_{2}(g)+\mathrm{O}_{2}(g)\), maintaining the law of conservation of mass by including the correct number of atoms of each element on both sides of the equation.

Key Concepts

Conservation of Mass

The law of conservation of mass is a crucial principle in chemistry, which states that mass cannot be created or destroyed in a chemical reaction. This principle ensures that the total mass of the reactants equals the total mass of the products after a reaction.
In the chemical reaction \(2 \mathrm{O}_{3}(g) \rightarrow 3 \mathrm{O}_{2}(g)\), the mass of \(\mathrm{O}_{3}\) at the beginning must match the mass of \(\mathrm{O}_{2}\) at the end, even if the substances themselves have transformed.

• This law is fundamental for balancing chemical equations, as it requires that the same number and types of atoms are present before and after the reaction.
• Ensuring mass conservation helps chemists verify that no mass is lost, confirming the correctness of their chemical equations.

All atoms that appear in the reactants must also appear in the products, reflecting the mass balance in these transformations.

Chemical Reactions

Chemical reactions are processes that involve the transformation of substances through the breaking and forming of chemical bonds. During chemical reactions, reactants are converted into products, often resulting in new substances with different properties.
A balanced chemical equation not only highlights the reactants and products involved but also ensures compliance with the law of conservation of mass.

• Each chemical reaction is unique in how it transforms reactants into products, which makes balancing equations essential for understanding chemical processes.
• In the "water-splitting" reaction, originally given as \(\mathrm{H}_{2} \mathrm{O}(l) \rightarrow \mathrm{H}_{2}(g)+\mathrm{O}_{2}(g)\), the balanced version \(2 \mathrm{H}_{2} \mathrm{O}(l) \rightarrow 2 \mathrm{H}_{2}(g)+\mathrm{O}_{2}(g)\) confirms that atoms of hydrogen and oxygen are conserved in the reaction.

Balancing equations also involves ensuring the stoichiometry—the correct proportions of reactants and products.

Stoichiometry

Stoichiometry is the calculation of reactants and products in chemical reactions. It uses the coefficients of a balanced chemical equation to determine the relative amounts of each substance. This concept is fundamental for predicting how much of each reactant is needed and how much product will be formed in a reaction.

• The coefficients in a balanced equation reflect the stoichiometric ratios, essential for mole-to-mole conversions.
• In \(2 \mathrm{H}_{2} \mathrm{O}(l) \rightarrow 2 \mathrm{H}_{2}(g)+\mathrm{O}_{2}(g)\), the ratio 2:2:1 indicates that two moles of water produce two moles of hydrogen gas and one mole of oxygen gas.

Stoichiometry allows chemists to measure and predict material usage and yield, offering insight into the quantitative relationships within a reaction. Understanding and applying stoichiometry is vital for any budding chemist, facilitating precise calculations in the lab and industry.