How many total moles of electrons are transferred when 1 mole of `Cr_(2)O_(7)^(2-)` oxidized `Fe^(2+)` to `Fe^(3+)` in acidic medium?

Explanation

To determine how many total moles of electrons are transferred when 1 mole of \( \text{Cr}_2\text{O}_7^{2-} \) oxidizes \( \text{Fe}^{2+} \) to \( \text{Fe}^{3+} \) in acidic medium, we can follow these steps:

### Step 1: Identify the oxidation states
- The oxidation state of chromium in \( \text{Cr}_2\text{O}_7^{2-} \) can be calculated as follows:
\[ 2x + 7(-2) = -2 \implies 2x - 14 = -2 \implies 2x = 12 \implies x = +6 \]
So, the oxidation state of chromium in \( \text{Cr}_2\text{O}_7^{2-} \) is +6.

- The oxidation state of iron in \( \text{Fe}^{2+} \) is +2, and in \( \text{Fe}^{3+} \) it is +3.

### Step 2: Determine the change in oxidation states
- Chromium changes from +6 in \( \text{Cr}_2\text{O}_7^{2-} \) to +3 in \( \text{Cr}^{3+} \). The change in oxidation state is:
\[ +6 \text{ to } +3 \implies 3 \text{ electrons are gained per chromium atom.} \]

- For iron, the change is from +2 to +3, which means:
\[ +2 \text{ to } +3 \implies 1 \text{ electron is lost per iron atom.} \]

### Step 3: Balance the reaction
- Since there are 2 chromium atoms in \( \text{Cr}_2\text{O}_7^{2-} \), the total number of electrons gained by chromium is:
\[ 2 \text{ Cr} \times 3 \text{ electrons} = 6 \text{ electrons.} \]

- To balance the number of electrons lost by iron, we need 6 moles of \( \text{Fe}^{2+} \) to provide the 6 electrons needed for the reduction of \( \text{Cr}_2\text{O}_7^{2-} \):
\[ 6 \text{ Fe}^{2+} \rightarrow 6 \text{ Fe}^{3+} + 6 \text{ electrons.} \]

### Step 4: Write the balanced half-reaction
- The overall balanced half-reaction in acidic medium can be written as:
\[ \text{Cr}_2\text{O}_7^{2-} + 6 \text{Fe}^{2+} + 14 \text{H}^+ \rightarrow 2 \text{Cr}^{3+} + 6 \text{Fe}^{3+} + 7 \text{H}_2\text{O} \]

### Conclusion
- From the balanced reaction, we see that a total of 6 moles of electrons are transferred when 1 mole of \( \text{Cr}_2\text{O}_7^{2-} \) oxidizes \( \text{Fe}^{2+} \) to \( \text{Fe}^{3+} \).

Thus, the answer is **6 moles of electrons**.

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