To determine which of the given options is the correctly balanced chemical equation for the reaction between [tex]\( Ca(OH)_2 \)[/tex] and [tex]\( HNO_3 \)[/tex], we need to follow these steps:
1. Identify the reactants and their products:
- Reactants: [tex]\( Ca(OH)_2 \)[/tex] (Calcium hydroxide) and [tex]\( HNO_3 \)[/tex] (Nitric acid).
- Products: Water [tex]\( H_2O \)[/tex], Calcium nitrate [tex]\( Ca(NO_3)_2 \)[/tex].
2. Determine the molecular formulas for the reactants and their respective products:
- Calcium hydroxide is [tex]\( Ca(OH)_2 \)[/tex].
- Nitric acid is [tex]\( HNO_3 \)[/tex].
- When these react, they produce water [tex]\( H_2O \)[/tex] and calcium nitrate [tex]\( Ca(NO_3)_2 \)[/tex].
3. Write the unbalanced chemical equation:
- [tex]\( Ca(OH)_2 + HNO_3 \rightarrow H_2O + Ca(NO_3)_2 \)[/tex].
4. Balance the chemical equation:
- Balance the numbers of atoms of each element on both sides of the equation.
Let's balance it step-by-step:
1. [tex]\( Ca(OH)_2 \)[/tex] has 1 calcium (Ca), 2 hydroxides (OH).
2. [tex]\( HNO_3 \)[/tex] is a source of hydrogen (H), nitrogen (N), and oxygen (O).
From the products side:
- Calcium nitrate [tex]\( Ca(NO_3)_2 \)[/tex] has 1 calcium (Ca), 2 nitrate groups [tex]\( NO_3 \)[/tex].
- Water [tex]\( H_2O \)[/tex] has 2 hydrogens and 1 oxygen.
The balanced equation should have:
- 1 calcium atom on each side.
- The same number of hydrogen, nitrogen, and oxygen atoms on both sides.
Match the number of [tex]\( NO_3 \)[/tex] groups between reactants and products, which need 2 [tex]\( HNO_3 \)[/tex] molecules:
[tex]\[ Ca(OH)_2 + 2HNO_3 \rightarrow 2H_2O + Ca(NO_3)_2 \][/tex]
This equation is balanced because:
- There is 1 Ca on both sides.
- There are 2 nitrate groups [tex]\( NO_3 \)[/tex] on both sides.
- There are 2 water molecules (each with 2H atoms and 1O atom, totaling 4H and 2O atoms, which balances the 2 hydroxide groups from [tex]\( Ca(OH)_2 \)[/tex]).
Therefore, the correct choice is:
[tex]\[ \boxed{Ca(OH)_2 + 2HNO_3 \rightarrow 2H_2O + Ca(NO_3)_2} \][/tex]
This corresponds to the fourth option: [tex]\( Ca(OH)_2 + 2HNO_3 \rightarrow 2H_2O + Ca(NO_3)_2 \)[/tex].
So, the correct answer is the 4th option.
