Which represents the correct equilibrium constant expression for the reaction below?

[tex]\[
Cu (s) + 2 Ag^{+} (aq) \longleftrightarrow Cu^{2+} (aq) + 2 Ag (s)
\][/tex]

A. [tex]\[ K_{eq} = \frac{[Cu]\left[Ag^{+}\right]^2}{\left[Cu^{2+}\right][Ag]^2} \][/tex]

B. [tex]\[ K_{eq} = \frac{\left[Cu^{2+}\right]\left[Ag^2\right]}{[Cu]\left[Ag^{+}\right]^2} \][/tex]

C. [tex]\[ K_{eq} = \frac{\left[Ag^{+}\right]^2}{\left[Cu^{2+}\right]} \][/tex]

D. [tex]\[ K_{eq} = \frac{\left[Cu^{2+}\right]}{\left[Ag^{+}\right]^2} \][/tex]

To find the correct equilibrium constant expression for the given reaction, we need to understand the components involved and how they relate to each other in terms of their states (solid, aqueous).

The reaction given is:
[tex]\[ Cu (s) + 2 Ag^{+}(aq) \longleftrightarrow Cu^{2+}(aq) + 2 Ag (s) \][/tex]

When writing the equilibrium constant expression (Keq), we only include the concentrations of the species in the aqueous phase (aq) or gases. Solids and pure liquids are not included in the expression because their concentrations are constant and do not affect the equilibrium.

For the given reaction:
1. Cu (s) is a solid.
2. 2 Ag^{+} (aq) is an aqueous ion.
3. Cu^{2+} (aq) is an aqueous ion.
4. 2 Ag (s) is a solid.

Given these states, only the aqueous species, [tex]\( Cu^{2+} (aq) \)[/tex] and [tex]\( Ag^{+} (aq) \)[/tex], will be included in the equilibrium constant expression.

The general form for Keq is:
[tex]\[ Keq = \frac{\text{products}}{\text{reactants}} \][/tex]

For our reaction:
- The product side includes [tex]\( Cu^{2+} \)[/tex], an aqueous ion.
- The reactant side includes [tex]\( 2 Ag^{+} \)[/tex], an aqueous ion.

Therefore, the equilibrium constant expression for the reaction is:
[tex]\[ Keq = \frac{[Cu^{2+}]}{[Ag^{+}]^2} \][/tex]

Let's match this expression with the given options:
1. [tex]\( Keq = \frac{[Cu][Ag^{+}]^2}{[Cu^{2+}][Ag]^2} \)[/tex] - This option is incorrect as it includes the concentrations of solids.
2. [tex]\( Keq = \frac{[Cu^{2+}][Ag^2]}{[Cu][Ag^{+}]^2} \)[/tex] - This option is incorrect as it erroneously includes [tex]\( [Ag^2] \)[/tex] and [tex]\( [Cu] \)[/tex], which are not correct forms and include solids.
3. [tex]\( Keq = \frac{[Ag^{+}]^2}{[Cu^{2+}]} \)[/tex] - This option is incorrect as it inverts the correct expression.
4. [tex]\( Keq = \frac{[Cu^{2+}]}{[Ag^{+}]^2} \)[/tex] - This is the correct equilibrium expression.

Thus, the correct representation of the equilibrium constant expression is:
[tex]\[ Keq = \frac{[Cu^{2+}]}{[Ag^{+}]^2} \][/tex]

The answer is the fourth option, which is:
[tex]\[ \boxed{4} \][/tex]