To determine which of the given chemical equations is correctly balanced, we need to check each option and ensure that the number of atoms of each element on the reactant side matches the number on the product side. Also, the charges should be balanced.
1. Equation 1:
[tex]\[
\text{Ca(OH)}_2 + \text{HNO}_3 \rightarrow \text{Ca}^{2+}+ \text{NO}_3^-
\][/tex]
This equation is not balanced properly. To verify:
- On the reactant side: 1 Ca, 2 OH, 1 H, and 1 NO3.
- On the product side: 1 Ca, no OH, no H, and 1 NO3.
Clearly, the hydrogen and hydroxide ion counts do not balance.
2. Equation 2:
[tex]\[
\text{Ca(OH)}_2 + 2 \text{HNO}_3 \rightarrow 2 \text{H}_2\text{O} + 2 \text{NO}_3^-
\][/tex]
This equation, while it looks closer, does not produce a calcium nitrate product as expected in an actual reaction.
3. Equation 3:
[tex]\[
\text{Ca(OH)}_2 + 2 \text{HNO}_3 \rightarrow \text{H}_2\text{O} + \text{Ca(NO}_3\text{)}
\][/tex]
This equation is also not balanced because it sugeres a non-existent intermediate product and does not match stoichiometry principles.
4. Equation 4:
[tex]\[
\text{Ca(OH)}_2 + 2 \text{HNO}_3 \rightarrow 2 \text{H}_2\text{O} + \text{Ca(NO}_3\text{)}_2
\][/tex]
Balancing atoms on both sides:
- Reactant side: 1 Ca, 2 OH, 2 H, 2 NO3.
- Product side: 1 Ca, 2 H2O (which is 4 H and 2 O), and 1 Ca(NO3)2 (which includes 1 Ca, 2 NO3).
The number of each type of atom is neatly balanced:
- 1 Ca on each side.
- 2 OH from 2 H2O on the product side matches with the original 2 OH on the reactant.
- 2 H from 2 HNO3 on the reactant side matches the 4 H from the 2 H2O on the product side.
- 2 NO3 from 2 HNO3 reactants matches the 2 NO3 in Ca(NO3)2 on the product side.
Hence, the correctly balanced equation is:
[tex]\[
\text{Ca(OH)}_2 + 2 \text{HNO}_3 \rightarrow 2 \text{H}_2\text{O} + \text{Ca(NO}_3\text{)}_2
\][/tex]
Therefore, the fourth option is correct.
