Which of the following is an example of homogeneous equilibrium ?

Options

A. (a) `2SO_(2(g))+O_(2(g))hArr2SO_(3(g))`
B. (b) `C_((s))+H_(2)O_((g))hArrCO_((g))+H_(2(g))`
C. (c) `CaCO_(3(s))hArrCaO_((s))+CO_(2(g))`
D. (d) `NH_(4)NS_((s))hArrNH_(3(g))+H_(2)S_((g))`

Answer

To determine which of the given options is an example of homogeneous equilibrium, we need to understand the concept of homogeneous and heterogeneous equilibria.

### Step-by-Step Solution:

1. **Define Homogeneous Equilibrium**:
- Homogeneous equilibrium occurs when all reactants and products are in the same phase (state), either all gases, all liquids, or all solids.

2. **Define Heterogeneous Equilibrium**:
- Heterogeneous equilibrium occurs when reactants and products are in different phases. For example, a reaction involving solids and gases or liquids and gases.

3. **Analyze the Options**:
- **Option 1**: \(2SO_2(g) + O_2(g) \rightleftharpoons 2SO_3(g)\)
- All species (reactants and products) are gases. This is an example of homogeneous equilibrium.
- **Option 2**: \(C(s) + H_2O(g) \rightleftharpoons CO(g) + H_2(g)\)
- Here, carbon is a solid, while water, carbon monoxide, and hydrogen are gases. This is an example of heterogeneous equilibrium.
- **Option 3**: \(CaCO_3(s) \rightleftharpoons CaO(s) + CO_2(g)\)
- Calcium carbonate and calcium oxide are solids, while carbon dioxide is a gas. This is also an example of heterogeneous equilibrium.
- **Option 4**: \(NH_4NS(s) \rightleftharpoons NH_3(g) + H_2S(g)\)
- Ammonium thiocyanate is a solid, while ammonia and hydrogen sulfide are gases. This is again an example of heterogeneous equilibrium.

4. **Conclusion**:
- The only option that represents homogeneous equilibrium is **Option 1**: \(2SO_2(g) + O_2(g) \rightleftharpoons 2SO_3(g)\).

### Final Answer:
The correct option is **Option 1: \(2SO_2(g) + O_2(g) \rightleftharpoons 2SO_3(g)\)**.