\( \left. \begin{array} { l }{ Ca ( OH ) _ { 2 } + 2 HNO _ { 3 } \rightarrow Ca ( NO _ { 3 } ) _ { 2 } + H ( OH ) } \\ { 3 Fe + 4 H _ { 2 } O \rightarrow Fe _ { 3 } O _ { 4 } + 4 H _ { 2 } } \end{array} \right. \)

Let's analyze the two chemical reactions provided and balance them step by step. ### Reaction 1: \[ Ca(OH)_2 + 2 HNO_3 \rightarrow Ca(NO_3)_2 + H_2O \] 1. **Identify the reactants and products:** - Reactants: Calcium hydroxide \( Ca(OH)_2 \) and Nitric acid \( HNO_3 \) - Products: Calcium nitrate \( Ca(NO_3)_2 \) and Water \( H_2O \) 2. **Count the number of atoms for each element:** - **Reactants:** - \( Ca: 1 \) - \( O: 2 \) (from \( Ca(OH)_2 \)) + \( 6 \) (from \( 2 HNO_3 \)) = \( 8 \) - \( H: 2 \) (from \( Ca(OH)_2 \)) + \( 2 \) (from \( 2 HNO_3 \)) = \( 4 \) - \( N: 2 \) (from \( 2 HNO_3 \)) - **Products:** - \( Ca: 1 \) - \( O: 6 \) (from \( Ca(NO_3)_2 \)) + \( 1 \) (from \( H_2O \)) = \( 7 \) - \( H: 2 \) (from \( H_2O \)) - \( N: 2 \) (from \( Ca(NO_3)_2 \)) 3. **Balancing the equation:** - The number of Calcium and Nitrogen atoms are balanced. - The Hydrogen and Oxygen atoms are not balanced. We need to adjust the products to ensure that the number of atoms on both sides is equal. The balanced equation is: \[ Ca(OH)_2 + 2 HNO_3 \rightarrow Ca(NO_3)_2 + 2 H_2O \] ### Reaction 2: \[ 3 Fe + 4 H_2O \rightarrow Fe_3O_4 + 4 H_2 \] 1. **Identify the reactants and products:** - Reactants: Iron \( Fe \) and Water \( H_2O \) - Products: Magnetite \( Fe_3O_4 \) and Hydrogen gas \( H_2 \) 2. **Count the number of atoms for each element:** - **Reactants:** - \( Fe: 3 \) - \( O: 4 \) (from \( 4 H_2O \)) - \( H: 8 \) (from \( 4 H_2O \)) - **Products:** - \( Fe: 3 \) (from \( Fe_3O_4 \)) - \( O: 4 \) (from \( Fe_3O_4 \)) - \( H: 4 \) (from \( 4 H_2 \)) 3. **Balancing the equation:** - The number of Iron and Oxygen atoms are balanced. - The Hydrogen atoms are not balanced. We need to adjust the products to ensure that the number of atoms on both sides is equal. The balanced equation is: \[ 3 Fe + 4 H_2O \rightarrow Fe_3O_4 + 4 H_2 \] ### Final Balanced Reactions: 1. \( Ca(OH)_2 + 2 HNO_3 \rightarrow Ca(NO_3)_2 + 2 H_2O \) 2. \( 3 Fe + 4 H_2O \rightarrow Fe_3O_4 + 4 H_2 \) Both reactions are now balanced.