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+)` increase
B. `Fe^(3+)` decrease
C. `(Fe^(2+))/(Fe^(3+))` remains unchanged
D. `Fe^(2+)` decrease

Explanation

To solve the problem, we need to analyze the given standard electrode potentials and the reactions involved. Here’s a step-by-step breakdown of the solution:

### Step 1: Identify the Reactions
We have two half-reactions based on the standard electrode potentials provided:

1. **Reduction of Fe²⁺ to Fe:**
\[ \text{Fe}^{2+} + 2e^- \rightarrow \text{Fe} \quad (E^\circ = -0.44 \, \text{V}) \]

2. **Reduction of Fe³⁺ to Fe²⁺:**
\[ \text{Fe}^{3+} + e^- \rightarrow \text{Fe}^{2+} \quad (E^\circ = +0.77 \, \text{V}) \]

### Step 2: Determine the Direction of Reactions
In an electrochemical cell:
- The species with a higher reduction potential will be reduced (gain electrons).
- The species with a lower reduction potential will be oxidized (lose electrons).

Here, Fe³⁺ has a higher reduction potential (+0.77 V) compared to Fe²⁺ (-0.44 V). Therefore, Fe³⁺ will be reduced to Fe²⁺, and Fe will be oxidized to Fe²⁺.

### Step 3: Write the Oxidation Reaction
Since Fe is oxidized, we reverse the first half-reaction:
\[ \text{Fe} \rightarrow \text{Fe}^{2+} + 2e^- \quad (E^\circ = +0.44 \, \text{V}) \]

### Step 4: Combine the Half-Reactions
Now, we can combine the two half-reactions. To balance the electrons, we multiply the second half-reaction by 2:
\[ 2 \, \text{Fe}^{3+} + 2e^- \rightarrow 2 \, \text{Fe}^{2+} \quad (E^\circ = +0.77 \, \text{V}) \]

Now, adding the two reactions:
\[ \text{Fe} + 2 \, \text{Fe}^{3+} \rightarrow 2 \, \text{Fe}^{2+} \]

### Step 5: Analyze the Changes in Concentration
From the combined reaction:
- **Reactants:** 1 Fe and 2 Fe³⁺
- **Products:** 2 Fe²⁺

As the reaction proceeds:
- The concentration of Fe³⁺ decreases because it is being consumed.
- The concentration of Fe²⁺ increases because it is being produced.

### Conclusion
Since Fe³⁺ is being reduced to Fe²⁺, the concentration of Fe³⁺ will decrease over time.

### Final Answer
The correct conclusion is that the concentration of Fe³⁺ decreases.