Question

which represents the correct equilibrium constant expression for the reaction below?
cu(s) + 2ag⁺(aq) ⇌ cu²⁺(aq) + 2ag(s)
○ $k_{eq} = \frac{cuag^+^2}{cu^{2+}ag^2}$
○ $k_{eq} = \frac{cu^{2+}ag^2}{cuag^+^2}$
○ $k_{eq} = \frac{ag^+^2}{cu^{2+}}$
○ $k_{eq} = \frac{cu^{2+}}{ag^+^2}$

Explanation:

Step1: Recall Equilibrium Constant Rules

For a reaction \( aA + bB
ightleftharpoons cC + dD \), the equilibrium constant \( K_{eq}=\frac{[C]^c[D]^d}{[A]^a[B]^b} \), where solids (and pure liquids) are not included in the expression (their concentrations are considered constant, so they are omitted).

Step2: Identify Phases and Exponents

In the reaction \( \text{Cu}(s) + 2\text{Ag}^+(aq)
ightleftharpoons \text{Cu}^{2+}(aq) + 2\text{Ag}(s) \), \( \text{Cu}(s) \) and \( \text{Ag}(s) \) are solids, so they are excluded from the \( K_{eq} \) expression. The coefficients for \( \text{Ag}^+ \) is 2, \( \text{Cu}^{2+} \) is 1. So substituting into the formula, we get \( K_{eq}=\frac{[\text{Cu}^{2+}]^1}{[\text{Ag}^+]^2} \), which simplifies to \( K_{eq} = \frac{[Cu^{2+}]}{[Ag^+]^2} \).

Answer:

\( K_{eq} = \frac{[Cu^{2+}]}{[Ag^+]^2} \)