Sure, let's determine which general equation represents a double-displacement reaction.
A double-displacement reaction, also known as a double replacement reaction, typically occurs when parts of two ionic compounds are exchanged and form two new compounds. The general form of this reaction can be represented as:
[tex]\[ AB + CD \rightarrow AD + CB \][/tex]
Now, let's evaluate each of the given options:
A. [tex]\( A + B \rightarrow AB \)[/tex]
This represents a combination or synthesis reaction where two reactants combine to form a single product. It is not a double-displacement reaction.
B. [tex]\( AB \rightarrow A + B \)[/tex]
This represents a decomposition reaction where a single compound breaks down into two or more simpler substances. It is not a double-displacement reaction.
C. [tex]\( AB + CD \rightarrow AD + CB \)[/tex]
This shows two compounds [tex]\( AB \)[/tex] and [tex]\( CD \)[/tex] reacting to form two new compounds [tex]\( AD \)[/tex] and [tex]\( CB \)[/tex]. This is a classic example of a double-displacement reaction.
D. [tex]\( AB + CD \rightarrow AC + BD \)[/tex]
This represents a hypothetical reaction where the cation of [tex]\( AB \)[/tex] combines with the anion of [tex]\( CD \)[/tex] and vice versa, but this does not accurately represent a common type of reaction in typical double-displacement scenarios.
Based on our analysis, the correct equation that represents a double-displacement reaction is illustrated by:
[tex]\[ AB + CD \rightarrow AD + CB \][/tex]
Therefore, the correct answer is:
C. [tex]\( AB + CD \rightarrow AD + CB \)[/tex]
