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

Options

A. `Kp = P_(CO_(2))`
B. `Kp = P_(CO_(2)) xx (P_(C_(2)) xx P_(MgO))/(P_(MgCO_(3))`
C. `Kp= (P_(CO_(3)) + P_(MgO))/(P_(MgCO_(3)))`
D. `Kp = (P_(MgCO_(3)))/(P_(CO_(2)) xx P_(MgO))`

Answer

To find 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: Write the expression for the equilibrium constant

The equilibrium constant \( K_p \) is defined in terms of the partial pressures of the gaseous products over the reactants. For the general reaction:

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

the expression for \( K_p \) is given by:

\[ K_p = \frac{(P_C)^c (P_D)^d}{(P_A)^a (P_B)^b} \]

### Step 2: Identify the reactants and products

In our reaction:

- Reactant: \( \text{MgCO}_3 (s) \) (solid)
- Products: \( \text{MgO} (s) \) (solid) and \( \text{CO}_2 (g) \) (gas)

### Step 3: Consider the states of the substances

Since both \( \text{MgCO}_3 \) and \( \text{MgO} \) are solids, they do not appear in the equilibrium expression. The equilibrium expression will only include the gaseous products.

### Step 4: Write the equilibrium expression for this reaction

Thus, the equilibrium constant \( K_p \) for the reaction will only include the gaseous product \( \text{CO}_2 \):

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

### Step 5: Conclusion

Therefore, the equilibrium constant \( K_p \) for the reaction is:

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

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