1.0 mole of Fe reacts completely with 0.65 mole of `O_(2)` to give a mixture of only FeO and `Fe_(2)O_(3)` the mole ratio of ferrous oxide to ferric oxide is

Options

A. `2:2`
B. `4:3`
C. `1:2`
D. `2:7`

Explanation

To solve the problem of determining the mole ratio of ferrous oxide (FeO) to ferric oxide (Fe2O3) produced when 1 mole of Fe reacts with 0.65 mole of O2, we can follow these steps:

### Step-by-Step Solution:

1. **Write the Balanced Chemical Equations**:
- The formation of ferrous oxide (FeO):
\[ 4Fe + O_2 \rightarrow 4FeO \]
- The formation of ferric oxide (Fe2O3):
\[ 4Fe + 3O_2 \rightarrow 2Fe_2O_3 \]

2. **Define Variables**:
- Let \( A \) be the moles of FeO produced.
- Let \( B \) be the moles of Fe2O3 produced.

3. **Set Up the Equations Based on Moles of Fe**:
- From the equations, we see that:
- For FeO: 4 moles of Fe produce 4 moles of FeO, so \( A \) moles of FeO will require \( \frac{A}{2} \) moles of O2.
- For Fe2O3: 4 moles of Fe produce 2 moles of Fe2O3, so \( B \) moles of Fe2O3 will require \( \frac{3B}{4} \) moles of O2.

4. **Total Moles of Fe**:
- The total moles of Fe used is:
\[ A + B = 1 \quad \text{(since we started with 1 mole of Fe)} \]

5. **Total Moles of O2**:
- The total moles of O2 used is:
\[ \frac{A}{2} + \frac{3B}{4} = 0.65 \]

6. **Substituting B in Terms of A**:
- From \( A + B = 1 \), we can express \( B \) as:
\[ B = 1 - A \]

7. **Substituting B into the O2 Equation**:
- Substitute \( B \) into the O2 equation:
\[ \frac{A}{2} + \frac{3(1 - A)}{4} = 0.65 \]

8. **Simplifying the O2 Equation**:
- Multiply through by 4 to eliminate the fractions:
\[ 2A + 3 - 3A = 2.6 \]
- Combine like terms:
\[ -A + 3 = 2.6 \]
- Solve for \( A \):
\[ -A = 2.6 - 3 \implies -A = -0.4 \implies A = 0.4 \]

9. **Finding B**:
- Substitute \( A \) back into \( B = 1 - A \):
\[ B = 1 - 0.4 = 0.6 \]

10. **Calculating the Moles of FeO and Fe2O3**:
- Moles of FeO = \( A = 0.4 \)
- Moles of Fe2O3 = \( B/2 = 0.6/2 = 0.3 \)

11. **Finding the Mole Ratio**:
- The mole ratio of FeO to Fe2O3 is:
\[ \text{Ratio} = \frac{0.4}{0.3} = \frac{4}{3} \]

### Final Answer:
The mole ratio of ferrous oxide (FeO) to ferric oxide (Fe2O3) is **4:3**.