Write the expressions for equilbrium constant `K_(c)` and `K_(P)` and classify in Homogeneous and Hetereogeneous equilbrium:
(i) `N_(2)O_(4)(g)hArr2NO_(2)(g)`
(ii) `3Fe(S)+4H_(2)O(g)hArrFe_(3)O_(4)(S)+4H_(2)(g)`
(iii) `NH_(4)HS(S)hArrNH_(3)(g)+H_(2)S(g)`
(iv) ` CH_(3)COOH(f)+C_(2)H_(5)OH(f)hArrCH_(3)COOC_(2)H_(5)(f)+H_(2)O(f)`
(V) `MgCO_(3)(S)hArrMgO(S)+CO_(2))g)`
(vi) `2H_(2)S(g)hArr2H_(2)S(g)hArr2H_(2)(g)+S_(2)(g)`
(vii) `SO_(2)(g)+NO_(2)(g)+NO_(2)(g)hArrSO_(3)(g)+NO(g)`
(viii) ` NH_(4)NO_(2)(S)hArrN_(2)(g)+2H_(2)O(f)`

Answer

To solve the problem, we will write the expressions for the equilibrium constants \( K_c \) and \( K_p \) for each reaction and classify them as homogeneous or heterogeneous equilibria.

### Step-by-Step Solution:

**(i) \( N_2O_4(g) \rightleftharpoons 2NO_2(g) \)**
- **Type**: Homogeneous equilibrium (all gases)
- **Expression for \( K_c \)**:
\[ K_c = \frac{[NO_2]^2}{[N_2O_4]} \]
- **Expression for \( K_p \)**:
\[ K_p = \frac{(P_{NO_2})^2}{P_{N_2O_4}} \]

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**(ii) \( 3Fe(s) + 4H_2O(g) \rightleftharpoons Fe_3O_4(s) + 4H_2(g) \)**
- **Type**: Heterogeneous equilibrium (solids and gases)
- **Expression for \( K_c \)**: (solids do not appear in the expression)
\[ K_c = \frac{[H_2]^4}{[H_2O]^4} \]
- **Expression for \( K_p \)**:
\[ K_p = \frac{(P_{H_2})^4}{(P_{H_2O})^4} \]

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**(iii) \( NH_4HS(s) \rightleftharpoons NH_3(g) + H_2S(g) \)**
- **Type**: Heterogeneous equilibrium (solid and gases)
- **Expression for \( K_c \)**:
\[ K_c = [NH_3][H_2S] \]
- **Expression for \( K_p \)**:
\[ K_p = P_{NH_3} \cdot P_{H_2S} \]

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**(iv) \( CH_3COOH(l) + C_2H_5OH(l) \rightleftharpoons CH_3COOC_2H_5(l) + H_2O(l) \)**
- **Type**: Homogeneous equilibrium (all liquids)
- **Expression for \( K_c \)**:
\[ K_c = \frac{[CH_3COOC_2H_5][H_2O]}{[CH_3COOH][C_2H_5OH]} \]
- **Expression for \( K_p \)**: Not applicable, as all components are liquids.

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**(v) \( MgCO_3(s) \rightleftharpoons MgO(s) + CO_2(g) \)**
- **Type**: Heterogeneous equilibrium (solids and gas)
- **Expression for \( K_c \)**:
\[ K_c = [CO_2] \]
- **Expression for \( K_p \)**:
\[ K_p = P_{CO_2} \]

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**(vi) \( 2H_2S(g) \rightleftharpoons 2H_2(g) + S_2(g) \)**
- **Type**: Homogeneous equilibrium (all gases)
- **Expression for \( K_c \)**:
\[ K_c = \frac{[H_2]^2[S_2]}{[H_2S]^2} \]
- **Expression for \( K_p \)**:
\[ K_p = \frac{(P_{H_2})^2 \cdot P_{S_2}}{(P_{H_2S})^2} \]

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**(vii) \( SO_2(g) + 2NO_2(g) \rightleftharpoons SO_3(g) + NO(g) \)**
- **Type**: Homogeneous equilibrium (all gases)
- **Expression for \( K_c \)**:
\[ K_c = \frac{[SO_3][NO]}{[SO_2][NO_2]^2} \]
- **Expression for \( K_p \)**:
\[ K_p = \frac{P_{SO_3} \cdot P_{NO}}{P_{SO_2} \cdot (P_{NO_2})^2} \]

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**(viii) \( NH_4NO_2(s) \rightleftharpoons N_2(g) + 2H_2O(g) \)**
- **Type**: Heterogeneous equilibrium (solid and gases)
- **Expression for \( K_c \)**:
\[ K_c = [N_2][H_2O]^2 \]
- **Expression for \( K_p \)**:
\[ K_p = P_{N_2} \cdot (P_{H_2O})^2 \]