In the reaction `Al + Fe_(3) O_(4) rarr Al_(2) O_(3) + Fe-`
what is the total no. of electrons transferred during the change -

Options

A. 16
B. 24
C. 8
D. 12

Explanation

To determine the total number of electrons transferred in the reaction:

\[ \text{Al} + \text{Fe}_3\text{O}_4 \rightarrow \text{Al}_2\text{O}_3 + \text{Fe} \]

we need to follow these steps:

### Step 1: Balance the Reaction
First, we need to balance the chemical equation.

1. **Identify the number of atoms of each element on both sides:**
- Left: Al = 1, Fe = 3, O = 4
- Right: Al = 2, Fe = 1, O = 3

2. **Balance the oxygen atoms:**
- To balance the oxygen, we can multiply Al₂O₃ by 4 and Fe by 9:
\[ 4 \text{Al} + 3 \text{Fe}_3\text{O}_4 \rightarrow 2 \text{Al}_2\text{O}_3 + 9 \text{Fe} \]

3. **Count atoms again:**
- Left: Al = 4, Fe = 9, O = 12
- Right: Al = 4, Fe = 9, O = 12

The balanced equation is:
\[ 4 \text{Al} + 3 \text{Fe}_3\text{O}_4 \rightarrow 2 \text{Al}_2\text{O}_3 + 9 \text{Fe} \]

### Step 2: Determine Oxidation States
Next, we need to determine the oxidation states of the elements involved in the reaction.

- **Aluminum (Al)**:
- In elemental form (reactant side), Al has an oxidation state of 0.
- In Al₂O₃, Al has an oxidation state of +3.

- **Iron (Fe)**:
- In Fe₃O₄, Fe has an average oxidation state of +8/3 (considering the mixture of FeO and Fe₂O₃).
- In elemental form (product side), Fe has an oxidation state of 0.

### Step 3: Calculate Electrons Transferred
1. **For Aluminum:**
- Each Al atom goes from 0 to +3, losing 3 electrons.
- For 4 Al atoms:
\[ 4 \text{Al} \rightarrow 4 \times 3 = 12 \text{ electrons lost} \]

2. **For Iron:**
- Each Fe atom goes from +8/3 to 0, gaining electrons.
- For 9 Fe atoms:
\[ 9 \text{Fe} \rightarrow 9 \times \left( \frac{8}{3} \right) = 24 \text{ electrons gained} \]

### Step 4: Total Electrons Transferred
The total number of electrons transferred in the reaction is the sum of the electrons lost by aluminum and the electrons gained by iron. Since both values are equal, we can confirm the electron transfer is balanced.

Thus, the total number of electrons transferred is:
\[ \text{Total Electrons} = 24 \text{ electrons} \]

### Final Answer:
The total number of electrons transferred during the change is **24 electrons**.

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