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. (c) You can balance the "water-splitting" reaction \(\mathrm{H}_{2} \mathrm{O}(I) \rightarrow \mathrm{H}_{2}(g)+\mathrm{O}_{2}(g)\) 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 to ensure that the number of atoms of each element remains the same on both the reactant and product side. This is in line with the law of conservation of mass, which states that mass cannot be created nor destroyed in chemical reactions. So, the reason we balance chemical equations is not directly related to the conservation of energy but the conservation of mass. Therefore, the statement is: \( \boxed{\textbf{False}} \)

Given the balanced chemical equation: \( 2\,\mathrm{O}_{3}(g) \rightarrow 3\,\mathrm{O}_{2}(g) \) This equation tells us that every two molecules of ozone (\(\mathrm{O}_{3}\)), upon going to completion, are converted into three molecules of molecular oxygen (\(\mathrm{O}_{2}\)). According to the law of conservation of mass, the mass of the reactants should be equal to the mass of the products. Given the stoichiometry of the reaction, the conservation of mass should hold true. Hence, the statement is: \( \boxed{\textbf{True}} \)

The given water-splitting reaction reads: \( \mathrm{H}_{2}\,\mathrm{O}(l) \rightarrow \mathrm{H}_{2}(g) + \mathrm{O}_{2}(g) \) This reaction is not balanced as written, as there are only two hydrogen atoms and one oxygen atom on the reactant side, while there are two oxygen atoms in the product \(\mathrm{O}_{2}(g)\). To balance the equation, we can adjust the coefficients as follows: \( 2\, \mathrm{H}_{2}\,\mathrm{O}(l) \rightarrow 2\, \mathrm{H}_{2}(g) + \mathrm{O}_{2}(g) \) The suggested balanced equation: \( \mathrm{H}_{2}\,\mathrm{O}_{2}(l) \rightarrow \mathrm{H}_{2}(g) + \mathrm{O}_{2}(g) \) is incorrect as it introduces a new molecule (hydrogen peroxide) that is not involved in the actual reaction, creating a mismatch in terms of the structural and stoichiometric properties of the balanced equation. Thus, the statement is: \( \boxed{\textbf{False}} \)