Mole ratio of Fe in `FeO,Fe_2O_3 and Fe_3O_4` samples of equal weights is

Options

A. `1:2:3`
B. `0.9 : 1: 0.93`
C. `1:0.9:0.93`
D. `3:2:1`

Answer

To find the mole ratio of Fe in the compounds FeO, Fe₂O₃, and Fe₃O₄ when samples of equal weights are taken, we will follow these steps:

### Step 1: Define the mass of the samples
Assume the mass of each compound (FeO, Fe₂O₃, Fe₃O₄) is W grams.

### Step 2: Calculate moles of FeO
- **Molecular weight of FeO**:
- Atomic weight of Fe = 56 g/mol
- Atomic weight of O = 16 g/mol
- Molecular weight of FeO = 56 + 16 = 72 g/mol

- **Moles of FeO**:
\[ \text{Moles of FeO} = \frac{W}{72} \]

- **Moles of Fe in FeO**:
Since 1 mole of FeO contains 1 mole of Fe:
\[ \text{Moles of Fe in FeO} = \frac{W}{72} \]

### Step 3: Calculate moles of Fe₂O₃
- **Molecular weight of Fe₂O₃**:
- Molecular weight = (2 × 56) + (3 × 16) = 112 + 48 = 160 g/mol

- **Moles of Fe₂O₃**:
\[ \text{Moles of Fe₂O₃} = \frac{W}{160} \]

- **Moles of Fe in Fe₂O₃**:
Since 1 mole of Fe₂O₃ contains 2 moles of Fe:
\[ \text{Moles of Fe in Fe₂O₃} = 2 \times \frac{W}{160} = \frac{W}{80} \]

### Step 4: Calculate moles of Fe₃O₄
- **Molecular weight of Fe₃O₄**:
- Molecular weight = (3 × 56) + (4 × 16) = 168 + 64 = 232 g/mol

- **Moles of Fe₃O₄**:
\[ \text{Moles of Fe₃O₄} = \frac{W}{232} \]

- **Moles of Fe in Fe₃O₄**:
Since 1 mole of Fe₃O₄ contains 3 moles of Fe:
\[ \text{Moles of Fe in Fe₃O₄} = 3 \times \frac{W}{232} = \frac{3W}{232} \]

### Step 5: Find the mole ratio of Fe in all three compounds
Now we have:
- Moles of Fe in FeO = \(\frac{W}{72}\)
- Moles of Fe in Fe₂O₃ = \(\frac{W}{80}\)
- Moles of Fe in Fe₃O₄ = \(\frac{3W}{232}\)

To find the ratio, we can express these moles without W:
\[ \text{Ratio} = \frac{1}{72} : \frac{2}{160} : \frac{3}{232} \]

### Step 6: Simplify the ratio
To simplify, we can multiply each term by the least common multiple (LCM) of the denominators (72, 80, and 232). However, for simplicity, we can calculate the ratios directly:
- Convert to a common denominator or simply calculate the values:
- For FeO: \(1\)
- For Fe₂O₃: \(\frac{2}{80} = 0.025\)
- For Fe₃O₄: \(\frac{3}{232} \approx 0.01293\)

### Final Ratio
After simplification, we find the ratio of moles of Fe in FeO, Fe₂O₃, and Fe₃O₄:
\[ \text{Mole Ratio} \approx 1 : 0.025 : 0.01293 \]
This can be approximated to:
\[ 1 : 0.9 : 0.93 \]

### Conclusion
Thus, the mole ratio of Fe in FeO, Fe₂O₃, and Fe₃O₄ is approximately:
\[ \text{Final Ratio} = 1 : 0.9 : 0.93 \]