How many of these reactions are homogeneously catalyzed ?
(i) `2SO_(2)(g) + O_(2)(g) overset(NO(g))to 2SO_(3)(g)`
(ii) `C_(12)H_(22)O_(11)(aq.) + H_(2)O(l) overset(H_(2)SO_(4)(l))to underset("Glucose")(C_(6)H_(12)O_(6)(aq.)) + underset("Fructose")(C_(6)H_(12)O_(6)(aq.))`
(iii) `2SO_(3)(g) + O_(2)(g) overset(Pt(s))to 2SO_(3)(g)`
(iv) `N_(2)(g) + 3H_(2)(g) overset(Fe(s))to 2NH_(3)(g)`
(v) `4NH_(3)(g) + 5O_(2)(g) overset(Pt(s))to 4NO(g) + 6H_(2)O(g)`
(vi) `CH_(3)COOCH_(3)(l) overset(HCl(l))to CH_(3)COOH(aq)`
(vii) Vegetable oils `(l) + H_(2)(g)overset(Ni(s))to` Vegetable ghee (s).

Answer

To determine how many of the given reactions are homogeneously catalyzed, we need to analyze each reaction based on the phase of the reactants and the catalyst. Homogeneous catalysis occurs when the catalyst and the reactants are in the same phase (either all gases, all liquids, or all solids).

Let's analyze each reaction step by step:

1. **Reaction (i)**: `2SO₂(g) + O₂(g) ⟶ 2SO₃(g) (catalyzed by NO(g))`
- **Phases**: All reactants (SO₂ and O₂) and the catalyst (NO) are in the gaseous phase.
- **Conclusion**: This reaction is homogeneously catalyzed.

2. **Reaction (ii)**: `C₁₂H₂₂O₁₁(aq) + H₂O(l) ⟶ C₆H₁₂O₆(aq) + C₆H₁₂O₆(aq) (catalyzed by H₂SO₄(l))`
- **Phases**: The reactants (sucrose and water) are in aqueous and liquid phases, and the catalyst (H₂SO₄) is also in liquid phase.
- **Conclusion**: This reaction is homogeneously catalyzed.

3. **Reaction (iii)**: `2SO₃(g) + O₂(g) ⟶ 2SO₂(g) (catalyzed by Pt(s))`
- **Phases**: The reactants (SO₃ and O₂) are in gaseous phase, but the catalyst (Pt) is in solid phase.
- **Conclusion**: This reaction is not homogeneously catalyzed.

4. **Reaction (iv)**: `N₂(g) + 3H₂(g) ⟶ 2NH₃(g) (catalyzed by Fe(s))`
- **Phases**: The reactants (N₂ and H₂) are in gaseous phase, but the catalyst (Fe) is in solid phase.
- **Conclusion**: This reaction is not homogeneously catalyzed.

5. **Reaction (v)**: `4NH₃(g) + 5O₂(g) ⟶ 4NO(g) + 6H₂O(g) (catalyzed by Pt(s))`
- **Phases**: The reactants (NH₃ and O₂) are in gaseous phase, but the catalyst (Pt) is in solid phase.
- **Conclusion**: This reaction is not homogeneously catalyzed.

6. **Reaction (vi)**: `CH₃COOCH₃(l) ⟶ CH₃COOH(aq) (catalyzed by HCl(l))`
- **Phases**: The reactant (methyl acetate) is in liquid phase, and the catalyst (HCl) is also in liquid phase.
- **Conclusion**: This reaction is homogeneously catalyzed.

7. **Reaction (vii)**: `Vegetable oils(l) + H₂(g) ⟶ Vegetable ghee(s) (catalyzed by Ni(s))`
- **Phases**: The reactants (vegetable oils) are in liquid phase, but the catalyst (Ni) is in solid phase.
- **Conclusion**: This reaction is not homogeneously catalyzed.

### Summary of Results:
- Homogeneously catalyzed reactions: (i), (ii), and (vi).
- Total number of homogeneously catalyzed reactions: **3**.