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The reaction given is:

\[
4 \, \text{Fe} + 3 \, \text{O}_2 \rightarrow 2 \, \text{Fe}_2\text{O}_3
\]

The problem asks how many grams of oxygen gas (O\(_2\)) are needed to produce 0.400 moles of Fe\(_2\)O\(_3\).

### Step 1: Mole ratio from the balanced equation
From the balanced equation, the mole ratio of O\(_2\) to Fe\(_2\)O\(_3\) is:

\[
3 \, \text{moles of O}_2 : 2 \, \text{moles of Fe}_2\text{O}_3
\]

So, for every 2 moles of Fe\(_2\)O\(_3\), 3 moles of O\(_2\) are required.

### Step 2: Determine moles of O\(_2\) needed
We know that 0.400 moles of Fe\(_2\)O\(_3\) are produced. Using the mole ratio, we calculate the moles of O\(_2\) needed:

\[
\text{moles of O}_2 = 0.400 \, \text{mol Fe}_2\text{O}_3 \times \frac{3 \, \text{mol O}_2}{2 \, \text{mol Fe}_2\text{O}_3} = 0.600 \, \text{mol O}_2
\]

### Step 3: Convert moles of O\(_2\) to grams
The molar mass of O\(_2\) is:

\[
\text{molar mass of O}_2 = 2 \times 16.00 \, \text{g/mol} = 32.00 \, \text{g/mol}
\]

Now, we can convert the moles of O\(_2\) to grams:

\[
\text{mass of O}_2 = 0.600 \, \text{mol O}_2 \times 32.00 \, \text{g/mol} = 19.20 \, \text{g}
\]

### Final Answer:
To produce 0.400 moles of Fe\(_2\)O\(_3\), 19.20 grams of O\(_2\) are needed.

Would you like more details or have any questions?

Here are some related questions to consider:
1. How would the result change if 0.800 moles of Fe\(_2\)O\(_3\) were produced?
2. What is the mass of Fe required to react with 0.600 moles of O\(_2\)?
3. How can we experimentally measure the mass of O\(_2\) in a chemical reaction?
4. What role does the stoichiometric ratio play in predicting product yields?
5. How do you determine limiting reactants in chemical reactions?

**Tip:** Always double-check the molar masses of elements and compounds for accuracy in stoichiometric calculations.

How many grams of O2 are needed to produce 0.400 mole Fe2O3 in the following reaction? 4Fe + 3O2 → 2Fe2O3

Solve the stoichiometry problem to determine the grams of O2 needed to produce 0.400 moles of Fe2O3 in the reaction 4Fe + 3O2 → 2Fe2O3. Includes key chemistry concepts like mole ratios, the mole concept, and chemical equation balancing. Perfect for college-level general chemistry students.

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