Sure, let's analyze each of the given chemical reactions to determine which one is a single-replacement reaction.
1. Combustion Reaction:
[tex]\[
\text{A. } CH_4 + 2 O_2 \rightarrow CO_2 + 2 H_2O
\][/tex]
This reaction is a combustion reaction because a hydrocarbon (methane, [tex]\( CH_4 \)[/tex]) reacts with oxygen ([tex]\( O_2 \)[/tex]) producing carbon dioxide ([tex]\( CO_2 \)[/tex]) and water ([tex]\( H_2O \)[/tex]) as products.
2. Combination Reaction:
[tex]\[
\text{B. } H_2 + Cl_2 \rightarrow 2 HCl
\][/tex]
This reaction is a combination (or synthesis) reaction because two reactants ([tex]\( H_2 \)[/tex] and [tex]\( Cl_2 \)[/tex]) combine to form a single product ([tex]\( 2 HCl \)[/tex]).
3. Double-Replacement Reaction:
[tex]\[
\text{C. } CaCl_2 + Na_2CO_3 \rightarrow CaCO_3 + 2 NaCl
\][/tex]
This reaction is a double-replacement reaction because the cations ([tex]\( Ca^{2+} \)[/tex] and [tex]\( Na^+ \)[/tex]) and anions ([tex]\( Cl^- \)[/tex] and [tex]\( CO_3^{2-} \)[/tex]) in the reactants switch places, forming new compounds ([tex]\( CaCO_3 \)[/tex] and [tex]\( 2 NaCl \)[/tex]).
4. Single-Replacement Reaction:
[tex]\[
\text{D. } 2 AgNO_3 + Cu \rightarrow 2 Ag + Cu(NO_3)_2
\][/tex]
This reaction is a single-replacement (or single-displacement) reaction because one element ([tex]\( Cu \)[/tex]) displaces another element ([tex]\( Ag \)[/tex]) in the compound [tex]\( AgNO_3 \)[/tex], forming a new element ([tex]\( 2 Ag \)[/tex]) and a new compound ([tex]\( Cu(NO_3)_2 \)[/tex]).
Based on the above explanations, the single-replacement reaction is:
[tex]\[
\boxed{D. \ 2\ AgNO_3\ +\ Cu \rightarrow\ 2\ Ag\ + Cu\left(NO_3\right)_2}
\][/tex]
