Which of the following statements is/are correct about the followig reaction? `Fe_(3)O_(4)overset(Delta)toFe_(2)O_(3)`.

Options

A. The equivalent weight of `Fe_(3)O_(4)` is `M_(1)(M_(1)=` molecular weight of `Fe_(2)O_(4))`
B. The equivalent weight of `Fe_(3)O_(4)` is `(M_(1))/(3)`.
C. The equivalent weight of `Fe_(2)O_(3)` is `(3M_(2))/(2)(M_(2)=` molecular weight of `Fe_(2)O_(3))`.
D. The equivalent weight of `Fe_(2)O_(3)` is `(M_(2))/(2)`.

Explanation

To determine which statements are correct about the reaction \( \text{Fe}_3\text{O}_4 \xrightarrow{\Delta} \text{Fe}_2\text{O}_3 \), we need to analyze the reaction in terms of equivalent weight and valency factor. Here’s a step-by-step breakdown of the solution:

### Step 1: Identify the Reaction
The reaction given is:
\[ \text{Fe}_3\text{O}_4 \xrightarrow{\Delta} \text{Fe}_2\text{O}_3 \]
This indicates that iron(II,III) oxide (\( \text{Fe}_3\text{O}_4 \)) is being converted to iron(III) oxide (\( \text{Fe}_2\text{O}_3 \)) upon heating.

### Step 2: Determine Oxidation States
In \( \text{Fe}_3\text{O}_4 \):
- The oxidation state of Fe can be calculated as follows:
- Let the oxidation state of Fe be \( x \).
- The formula can be represented as \( 3x + 4(-2) = 0 \).
- This gives \( 3x - 8 = 0 \) or \( x = \frac{8}{3} \) (approximately +2.67).

In \( \text{Fe}_2\text{O}_3 \):
- The oxidation state of Fe is +3.

### Step 3: Calculate Change in Oxidation State
- The change in oxidation state for Fe from \( \text{Fe}_3\text{O}_4 \) to \( \text{Fe}_2\text{O}_3 \) is:
- From +2.67 to +3, which is an increase of approximately 0.33 per Fe atom.
- Since there are 3 Fe atoms in \( \text{Fe}_3\text{O}_4 \), the total change in oxidation state is \( 3 \times 0.33 \approx 1 \).

### Step 4: Determine Valency Factor
- The valency factor is defined as the total change in oxidation state per mole of the substance.
- For \( \text{Fe}_3\text{O}_4 \), the valency factor is 1 (as calculated from the change in oxidation state).

### Step 5: Calculate Equivalent Weight
- The equivalent weight can be calculated using the formula:
\[ \text{Equivalent Weight} = \frac{\text{Molecular Weight}}{\text{Valency Factor}} \]

1. **For \( \text{Fe}_3\text{O}_4 \)**:
- Molecular weight of \( \text{Fe}_3\text{O}_4 \) = \( 3 \times 55.85 + 4 \times 16 = 231.55 \, \text{g/mol} \).
- Equivalent weight = \( \frac{231.55}{1} = 231.55 \, \text{g/equiv} \).

2. **For \( \text{Fe}_2\text{O}_3 \)**:
- Molecular weight of \( \text{Fe}_2\text{O}_3 \) = \( 2 \times 55.85 + 3 \times 16 = 159.7 \, \text{g/mol} \).
- Equivalent weight = \( \frac{159.7}{1} = 159.7 \, \text{g/equiv} \).

### Step 6: Analyze the Statements
Based on the calculations:
- The equivalent weight of \( \text{Fe}_3\text{O}_4 \) is \( 231.55 \, \text{g/equiv} \).
- The equivalent weight of \( \text{Fe}_2\text{O}_3 \) is \( 159.7 \, \text{g/equiv} \).

### Conclusion
From the analysis, we conclude that:
- Only the statement regarding the equivalent weight of \( \text{Fe}_3\text{O}_4 \) being equal to its molecular weight divided by 1 is correct.