The equilibrium constant for the given reaction,
` CaCO_(3(g)) rarr CaO_(s) +CO_(2(g)) ` is given by :

Options

A. `K_(c)=([CaO]*[CO_(2)])/([CaCo_(3)])`
B. `K_(c)=([CaO])/([CaCO_(3)])`
C. `K_(c)=[CO_(2)]`
D. `K_(c)=([CaO])/([CO_(2)])`

Answer

To determine the equilibrium constant (K) for the reaction:

\[ \text{CaCO}_3 (g) \rightleftharpoons \text{CaO} (s) + \text{CO}_2 (g) \]

we follow these steps:

### Step 1: Write the balanced chemical equation
The given reaction is already balanced:
\[ \text{CaCO}_3 (g) \rightleftharpoons \text{CaO} (s) + \text{CO}_2 (g) \]

### Step 2: Identify the states of each component
- Calcium carbonate (CaCO₃) is in the gaseous state (g).
- Calcium oxide (CaO) is a solid (s).
- Carbon dioxide (CO₂) is in the gaseous state (g).

### Step 3: Write the expression for the equilibrium constant (K)
The equilibrium constant expression is derived from the concentrations of the products and reactants at equilibrium. For a general reaction:

\[ aA + bB \rightleftharpoons cC + dD \]

The equilibrium constant (K) is expressed as:

\[ K = \frac{[C]^c [D]^d}{[A]^a [B]^b} \]

In our case, since CaO is a solid, its concentration does not appear in the equilibrium expression. Therefore, the expression for K becomes:

\[ K = \frac{[\text{CO}_2]}{[\text{CaCO}_3]} \]

### Step 4: Substitute the states into the expression
Since CaO is a solid, we consider its concentration as 1 (as solids do not affect the equilibrium constant). Thus, we simplify the equilibrium constant expression to:

\[ K = \frac{[\text{CO}_2]}{1 \cdot [\text{CaCO}_3]} \]

### Step 5: Final expression for the equilibrium constant
The final expression for the equilibrium constant (K) for the reaction is:

\[ K = \frac{[\text{CO}_2]}{[\text{CaCO}_3]} \]

### Conclusion
Thus, the equilibrium constant for the reaction is:

\[ K = \frac{[\text{CO}_2]}{[\text{CaCO}_3]} \]