To balance the given chemical equation: [tex]\( \text{HNO}_3 + \text{Ca(OH)}_2 \rightarrow \text{Ca(NO}_3\text{)}_2 + \text{H}_2\text{O} \)[/tex], let's follow a step-by-step approach:
1. Write down the unbalanced equation:
[tex]\[
\text{HNO}_3 + \text{Ca(OH)}_2 \rightarrow \text{Ca(NO}_3\text{)}_2 + \text{H}_2\text{O}
\][/tex]
2. Identify the number of atoms of each element on both sides of the equation:
- Reactants side:
- H (Hydrogen): 1 (from HNO3) + 2 (from Ca(OH)2) = 3
- N (Nitrogen): 1 (from HNO3)
- O (Oxygen): 3 (from HNO3) + 2 (from Ca(OH)2) = 5
- Ca (Calcium): 1 (from Ca(OH)2)
- Products side:
- H (Hydrogen): 2 (from H2O)
- N (Nitrogen): 2 (from Ca(NO3)2)
- O (Oxygen): 6 (from Ca(NO3)2) + 1 (from H2O) = 7
- Ca (Calcium): 1 (from Ca(NO3)2)
3. Balance the atoms one by one:
- Balance Calcium (Ca):
[tex]\(\text{Ca}\)[/tex] is already balanced with 1 atom on each side.
- Balance Nitrogen (N):
There are 1 nitrogen atom on the reactants side and 2 on the products side. Therefore, to balance Nitrogen, we'll need 2 molecules of HNO3 on the reactants side:
[tex]\[
2\text{HNO}_3 + \text{Ca(OH)}_2 \rightarrow \text{Ca(NO}_3\text{)}_2 + \text{H}_2\text{O}
\][/tex]
- Now, Nitrogen is balanced.
- Balance Oxygen (O):
- On the reactants side: [tex]\(2 \times 3\)[/tex] (from HNO3) + 2 (from Ca(OH)2) = 8
- On the products side: 6 (from Ca(NO3)2) + 1 (from H2O) = 7
Notice that while adding H2O later will balance O and H simultaneously, right now, our O count doesn't balance at 8.
- Balance Hydrogen (H):
- On reactants side, we have: [tex]\(2 \times 1\)[/tex] (from HNO3) + 2 (from Ca(OH)2) = 4
- On products side, we need to balance with water (H2O), which holds two H per molecule.
- Thus, we balance by having 2 water molecules:
[tex]\[
2\text{HNO}_3 + \text{Ca(OH)}_2 \rightarrow \text{Ca(NO}_3\text{)}_2 + 2\text{H}_2\text{O}
\][/tex]
- Now, Hydrogen is balanced with 4 atoms on each side.
4. Final check:
- Hydrogen: [tex]\(2 \times 1 + 2 = 4\)[/tex] in reactants and [tex]\(2 \times 2 = 4\)[/tex] in products.
- Nitrogen: [tex]\(2\)[/tex] in reactants and [tex]\(2\)[/tex] in products.
- Oxygen: [tex]\(2 \times 3 (HNO3) + 2 (Ca(OH)2) = 8\)[/tex] in reactants and [tex]\(6 (Ca(NO3)2) + 2 (H2O) = 8\)[/tex] in products.
- Calcium: [tex]\(1\)[/tex] in reactants and [tex]\(1\)[/tex] in products.
Thus, the balanced chemical equation is:
[tex]\[
2\text{HNO}_3 + \text{Ca(OH)}_2 \rightarrow \text{Ca(NO}_3\text{)}_2 + 2\text{H}_2\text{O}
\][/tex]
This indicates that the stoichiometric coefficients for [tex]\( \text{HNO}_3, \text{Ca(OH)}_2, \text{Ca(NO}_3\text{)}_2, \text{H}_2\text{O} \)[/tex] are [tex]\( 2, 1, 1, 2 \)[/tex] respectively.
