To determine the equilibrium constant expression for the reaction:
[tex]$
CaCO_3(s) \leftrightarrow CaO(s) + CO_2(g)
$[/tex]
we need to recall a fundamental concept in chemical equilibrium. The equilibrium constant expression, [tex]\( K_{\text{eq}} \)[/tex], only includes the concentrations of aqueous and gaseous species. Solid and pure liquid species are not included in the expression because their concentrations are constants that do not change during the reaction.
Here are the steps to derive the correct equilibrium constant expression:
1. Identify the phases of each species in the reaction:
- [tex]\( CaCO_3(s) \)[/tex]: Solid
- [tex]\( CaO(s) \)[/tex]: Solid
- [tex]\( CO_2(g) \)[/tex]: Gas
2. Exclude solids from the equilibrium constant expression:
Since solids are not included, we only consider the gaseous species [tex]\( CO_2 \)[/tex].
3. Formulate the equilibrium constant expression:
The equilibrium constant expression will only involve the concentration of the gaseous species [tex]\( CO_2 \)[/tex]. Therefore, the equilibrium constant expression [tex]\( K_{\text{eq}} \)[/tex] is:
[tex]$
K_{\text{eq}} = [CO_2]
$[/tex]
Thus, the correct equilibrium constant expression for the reaction is:
[tex]$
K_{\text{eq}} = \left[ CO_2 \right]
```
This matches the option:
$[/tex]
K_{\text{eq}} = \left[ CO_2 \right]
``
