To determine which of the given reactions is a double replacement reaction, let's carefully examine each reaction type.
1. [tex]\( Ca(OH)_2 + H_2SO_4 \rightarrow CaSO_4 + 2H_2O \)[/tex]
In a double replacement reaction, two compounds react, and their cations and anions exchange places, forming two new compounds.
- Reactants: [tex]\( Ca(OH)_2 \)[/tex] and [tex]\( H_2SO_4 \)[/tex]
- Products: [tex]\( CaSO_4 \)[/tex] and [tex]\( 2H_2O \)[/tex]
The cations [tex]\( Ca^{2+} \)[/tex] from [tex]\( Ca(OH)_2 \)[/tex] and [tex]\( H^+ \)[/tex] from [tex]\( H_2SO_4 \)[/tex] switch places with the anions [tex]\( OH^- \)[/tex] and [tex]\( SO_4^{2-} \)[/tex], forming the new compounds [tex]\( CaSO_4 \)[/tex] and [tex]\( H_2O \)[/tex].
This reaction fits the definition of a double replacement reaction.
2. [tex]\( CH_4 + 2O_2 \rightarrow CO_2 + 2H_2O \)[/tex]
This is a combustion reaction, where a hydrocarbon (methane, [tex]\( CH_4 \)[/tex]) reacts with oxygen ([tex]\( O_2 \)[/tex]) to produce carbon dioxide ([tex]\( CO_2 \)[/tex]) and water ([tex]\( H_2O \)[/tex]). There is no exchange of cations and anions between two compounds, so it is not a double replacement reaction.
3. [tex]\( 8Fe + S_8 \rightarrow 8FeS \)[/tex]
This is a synthesis reaction, where iron ([tex]\( Fe \)[/tex]) and sulfur ([tex]\( S_8 \)[/tex]) combine to form iron sulfide ([tex]\( FeS \)[/tex]). There is no exchange of ions between two compounds, so it does not fit the criteria for a double replacement reaction.
4. [tex]\( Zn + H_2SO_4 \rightarrow ZnSO_4 + H_2 \)[/tex]
This is a single replacement (displacement) reaction, where zinc ([tex]\( Zn \)[/tex]) displaces hydrogen from sulfuric acid ([tex]\( H_2SO_4 \)[/tex]) to form zinc sulfate ([tex]\( ZnSO_4 \)[/tex]) and hydrogen gas ([tex]\( H_2 \)[/tex]). Again, there is no exchange of cations and anions between two compounds, so it is not a double replacement reaction.
Based on this analysis, the only double replacement reaction is:
[tex]\[ Ca(OH)_2 + H_2SO_4 \rightarrow CaSO_4 + 2H_2O \][/tex]
So, the answer is [tex]\( 1 \)[/tex].
