Equilibrium constant Kp for following reaction:
`MgCO_(3) (s) hArr MgO(s) + CO_(2) (g)`

Options

A. `K_p=P_(CO_2)`
B. `K_p=P_(CO_2) xx (P_(CO_2)xxP_(MgO))/(P_(MgCO_3))`
C. `K_p=(P_(CO_2)xxP_(MgO))/(P_(MgCO_3))`
D. `K_p=(P_(MgCO_3))/(P_(CO_2)xxP_(Mgo))`

Answer

To determine the equilibrium constant \( K_p \) for the reaction:

\[ \text{MgCO}_3 (s) \rightleftharpoons \text{MgO} (s) + \text{CO}_2 (g) \]

we follow these steps:

### Step 1: Identify the components of the reaction
In this reaction, we have:
- Reactant: Magnesium carbonate (\( \text{MgCO}_3 \)) in solid form
- Products: Magnesium oxide (\( \text{MgO} \)) in solid form and carbon dioxide (\( \text{CO}_2 \)) in gaseous form

### Step 2: Write the expression for \( K_p \)
The general expression for the equilibrium constant \( K_p \) is given by:

\[ K_p = \frac{(P_{\text{products}})^{\text{stoichiometry}}}{(P_{\text{reactants}})^{\text{stoichiometry}}} \]

### Step 3: Consider only gaseous components
Since \( K_p \) only includes gases, we will only consider the gaseous product \( \text{CO}_2 \) and ignore the solids \( \text{MgCO}_3 \) and \( \text{MgO} \) because their concentrations do not change during the reaction and do not affect the equilibrium constant.

### Step 4: Write the \( K_p \) expression for the reaction
Given that \( \text{MgO} \) and \( \text{MgCO}_3 \) are solids, we can simplify the expression:

\[ K_p = \frac{(P_{\text{CO}_2})^1}{(1)} = P_{\text{CO}_2} \]

### Step 5: Conclusion
Thus, the equilibrium constant \( K_p \) for the reaction is:

\[ K_p = P_{\text{CO}_2} \]

### Final Answer
The value of \( K_p \) for the reaction is equal to the partial pressure of carbon dioxide (\( P_{\text{CO}_2} \)).

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