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)$.

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.

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.

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.