The spontaneous redox reaction`//s` among the follow is`//` are
`(a)` `2Fe^(3+)+Fe rarr 3Fe^(++)`
`(b)Hg_(2)^(++) rarr Hg^(++)+Hg`
`(c )` `3AgCl+NO+2H_(2)O rarr 3Ag+3Cl^(-)+NO_(3)^(-)+4H^(+)`
Given that
`E_(Fe(+++)//Fe^(++))^(.)=0.77V" "E_(Fe^(++)//Fe)^(.)=-0.44V`
`E_(Hg^(+-)//Hg)^(.)=0.85V" "E_(Hg^(++)//Hg_(2))^(.)=0.92V`
`E_(AgCl//Ag)^(.)=0.22V " "E_(NO_(3)//NO)^(.)=0.96V`

Options

A. `a`
B. `a,b,c`
C. `a,b`
D. `a,c`

Explanation

To determine which of the given redox reactions are spontaneous, we need to calculate the standard cell potential (E°cell) for each reaction using the provided standard reduction potentials. A reaction is spontaneous if E°cell is positive.

### Step-by-Step Solution:

1. **Identify the Reactions and Their Components:**
- (a) \(2Fe^{3+} + Fe \rightarrow 3Fe^{2+}\)
- (b) \(Hg_2^{2+} \rightarrow Hg^{2+} + Hg\)
- (c) \(3AgCl + NO + 2H_2O \rightarrow 3Ag + 3Cl^{-} + NO_3^{-} + 4H^{+}\)

2. **Standard Reduction Potentials Provided:**
- \(E^{\circ}(Fe^{3+}/Fe^{2+}) = 0.77 \, V\)
- \(E^{\circ}(Fe^{2+}/Fe) = -0.44 \, V\)
- \(E^{\circ}(Hg^{2+}/Hg) = 0.85 \, V\)
- \(E^{\circ}(Hg_2^{2+}/Hg) = 0.92 \, V\)
- \(E^{\circ}(AgCl/Ag) = 0.22 \, V\)
- \(E^{\circ}(NO_3^{-}/NO) = 0.96 \, V\)

3. **Calculate E°cell for Each Reaction:**

**For Reaction (a):**
- Reduction: \(Fe^{3+} + e^{-} \rightarrow Fe^{2+}\) (E° = 0.77 V)
- Oxidation: \(Fe \rightarrow Fe^{2+} + 2e^{-}\) (E° = -0.44 V)
- E°cell = E°cathode - E°anode
- E°cell = \(0.77 - (-0.44) = 0.77 + 0.44 = 1.21 \, V\) (Spontaneous)

**For Reaction (b):**
- Reduction: \(Hg^{2+} + 2e^{-} \rightarrow Hg\) (E° = 0.85 V)
- Oxidation: \(Hg_2^{2+} \rightarrow 2Hg + 2e^{-}\) (E° = -0.92 V)
- E°cell = E°cathode - E°anode
- E°cell = \(0.85 - 0.92 = -0.07 \, V\) (Not Spontaneous)

**For Reaction (c):**
- Reduction: \(Ag^{+} + e^{-} \rightarrow Ag\) (E° = 0.22 V)
- Oxidation: \(NO \rightarrow NO_3^{-} + 2H^{+} + 2e^{-}\) (E° = -0.96 V)
- E°cell = E°cathode - E°anode
- E°cell = \(0.22 - 0.96 = -0.74 \, V\) (Not Spontaneous)

4. **Conclusion:**
- Only Reaction (a) is spontaneous with E°cell = 1.21 V.
- Therefore, the answer is **Option 1: Only A** is a spontaneous reaction.