Write an expression for `K_(p) and K_(c)` for the following heterogeneous and homogenous equilibrium.
(i) `CaCO_(3)(s) hArr CaO(s) +CO(g)`
(ii) `H_(2)O(l)+CO_(2)(g) hArr H_(2)CO_(3)(aq)`
(iii) `2NH_(3)(g) hArr N_(2)(g) +3H_(2)(g)`
(iv) `2HgO(s) hArr 2Hg (l) +O_(2)(g)`

Answer

To solve the problem of writing expressions for \( K_p \) and \( K_c \) for the given equilibria, we will analyze each reaction step by step.

### (i) Reaction: \( \text{CaCO}_3(s) \rightleftharpoons \text{CaO}(s) + \text{CO}(g) \)

1. **Identify the states of matter**:
- Reactants: \( \text{CaCO}_3 \) (solid)
- Products: \( \text{CaO} \) (solid), \( \text{CO} \) (gas)

2. **Write the expression for \( K_c \)**:
- Since \( K_c \) only includes aqueous and gaseous species, we ignore the solids.
- Therefore, \( K_c = \frac{[\text{CO}]}{1} \) (the concentration of solids is not included).

3. **Write the expression for \( K_p \)**:
- For \( K_p \), we only consider the gaseous species.
- Thus, \( K_p = P_{\text{CO}} \) (the partial pressure of CO).

### Summary for (i):
- \( K_c = [\text{CO}] \)
- \( K_p = P_{\text{CO}} \)

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### (ii) Reaction: \( \text{H}_2\text{O}(l) + \text{CO}_2(g) \rightleftharpoons \text{H}_2\text{CO}_3(aq) \)

1. **Identify the states of matter**:
- Reactants: \( \text{H}_2\text{O} \) (liquid), \( \text{CO}_2 \) (gas)
- Product: \( \text{H}_2\text{CO}_3 \) (aqueous)

2. **Write the expression for \( K_c \)**:
- We include the aqueous species and gaseous species but ignore the liquid.
- Therefore, \( K_c = \frac{[\text{H}_2\text{CO}_3]}{[\text{CO}_2]} \).

3. **Write the expression for \( K_p \)**:
- For \( K_p \), we only consider the gaseous species.
- Thus, \( K_p = \frac{1}{P_{\text{CO}_2}} \) (the partial pressure of CO2).

### Summary for (ii):
- \( K_c = \frac{[\text{H}_2\text{CO}_3]}{[\text{CO}_2]} \)
- \( K_p = \frac{1}{P_{\text{CO}_2}} \)

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### (iii) Reaction: \( 2\text{NH}_3(g) \rightleftharpoons \text{N}_2(g) + 3\text{H}_2(g) \)

1. **Identify the states of matter**:
- All species are in the gaseous state.

2. **Write the expression for \( K_c \)**:
- \( K_c = \frac{[\text{N}_2][\text{H}_2]^3}{[\text{NH}_3]^2} \).

3. **Write the expression for \( K_p \)**:
- \( K_p = \frac{P_{\text{N}_2} \cdot P_{\text{H}_2}^3}{P_{\text{NH}_3}^2} \).

### Summary for (iii):
- \( K_c = \frac{[\text{N}_2][\text{H}_2]^3}{[\text{NH}_3]^2} \)
- \( K_p = \frac{P_{\text{N}_2} \cdot P_{\text{H}_2}^3}{P_{\text{NH}_3}^2} \)

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### (iv) Reaction: \( 2\text{HgO}(s) \rightleftharpoons 2\text{Hg}(l) + \text{O}_2(g) \)

1. **Identify the states of matter**:
- Reactants: \( \text{HgO} \) (solid)
- Products: \( \text{Hg} \) (liquid), \( \text{O}_2 \) (gas)

2. **Write the expression for \( K_c \)**:
- We ignore the solids and liquids.
- Therefore, \( K_c = [\text{O}_2] \).

3. **Write the expression for \( K_p \)**:
- For \( K_p \), we only consider the gaseous species.
- Thus, \( K_p = P_{\text{O}_2} \).

### Summary for (iv):
- \( K_c = [\text{O}_2] \)
- \( K_p = P_{\text{O}_2} \)

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### Final Summary of All Reactions:
1. (i) \( K_c = [\text{CO}] \), \( K_p = P_{\text{CO}} \)
2. (ii) \( K_c = \frac{[\text{H}_2\text{CO}_3]}{[\text{CO}_2]} \), \( K_p = \frac{1}{P_{\text{CO}_2}} \)
3. (iii) \( K_c = \frac{[\text{N}_2][\text{H}_2]^3}{[\text{NH}_3]^2} \), \( K_p = \frac{P_{\text{N}_2} \cdot P_{\text{H}_2}^3}{P_{\text{NH}_3}^2} \)
4. (iv) \( K_c = [\text{O}_2] \), \( K_p = P_{\text{O}_2} \)