Standard electrode potentials are
`Fe^(2+)//Fe, E^(@) = -0.44 V`
`Fe^(3+)//Fe^(2+), E^(@) = -0.77 V`
If `Fe^(3+), Fe^(2+)`, and Fe block are kept together, then

Options

A. `Fe^(3+)` increases
B. `Fe^(3+)` decreases
C. `Fe^(2+)//Fe^(3+)` remains uncharged
D. `Fe^(2+)` decreases

Explanation

To solve the problem, we need to analyze the given standard electrode potentials and determine what happens when \(Fe^{3+}\), \(Fe^{2+}\), and solid iron (Fe) are kept together.

### Step 1: Identify the reactions
We have two half-reactions based on the given standard electrode potentials:
1. \(Fe^{2+} + 2e^- \rightarrow Fe\) with \(E^\circ = -0.44 \, V\) (Reduction)
2. \(Fe^{3+} + e^- \rightarrow Fe^{2+}\) with \(E^\circ = -0.77 \, V\) (Reduction)

### Step 2: Determine the direction of the reactions
- The half-reaction with the higher (less negative) standard electrode potential will occur as a reduction (cathode), while the one with the lower (more negative) standard electrode potential will occur as oxidation (anode).
- Here, \(Fe^{2+} + 2e^- \rightarrow Fe\) has a higher potential than \(Fe^{3+} + e^- \rightarrow Fe^{2+}\), so \(Fe^{2+}\) will be reduced to \(Fe\), and \(Fe^{3+}\) will be oxidized to \(Fe^{2+}\).

### Step 3: Write the oxidation reaction
To find the oxidation reaction, we need to reverse the first reaction:
- Oxidation: \(Fe \rightarrow Fe^{2+} + 2e^-\)

### Step 4: Balance the number of electrons
Since the second reaction involves the transfer of one electron, we need to multiply the second reaction by 2 to balance the electrons:
- Reduction: \(2Fe^{3+} + 2e^- \rightarrow 2Fe^{2+}\)

### Step 5: Combine the reactions
Now, we can add the two balanced half-reactions:
1. \(Fe \rightarrow Fe^{2+} + 2e^-\) (Oxidation)
2. \(2Fe^{3+} + 2e^- \rightarrow 2Fe^{2+}\) (Reduction)

Combining these gives:
\[Fe + 2Fe^{3+} \rightarrow 2Fe^{2+}\]

### Step 6: Analyze the results
From the combined reaction, we can see that:
- Solid iron (Fe) is oxidized to \(Fe^{2+}\).
- \(Fe^{3+}\) is reduced to \(Fe^{2+}\).

### Conclusion
When \(Fe^{3+}\), \(Fe^{2+}\), and Fe are kept together:
- \(Fe^{3+}\) will decrease as it is converted to \(Fe^{2+}\).
- \(Fe^{2+}\) will increase as it is formed from the reduction of \(Fe^{3+}\).

### Answer
The correct conclusion is that \(Fe^{3+}\) will decrease, and \(Fe^{2+}\) will increase.

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