For the reactions `:`
`I: CaCO_(3)(s)hArr CaO(s)+CO_(2)(g),P_(CO_(2))=2 "atm"`
`II: CO_(2)(g)+C(s)hArr 2CO_(g),K=6 "atm"`
Hence, equilibrium constnat, `K_(p)` ( in the same units ) for the reaction
`CaCO_(3)(s)+C(s)hArr CaO(s)+2CO(g)` is

Options

A. 8
B. 4
C. 12
D. 3

Explanation

To solve the problem, we need to find the equilibrium constant \( K_p \) for the reaction:

\[ \text{CaCO}_3(s) + C(s) \rightleftharpoons \text{CaO}(s) + 2\text{CO}(g) \]

using the provided reactions:

1. \( \text{CaCO}_3(s) \rightleftharpoons \text{CaO}(s) + \text{CO}_2(g) \) with \( P_{\text{CO}_2} = 2 \, \text{atm} \)
2. \( \text{CO}_2(g) + C(s) \rightleftharpoons 2\text{CO}(g) \) with \( K = 6 \, \text{atm} \)

### Step 1: Write the equilibrium expression for the first reaction

For the first reaction:

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

The equilibrium constant \( K_1 \) can be expressed as:

\[ K_1 = \frac{P_{\text{CO}_2}}{1} = P_{\text{CO}_2} \]

Since \( P_{\text{CO}_2} = 2 \, \text{atm} \), we have:

\[ K_1 = 2 \, \text{atm} \]

### Step 2: Write the equilibrium expression for the second reaction

For the second reaction:

\[ \text{CO}_2(g) + C(s) \rightleftharpoons 2\text{CO}(g) \]

The equilibrium constant \( K_2 \) is given as:

\[ K_2 = 6 \, \text{atm} \]

### Step 3: Combine the reactions

To find the equilibrium constant for the target reaction, we need to add the first and second reactions.

Rearranging the first reaction gives:

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

Now, adding this to the second reaction:

\[ \text{CaO}(s) + \text{CO}_2(g) + C(s) \rightleftharpoons \text{CaCO}_3(s) + 2\text{CO}(g) \]

When we add these two reactions, the \( \text{CO}_2(g) \) cancels out, leading to:

\[ \text{CaCO}_3(s) + C(s) \rightleftharpoons \text{CaO}(s) + 2\text{CO}(g) \]

### Step 4: Calculate the equilibrium constant for the target reaction

When combining the equilibrium constants, we multiply them:

\[ K_p = K_1 \times K_2 \]

Substituting the values we have:

\[ K_p = 2 \, \text{atm} \times 6 \, \text{atm} = 12 \, \text{atm} \]

### Final Answer

Thus, the equilibrium constant \( K_p \) for the reaction \( \text{CaCO}_3(s) + C(s) \rightleftharpoons \text{CaO}(s) + 2\text{CO}(g) \) is:

\[ \boxed{12 \, \text{atm}} \]