How many of the following reactions are homogenous equilibrium reactions?
(1) `CH_(3)COOH(l)+C_(2)H_(5)OH(l)hArrCH_(3)COOC_(2)H_(5)(l)+H_(2)O(l)`
(2) `C(s)+CO_(2)(g)hArrCO(g)+H_(2)O(g)`
(3) `H_(2)(g)+CO_(2)(g)hArrCO(g)+H_(2)O(g)`
(4) `CO(g)+CI_(2)(g)hArrCOCI_(2)(g)`
(5) `NH_(4)HS_((s))hArrNH_(3)(g)+H_(2)S(g)`
(6) `CaCO_(3)(s)hArrCaO(s)+CO_(2)(s)`
(7) `N_(2)(g)+O_(2)(g)hArr2NO(g)`
(8) `CO_(2)(g)+C(s)hArr2CO(g)`
(9) `SO_(2)(g)+NO_(2)(g)hArrSO_(3)(g)+NO(g)`
(10) `NO(g)+(1)/(2)Br_(2)(l)hArr2NOBr(g)`

Answer

To determine how many of the given reactions are homogeneous equilibrium reactions, we need to analyze each reaction based on the definition of homogeneous equilibrium. A homogeneous equilibrium reaction is one where all reactants and products are in the same phase (all gases, all liquids, or all solids).

Let's analyze each reaction step by step:

1. **Reaction 1: `CH₃COOH(l) + C₂H₅OH(l) ⇌ CH₃COOC₂H₅(l) + H₂O(l)`**
- All reactants and products are in the liquid phase.
- **Conclusion:** This is a homogeneous equilibrium reaction. (Yes)

2. **Reaction 2: `C(s) + CO₂(g) ⇌ CO(g) + H₂O(g)`**
- Reactant is solid (C) and products are gases (CO and H₂O).
- **Conclusion:** This is not a homogeneous equilibrium reaction. (No)

3. **Reaction 3: `H₂(g) + CO₂(g) ⇌ CO(g) + H₂O(g)`**
- All reactants and products are in the gaseous phase.
- **Conclusion:** This is a homogeneous equilibrium reaction. (Yes)

4. **Reaction 4: `CO(g) + Cl₂(g) ⇌ COCl₂(g)`**
- All reactants and products are in the gaseous phase.
- **Conclusion:** This is a homogeneous equilibrium reaction. (Yes)

5. **Reaction 5: `NH₄HS(s) ⇌ NH₃(g) + H₂S(g)`**
- Reactant is solid (NH₄HS) and products are gases (NH₃ and H₂S).
- **Conclusion:** This is not a homogeneous equilibrium reaction. (No)

6. **Reaction 6: `CaCO₃(s) ⇌ CaO(s) + CO₂(g)`**
- Reactants are solid (CaCO₃, CaO) and product is gas (CO₂).
- **Conclusion:** This is not a homogeneous equilibrium reaction. (No)

7. **Reaction 7: `N₂(g) + O₂(g) ⇌ 2NO(g)`**
- All reactants and products are in the gaseous phase.
- **Conclusion:** This is a homogeneous equilibrium reaction. (Yes)

8. **Reaction 8: `CO₂(g) + C(s) ⇌ 2CO(g)`**
- Reactant is gas (CO₂) and product is solid (C) and gas (CO).
- **Conclusion:** This is not a homogeneous equilibrium reaction. (No)

9. **Reaction 9: `SO₂(g) + NO₂(g) ⇌ SO₃(g) + NO(g)`**
- All reactants and products are in the gaseous phase.
- **Conclusion:** This is a homogeneous equilibrium reaction. (Yes)

10. **Reaction 10: `NO(g) + (1/2)Br₂(l) ⇌ 2NOBr(g)`**
- Reactant is liquid (Br₂) and products are gases (NOBr).
- **Conclusion:** This is not a homogeneous equilibrium reaction. (No)

Now, let's summarize the results:
- Homogeneous equilibrium reactions: 1, 3, 4, 7, 9
- Total homogeneous equilibrium reactions = 5

**Final Answer:** There are 5 homogeneous equilibrium reactions.