Predict which of the following reactions would proceed spontaneously at 298 K? [Hint : Refer to Electrochemical series]

Options

A. `Co(s)+ Fe^(2+)(aq) rightarrow Co^(2+) (aq) + Fe(s)`
B. `Cd^(2+) (aq) + Fe(s)rightarrow Cd(s)+ Fe^(2+) (aq)`
C. `Cd(s)Co^(2+)(aq) rightarrow Cd^(2+) (aq) + Co(s))`
D. `Zn^(2+) ((aq))+^H_2rightarrow Zn((s)) + 2H^(+)`

Explanation

To determine which of the given reactions would proceed spontaneously at 298 K, we can use the concept of standard cell potential (E°cell) from the electrochemical series. A reaction is spontaneous if the E°cell is positive.

### Step-by-Step Solution:

1. **Identify the Reactions**:
We need to analyze the given reactions and identify the half-reactions involved in each.

2. **Determine the Half-Reactions**:
For each reaction, identify the oxidation and reduction half-reactions. The oxidation half-reaction will have a negative standard reduction potential, while the reduction half-reaction will have a positive standard reduction potential.

3. **Use the Electrochemical Series**:
Refer to the electrochemical series to find the standard reduction potentials (E°) for the half-reactions involved in each reaction.

4. **Calculate E°cell**:
The standard cell potential can be calculated using the formula:
\[ E°_{cell} = E°_{cathode} - E°_{anode} \]
- Where E°cathode is the reduction potential of the reduction half-reaction.
- E°anode is the reduction potential of the oxidation half-reaction.

5. **Evaluate Spontaneity**:
If E°cell is positive, the reaction is spontaneous. If E°cell is negative, the reaction is non-spontaneous.

6. **Analyze Each Reaction**:
- For each reaction, perform the calculations and determine the E°cell.
- Based on the calculated E°cell values, conclude which reactions are spontaneous.

### Example Analysis:

- **Reaction A**: CO is oxidized and Fe is reduced.
- E°(CO) = -0.28 V (oxidation)
- E°(Fe) = +0.77 V (reduction)
- E°cell = 0.77 - (-0.28) = 0.77 + 0.28 = +1.05 V (spontaneous)

- **Reaction B**: Fe is oxidized.
- E°(Fe) = +0.77 V (oxidation)
- E°(other species) = -0.44 V (reduction)
- E°cell = -0.44 - 0.77 = -1.21 V (non-spontaneous)

- **Reaction C**: Zn is reduced and H2 is oxidized.
- E°(Zn) = -0.76 V (reduction)
- E°(H2) = 0 V (oxidation)
- E°cell = 0 - (-0.76) = +0.76 V (spontaneous)

### Conclusion:
Based on the calculations, the reactions that proceed spontaneously at 298 K are those with positive E°cell values. In this case, reactions A and C are spontaneous.