To determine the correctly balanced chemical equation for the reaction of [tex]\( \text{Ca(OH)}_2 \)[/tex] and [tex]\( \text{HNO}_3 \)[/tex], we need to ensure that the number of each type of atom on the reactant side equals the number of each type of atom on the product side.
Let's examine each equation in detail:
1. Equation 1:
[tex]\[
\text{Ca(OH)}_2 + \text{HNO}_3 \rightarrow \text{Ca}^{2+} + \text{NO}_3^{-}
\][/tex]
- Reactants: 1 Ca, 2 OH, 1 H, 1 NO3
- Products: 1 Ca, 1 NO3
This equation is not balanced. There is only one nitrate ([tex]\( \text{NO}_3^{-} \)[/tex]) ion on the product side, and the hydrogen and hydroxide ions from the reactants are missing in the right proportion.
2. Equation 2:
[tex]\[
\text{Ca(OH)}_2 + 2 \text{HNO}_3 \rightarrow 2 \text{H}_2\text{O} + 2 \text{NO}_3^{-}
\][/tex]
- Reactants: 1 Ca, 2 OH, 2 HNO3 (comprising 2 H and 2 NO3)
- Products: 2 H2O (comprising 4 H and 2 O), and 2 NO3
This equation also does not balance correctly as there are no calcium ions on the product side and the water molecules are overrepresented.
3. Equation 3:
[tex]\[
\text{Ca(OH)}_2 + 2 \text{HNO}_7 \rightarrow \text{H}_2\text{O} + \text{CaNO}_2
\][/tex]
- Reactants: 1 Ca, 2 OH, 2 HNO7 (comprising 2 H, 2 N, and 14 O)
- Products: 1 H2O (comprising 2 H and 1 O), and CaNO2
This equation is incorrect as it involves an incorrect formula ([tex]\(\text{HNO}_7 \)[/tex]). It also fails to balance the number of atoms of each element properly.
4. Equation 4:
[tex]\[
\text{Ca(OH)}_2 + 2 \text{HNO}_3 \rightarrow 2 \text{H}_2\text{O} + \text{Ca}(\text{NO}_3)_2
\][/tex]
- Reactants: 1 Ca, 2 OH, 2 HNO3 (comprising 2 H, 2 N, and 6 O)
- Products: 2 H2O (comprising 4 H and 2 O), 1 Ca(NO3)2 (comprising 1 Ca, 2 N, and 6 O)
This equation is balanced:
- On the left: 1 Ca, 2 OH (2 O and 2 H), 2 HNO3 (2 H, 2 N, and 6 O)
- On the right: 1 Ca, 2 H2O (4 H and 2 O), 1 Ca(NO3)2 (2 N and 6 O)
Therefore, the correctly balanced chemical equation is:
[tex]\[
\boxed{\text{Ca(OH)}_2 + 2 \text{HNO}_3 \rightarrow 2 \text{H}_2\text{O} + \text{Ca}(\text{NO}_3)_2}
\][/tex]
