To determine the correct formula equation that corresponds to the word equation "calcium hydroxide + hydrochloric acid [tex]$\rightarrow$[/tex] calcium chloride + water," let's analyze each option provided.
1. Option 1:
[tex]\[
CaCl_2(l) \rightarrow Ca(s) + Cl_2(g)
\][/tex]
This equation represents the decomposition of calcium chloride into calcium and chlorine gas. It does not involve any reactants or products mentioned in the word equation. Thus, it is not the correct match.
2. Option 2:
[tex]\[
CaO(s) + H_2O(l) \rightarrow Ca(OH)_2(aq)
\][/tex]
This equation shows calcium oxide reacting with water to form calcium hydroxide. While it involves calcium hydroxide as a product, it does not match the word equation’s reactants and products correctly. Thus, it is not the correct match.
3. Option 3:
[tex]\[
NaOH(aq) + 2 HCl(aq) \rightarrow NaCl(aq) + 2 H_2O(l)
\][/tex]
This equation represents sodium hydroxide reacting with hydrochloric acid to produce sodium chloride and water. Although it involves hydrochloric acid and water, the other reactants and products (sodium hydroxide and sodium chloride) do not match those in the word equation. Thus, it is not the correct match.
4. Option 4:
[tex]\[
Ca(OH)_2(s) + 2 HCl(l) \rightarrow CaCl_2(aq) + 2 H_2O(l)
\][/tex]
This equation depicts calcium hydroxide reacting with hydrochloric acid to form calcium chloride and water. This matches perfectly with the given word equation:
[tex]\[
\text{calcium hydroxide} + \text{hydrochloric acid} \rightarrow \text{calcium chloride} + \text{water}
\][/tex]
Thus, the corresponding formula equation is:
[tex]\[
Ca(OH)_2(s) + 2 HCl(l) \rightarrow CaCl_2(aq) + 2 H_2O(l)
\][/tex]
Therefore, the correct answer is:
[tex]\[
\boxed{4}
\][/tex]
