`Cr_(2)O_(7)^(2-)` is reduced to `Cr^(3+)` by `Fe^(2+)` . Identify the correct statement from the following `:`

Options

A. 6 moles of `Fe^(2+)` are oxidised to `Fe^(3+)` ions
B. The solution becomes yellow
C. The solution becomes green
D. 3 moles of `Fe^(2+)` get oxidised to `Fe^(3+)`

Answer

To solve the problem of how `Cr_(2)O_(7)^(2-)` is reduced to `Cr^(3+)` by `Fe^(2+)`, we will break down the process into steps, identifying the oxidation and reduction reactions, and then determining the correct statements based on the stoichiometry of the reaction.

### Step 1: Identify the oxidation states
- In `Cr_(2)O_(7)^(2-)`, the oxidation state of chromium (Cr) can be calculated as follows:
- Let the oxidation state of Cr be \( x \).
- The total charge of the compound is -2.
- There are 7 oxygen atoms, each with an oxidation state of -2.

The equation can be set up as:
\[ 2x + 7(-2) = -2 \]
Simplifying this gives:
\[ 2x - 14 = -2 \implies 2x = 12 \implies x = +6 \]
- Therefore, the oxidation state of Cr in `Cr_(2)O_(7)^(2-)` is +6.

### Step 2: Determine the reduction process
- In the reaction, `Cr_(2)O_(7)^(2-)` is reduced to `Cr^(3+)`, which has an oxidation state of +3.
- The change in oxidation state for each chromium atom is:
\[ +6 \text{ (in Cr}_2\text{O}_7^{2-}) \rightarrow +3 \text{ (in Cr}^{3+}) \]
- The change in oxidation state for 2 chromium atoms is:
\[ 2 \times (6 - 3) = 6 \text{ electrons gained} \]

### Step 3: Identify the oxidation process
- The ferrous ion `Fe^(2+)` is oxidized to `Fe^(3+)`.
- The change in oxidation state for iron is:
\[ +2 \text{ (in Fe}^{2+}) \rightarrow +3 \text{ (in Fe}^{3+}) \]
- This involves the loss of 1 electron per Fe atom.

### Step 4: Balance the half-reactions
- For the reduction half-reaction:
\[ Cr_2O_7^{2-} + 14H^+ + 6e^- \rightarrow 2Cr^{3+} + 7H_2O \]
- For the oxidation half-reaction:
\[ 6Fe^{2+} \rightarrow 6Fe^{3+} + 6e^- \]

### Step 5: Combine the half-reactions
- Adding both half-reactions gives:
\[ Cr_2O_7^{2-} + 14H^+ + 6Fe^{2+} \rightarrow 2Cr^{3+} + 7H_2O + 6Fe^{3+} \]

### Step 6: Final observations
- From the balanced equation, we can see that 6 moles of `Fe^(2+)` are oxidized to `Fe^(3+)`.
- The color of the solution changes from red-orange (due to `Cr_(2)O_(7)^(2-)`) to green (due to `Cr^(3+)`).

### Conclusion
The correct statements based on the reaction are:
1. 6 moles of `Fe^(2+)` are oxidized to `Fe^(3+)`.
2. The color of the solution changes from red-orange to green.