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 understand some key principles of chemical equilibrium.
1. States of Matter: In equilibrium expressions, only the concentrations of gases and aqueous species are included. Solids and liquids are not included as their concentrations are considered constant.
2. Form of the Equilibrium Constant (K_eq): For a general reaction at equilibrium:
[tex]\[
aA + bB \longleftrightarrow cC + dD
\][/tex]
The equilibrium constant expression is given by:
[tex]\[
K_{\text{eq}} = \frac{[\text{C}]^c [\text{D}]^d}{[\text{A}]^a [\text{B}]^b}
\][/tex]
Here, [tex]\( [\text{C}] \)[/tex], [tex]\( [\text{D}] \)[/tex], [tex]\( [\text{A}] \)[/tex], and [tex]\( [\text{B}] \)[/tex] represent the molar concentrations of the reactants and products.
For the given reaction:
[tex]\[
\text{CaCO}_3(s) \longleftrightarrow \text{CaO}(s) + \text{CO}_2(g)
\][/tex]
- Reactants: [tex]\( \text{CaCO}_3(s) \)[/tex] is a solid.
- Products: [tex]\( \text{CaO}(s) \)[/tex] is a solid, and [tex]\( \text{CO}_2(g) \)[/tex] is a gas.
Following the rule, we do not include the concentrations of solid reactants or products in the equilibrium expression. Therefore, the equilibrium expression will only involve the gaseous component, which is [tex]\( \text{CO}_2 \)[/tex].
Thus, the equilibrium constant expression is:
[tex]\[
K_{\text{eq}} = [\text{CO}_2]
\][/tex]
Therefore, the correct answer is:
[tex]\[
K_{\text{eq}} = \left[ \text{CO}_2 \right]
\][/tex]
