To determine which two chemical equations represent double-replacement reactions, we need to analyze each equation and understand the characteristics of a double-replacement reaction. In a double-replacement reaction, two compounds exchange ions to form two new compounds. The general form of a double-replacement reaction is:
[tex]\[ AB + CD \rightarrow AD + CB \][/tex]
Let's examine each equation:
Equation A: [tex]\( 2 Na + MgCl_2 \rightarrow 2 NaCl + Mg \)[/tex]
This reaction involves sodium (Na) replacing magnesium (Mg) in magnesium chloride (MgCl₂), forming sodium chloride (NaCl) and elemental magnesium (Mg). This is a single replacement reaction, not a double-replacement reaction.
Equation B: [tex]\( HC_2H_3O_2 + LiOH \rightarrow LiC_2H_3O_2 + H_2O \)[/tex]
This reaction occurs between acetic acid (HC₂H₃O₂) and lithium hydroxide (LiOH) and produces lithium acetate (LiC₂H₃O₂) and water (H₂O). This is a neutralization reaction (acid-base reaction), not a double-replacement reaction.
Equation C: [tex]\( AgNO_3 + LiCl \rightarrow AgCl + LiNO_3 \)[/tex]
Here, silver nitrate (AgNO₃) reacts with lithium chloride (LiCl) to form silver chloride (AgCl) and lithium nitrate (LiNO₃). In this reaction, the anions (NO₃⁻ and Cl⁻) and cations (Ag⁺ and Li⁺) switch places, which is characteristic of a double-replacement reaction.
Equation D: [tex]\( CH_4 + 2 O_2 \rightarrow 2 H_2O + CO_2 \)[/tex]
This reaction involves the combustion of methane (CH₄) in the presence of oxygen (O₂) to produce water (H₂O) and carbon dioxide (CO₂). This is a combustion reaction, not a double-replacement reaction.
Based on the analysis above, the equation that represents a double-replacement reaction is:
C: [tex]\( AgNO_3 + LiCl \rightarrow AgCl + LiNO_3 \)[/tex]
Therefore, the two chemical equations that model double-replacement reactions are represented by the indices (3, 3).
