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 find the mole ratio of ferrous oxide (FeO) to ferric oxide (Fe2O3) when 1 mole of iron reacts with 0.65 moles of oxygen, we can follow these steps:

### Step 1: Write the chemical reactions
1. **For FeO formation**:
\[ 2Fe + O_2 \rightarrow 2FeO \]
This indicates that 2 moles of iron react with 1 mole of oxygen to produce 2 moles of FeO.

2. **For Fe2O3 formation**:
\[ 4Fe + 3O_2 \rightarrow 2Fe_2O_3 \]
This indicates that 4 moles of iron react with 3 moles of oxygen to produce 2 moles of Fe2O3.

### Step 2: Define variables for moles of products
Let:
- \( A \) = moles of FeO produced
- \( B \) = moles of Fe2O3 produced

### Step 3: Set up the equations based on the total moles of iron and oxygen
1. From the total moles of iron:
\[ A + B = 1 \quad \text{(since we have 1 mole of Fe)} \]

2. From the total moles of oxygen:
- For FeO: \( \frac{A}{2} \) moles of \( O_2 \) are needed.
- For Fe2O3: \( \frac{3B}{4} \) moles of \( O_2 \) are needed.
\[ \frac{A}{2} + \frac{3B}{4} = 0.65 \quad \text{(since we have 0.65 moles of O2)} \]

### Step 4: Solve the equations
1. Substitute \( B \) from the first equation into the second:
\[ B = 1 - A \]
Substitute into the oxygen equation:
\[ \frac{A}{2} + \frac{3(1 - A)}{4} = 0.65 \]
Simplifying:
\[ \frac{A}{2} + \frac{3}{4} - \frac{3A}{4} = 0.65 \]
Combine like terms:
\[ \frac{2A}{4} - \frac{3A}{4} = 0.65 - 0.75 \]
\[ -\frac{A}{4} = -0.10 \]
Multiply both sides by -4:
\[ A = 0.4 \]

2. Now find \( B \):
\[ B = 1 - A = 1 - 0.4 = 0.6 \]

### Step 5: Calculate the moles of FeO and Fe2O3
- Moles of FeO = \( A = 0.4 \)
- Moles of Fe2O3 = \( \frac{B}{2} = \frac{0.6}{2} = 0.3 \)

### Step 6: Find the mole ratio
The mole ratio of FeO to Fe2O3 is:
\[ \text{Mole Ratio} = \frac{0.4}{0.3} = \frac{4}{3} \]

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

---