To identify which equation illustrates a single-replacement reaction, let's first understand what a single-replacement reaction is. A single-replacement reaction, also known as a single-displacement reaction, occurs when one element replaces another element in a compound. The general form of a single-replacement reaction is:
[tex]\[ A + BC \rightarrow AC + B \][/tex]
where [tex]\(A\)[/tex] replaces [tex]\(B\)[/tex] in the compound [tex]\(BC\)[/tex], resulting in the formation of [tex]\(AC\)[/tex] and the release of [tex]\(B\)[/tex].
Now let's analyze each option to determine which one fits this definition:
### Option A:
[tex]\[ CaCl_2 + Na_2CO_3 \rightarrow CaCO_3 + 2 NaCl \][/tex]
In this reaction, calcium chloride ([tex]\(CaCl_2\)[/tex]) and sodium carbonate ([tex]\(Na_2CO_3\)[/tex]) react to form calcium carbonate ([tex]\(CaCO_3\)[/tex]) and sodium chloride ([tex]\(NaCl\)[/tex]). This is a double-replacement reaction, not a single-replacement reaction, because two compounds are reacting and the ions are swapping partners.
### Option B:
[tex]\[ Fe + CuSO_4 \rightarrow Cu + FeSO_4 \][/tex]
In this reaction, iron ([tex]\(Fe\)[/tex]) reacts with copper sulfate ([tex]\(CuSO_4\)[/tex]). The iron replaces copper in the compound, resulting in the formation of copper ([tex]\(Cu\)[/tex]) and iron sulfate ([tex]\(FeSO_4\)[/tex]). Here, an element (iron) is replacing another element (copper) in the compound copper sulfate. This fits the definition of a single-replacement reaction.
### Option C:
[tex]\[ Ba(NO_3)_2 + NiSO_4 \rightarrow BaSO_4 + Ni(NO_3)_2 \][/tex]
In this reaction, barium nitrate ([tex]\(Ba(NO_3)_2\)[/tex]) reacts with nickel sulfate ([tex]\(NiSO_4\)[/tex]) to form barium sulfate ([tex]\(BaSO_4\)[/tex]) and nickel nitrate ([tex]\(Ni(NO_3)_2\)[/tex]). This reaction involves the exchange of ions and is a double-replacement reaction, not a single-replacement reaction.
### Option D:
[tex]\[ 2 Fe + 3 Br_2 \rightarrow 2 FeBr_3 \][/tex]
In this reaction, iron ([tex]\(Fe\)[/tex]) reacts with bromine ([tex]\(Br_2\)[/tex]) to form iron(III) bromide ([tex]\(FeBr_3\)[/tex]). This reaction involves combining elements to form a single compound and does not fit the definition of a single-replacement reaction. It is a synthesis reaction.
Based on the analysis, the reaction that illustrates a single-replacement reaction is:
[tex]\[ B. Fe + CuSO_4 \rightarrow Cu + FeSO_4 \][/tex]
So, the correct answer is:
B. [tex]\( Fe + CuSO_4 \rightarrow Cu + FeSO_4 \)[/tex]
