To determine the equilibrium constant expression for the given reaction [tex]\( \text{CaCO}_3(s) \longleftrightarrow \text{CaO}(s) + \text{CO}_2(g) \)[/tex], we need to follow the principles of chemical equilibria.
1. Identify Phases: In the equation, calcium carbonate (CaCO[tex]\(_3\)[/tex]) and calcium oxide (CaO) are solids, and carbon dioxide (CO[tex]\(_2\)[/tex]) is a gas.
2. Role of Solids in Equilibrium Expression: In equilibrium expressions, concentrations of pure solids and pure liquids are considered to be constant because their concentrations do not change as the reaction proceeds. Therefore, we omit solids and pure liquids from the equilibrium constant expression.
3. Equilibrium Expression: Since we only include gaseous and aqueous species in the equilibrium constant expression, we focus on carbon dioxide (CO[tex]\(_2\)[/tex]), which is a gas.
Given that the solids are omitted from the expression, the equilibrium constant [tex]\( K_{eq} \)[/tex] for the reaction will only depend on the concentration (or partial pressure) of the gaseous component.
Thus, for the reaction [tex]\( \text{CaCO}_3(s) \longleftrightarrow \text{CaO}(s) + \text{CO}_2(g) \)[/tex], the equilibrium constant expression is:
[tex]\[ K_{\text{eq}} = [\text{CO}_2] \][/tex]
This reflects the concentration of carbon dioxide in the equilibrium state.
Therefore, the correct equilibrium constant expression is:
[tex]\[ K_{\text{eq}} = [\text{CO}_2] \][/tex]
Hence, the correct answer is:
[tex]\[ K_{\text{eq}} = \left[ \text{CO}_2 \right] \][/tex]
