To determine the correctly balanced chemical equation for the reaction between calcium hydroxide [tex]\((Ca(OH)_2)\)[/tex] and nitric acid [tex]\((HNO_3)\)[/tex], we need to follow these steps:
1. Identify the reactants and products:
- Reactants: [tex]\(Ca(OH)_2\)[/tex] and [tex]\(HNO_3\)[/tex]
- The products will be water [tex]\((H_2O)\)[/tex], calcium nitrate [tex]\((Ca(NO_3)_2)\)[/tex].
2. Write the unbalanced chemical equation:
[tex]\[
Ca(OH)_2 + HNO_3 \rightarrow H_2O + Ca(NO_3)_2
\][/tex]
3. Balance the chemical equation:
- Calcium (Ca) atoms: 1 on both sides.
- Nitrogen (N) atoms: We have 2 nitrogen atoms in [tex]\(Ca(NO_3)_2\)[/tex], so we need 2 [tex]\(HNO_3\)[/tex] molecules.
- Oxygen (O) atoms: There are 6 oxygen atoms in [tex]\(Ca(OH)_2\)[/tex] and 2 in [tex]\(2HNO_3\)[/tex], giving a total of 8 oxygen atoms on the left. On the right side, we have 6 in [tex]\(Ca(NO_3)_2\)[/tex] and 2 in the 2 [tex]\(H_2O\)[/tex], giving a total of 8 oxygen atoms.
- Hydrogen (H) atoms: 2 in [tex]\(Ca(OH)_2\)[/tex] and 2 in [tex]\(2HNO_3\)[/tex], giving a total of 4 hydrogen atoms. On the right, we will also need 2 [tex]\(H_2O\)[/tex] molecules which contribute to 4 hydrogen atoms.
So, balancing the equation step-by-step:
[tex]\[
Ca(OH)_2 + 2HNO_3 \rightarrow 2H_2O + Ca(NO_3)_2
\][/tex]
4. Verify the balanced equation:
- Calcium: 1 atom on both sides.
- Nitrogen: 2 atoms on both sides.
- Oxygen: 2 (from [tex]\(Ca(OH)_2\)[/tex]) + 4 (from 2 [tex]\(HNO_3\)[/tex]) = 6 atoms on the left; 6 (from [tex]\(Ca(NO_3)_2\)[/tex]), so a total of 8 atoms on the left, and 2 (from [tex]\(2H_2O\)[/tex]) + 6 (from [tex]\(Ca(NO_3)_2\)[/tex]) = 8 atoms on the right.
- Hydrogen: 4 hydrogen atoms from [tex]\(2H_2O\)[/tex].
Thus, the balanced chemical equation is:
[tex]\[ \boxed{ Ca(OH)_2 + 2HNO_3 \rightarrow 2H_2O + Ca(NO_3)_2 }\][/tex]
So, the fourth option [tex]\(Ca(OH)_2 + 2HNO_3 \rightarrow 2H_2O + Ca(NO_3)_2\)[/tex] is the correctly balanced chemical equation.
