To identify which of the given chemical reactions is a double displacement reaction, let's first recall what a double displacement reaction is. In a double displacement reaction, two compounds react, and the cations and anions of the reactants switch places, forming two new compounds. Among the reactions provided, we'll identify the one that fits this description.
Let's analyze each reaction one by one:
1. [tex]\( Ca(OH)_2(s) \rightarrow CaO(s) + H_2O(g) \)[/tex]
- This is a decomposition reaction where [tex]\( Ca(OH)_2 \)[/tex] breaks down into [tex]\( CaO \)[/tex] and [tex]\( H_2O \)[/tex].
2. [tex]\( C_2H_5OH(l) + O_2(g) \rightarrow CO_2(g) + H_2O(g) \)[/tex]
- This is a combustion reaction where ethanol [tex]\( (C_2H_5OH) \)[/tex] reacts with oxygen to produce carbon dioxide and water.
3. [tex]\( Zn(s) + 2HCl(aq) \rightarrow ZnCl_2(aq) + H_2(g) \)[/tex]
- This is a single displacement reaction where zinc displaces hydrogen in hydrochloric acid, forming zinc chloride and hydrogen gas.
4. [tex]\( Pb(NO_3)_2(aq) + 2HCl(aq) \rightarrow 2HNO_3(aq) + PbCl_2(s) \)[/tex]
- This reaction involves the exchange of ions between the two reactants. Lead nitrate ([tex]\( Pb(NO_3)_2 \)[/tex]) reacts with hydrochloric acid ([tex]\( HCl \)[/tex]), where the lead cation ([tex]\( Pb^{2+} \)[/tex]) pairs with the chloride anion ([tex]\( Cl^- \)[/tex]), and the hydrogen cation ([tex]\( H^+ \)[/tex]) pairs with the nitrate anion ([tex]\( NO_3^- \)[/tex]), resulting in the formation of lead chloride ([tex]\( PbCl_2 \)[/tex]) and nitric acid ([tex]\( HNO_3 \)[/tex]). This is characteristic of a double displacement reaction.
Therefore, the reaction that represents a double displacement reaction is:
[tex]\[ \boxed{4} \][/tex]
