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`

Explanation

To find the equivalent weight of iron (Fe) in the reaction \(3Fe + 4H_2O \rightarrow Fe_3O_4 + 4H_2\), we will follow these steps:

### Step 1: Understand the Reaction
The reaction involves iron (Fe) reacting with water (H₂O) to form iron(II,III) oxide (Fe₃O₄) and hydrogen gas (H₂).

### Step 2: Determine the Oxidation States
In Fe₃O₄, iron exists in two different oxidation states:
- FeO contributes iron in the +2 oxidation state.
- Fe₂O₃ contributes iron in the +3 oxidation state.

### Step 3: Calculate the Average Oxidation State of Iron in Fe₃O₄
To find the average oxidation state of iron in Fe₃O₄:
- Let \(x\) be the oxidation state of iron.
- The equation for Fe₃O₄ is:
\[ 3x - 8 = 0 \quad (\text{since there are 4 oxygen atoms with a -2 charge each}) \]
- Solving for \(x\):
\[ 3x = 8 \implies x = \frac{8}{3} \]

### Step 4: Determine the n-factor
The n-factor for iron in this reaction is the total change in oxidation state per formula unit of Fe₃O₄. Since iron can change from +2 to +3, we consider both oxidation states:
- For each Fe in +2 state, it can be oxidized to +3, contributing 1 to the n-factor.
- For each Fe in +3 state, it can be reduced to +2, contributing 1 to the n-factor.

Thus, the total n-factor for Fe in Fe₃O₄ is:
\[ n = 2 \text{ (from FeO)} + 1 \text{ (from Fe₂O₃)} = 3 \]

### Step 5: Calculate the Equivalent Weight
The equivalent weight (EW) is calculated using the formula:
\[ \text{Equivalent Weight} = \frac{\text{Atomic Weight}}{n} \]
Given the atomic weight of iron (Fe) is 56, we can substitute:
\[ \text{Equivalent Weight} = \frac{56}{\frac{8}{3}} = 56 \times \frac{3}{8} = 21 \text{ grams} \]

### Final Answer
The equivalent weight of iron in the reaction is **21 grams**.

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