Intramolecular redox
`(NH_(4))_(2)Cr_(2)O_(7) rarr N_(2) + Cr_(2)O_(3) + 4H_(2)O` Shows a gain and loss of how many electrons

Explanation

To determine the gain and loss of electrons in the reaction:

\[ (NH_4)_2Cr_2O_7 \rightarrow N_2 + Cr_2O_3 + 4H_2O \]

we will follow these steps:

### Step 1: Identify the oxidation states
- In \((NH_4)_2Cr_2O_7\):
- Nitrogen (N) in \(NH_4^+\) has an oxidation state of -3.
- Chromium (Cr) in \(Cr_2O_7^{2-}\) has an oxidation state of +6.
- Oxygen (O) has an oxidation state of -2.

- In the products:
- In \(N_2\), nitrogen has an oxidation state of 0.
- In \(Cr_2O_3\), chromium has an oxidation state of +3.
- In \(H_2O\), oxygen has an oxidation state of -2.

### Step 2: Determine the changes in oxidation states
- For nitrogen:
- From -3 (in \(NH_4^+\)) to 0 (in \(N_2\)):
- Change = 0 - (-3) = +3 (oxidation)

- For chromium:
- From +6 (in \(Cr_2O_7^{2-}\)) to +3 (in \(Cr_2O_3\)):
- Change = +3 - (+6) = -3 (reduction)

### Step 3: Calculate the total gain and loss of electrons
- Each nitrogen atom undergoes a change of +3, and there are 2 nitrogen atoms in \((NH_4)_2Cr_2O_7\):
- Total loss of electrons from nitrogen = 2 × 3 = 6 electrons.

- Each chromium atom undergoes a change of -3, and there are 2 chromium atoms:
- Total gain of electrons from chromium = 2 × 3 = 6 electrons.

### Conclusion
The overall reaction shows a loss of 6 electrons (from nitrogen) and a gain of 6 electrons (from chromium).

**Final Answer:**
- Gain of electrons: 6
- Loss of electrons: 6

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