In the following reaction:
`3Fe+4H_(2)OrarrFe_(3)O_(4)+4H_(2)`, if the atomic weight of iron is `56`, then its equivalent weight will be

Options

A. 42
B. 21
C. 63
D. 84

Answer

To find the equivalent weight of iron (Fe) in the given reaction, we will follow these steps:

### Step 1: Understand the Reaction
The reaction given is:
\[ 3Fe + 4H_2O \rightarrow Fe_3O_4 + 4H_2 \]
Here, we need to determine the equivalent weight of iron based on its oxidation states in the reactants and products.

### Step 2: Determine the Oxidation States
- In the reactant, elemental iron (Fe) has an oxidation state of 0.
- In the product, \( Fe_3O_4 \), iron exists in two different oxidation states:
- For \( FeO \), the oxidation state of iron is +2.
- For \( Fe_2O_3 \), the oxidation state of iron is +3.

### Step 3: Calculate the n-factor
The n-factor is defined as the number of electrons exchanged per atom of the element during the reaction. In this case:
- For the +2 oxidation state:
- Iron goes from 0 to +2, which means it loses 2 electrons.
- For the +3 oxidation state:
- Iron goes from 0 to +3, which means it loses 3 electrons.

### Step 4: Calculate the Equivalent Weight
The equivalent weight (EW) is calculated using the formula:
\[ \text{Equivalent Weight} = \frac{\text{Atomic Weight}}{n} \]

Given that the atomic weight of iron (Fe) is 56:
1. For the +2 oxidation state:
\[ EW_{+2} = \frac{56}{2} = 28 \]
2. For the +3 oxidation state:
\[ EW_{+3} = \frac{56}{3} \approx 18.67 \]

### Step 5: Calculate the Average Equivalent Weight
Since \( Fe_3O_4 \) contains 1 iron in the +2 state and 2 iron in the +3 state, we can calculate the average equivalent weight:
- Total contribution from +2 state: \( 1 \times 28 = 28 \)
- Total contribution from +3 state: \( 2 \times 18.67 \approx 37.34 \)

Now, we sum these contributions:
\[ \text{Total} = 28 + 37.34 = 65.34 \]

Now, divide by the total number of iron atoms (3):
\[ \text{Average Equivalent Weight} = \frac{65.34}{3} \approx 21.78 \]

### Conclusion
Thus, the equivalent weight of iron in the given reaction is approximately \( 21.78 \).

---