An iron nail rusts when exposed to oxygen. For the following reaction, 0.383 moles of iron are mixed with 0.502 moles of oxygen gas. What is the formula for the limiting reactant?
The correct answer and explanation is:
Correct Answer: O₂ (oxygen gas) is the limiting reactant
Explanation (300 words):
When iron (Fe) rusts, it reacts with oxygen (O₂) to form iron(III) oxide (Fe₂O₃), commonly known as rust. The balanced chemical equation for this reaction is: 4Fe+3O2→2Fe2O34Fe + 3O_2 \rightarrow 2Fe_2O_3
This tells us the mole ratio of Fe to O₂ is 4:3. That means 4 moles of iron react with 3 moles of oxygen gas.
We are given:
- 0.383 moles of Fe
- 0.502 moles of O₂
To determine the limiting reactant, we compare how much oxygen is needed to fully react with the given amount of iron.
Step 1: How much O₂ is needed to react with 0.383 mol of Fe?
Use the mole ratio from the balanced equation: O2 needed=34×0.383=0.28725 mol\text{O}_2 \text{ needed} = \frac{3}{4} \times 0.383 = 0.28725 \text{ mol}
So, only 0.287 mol of O₂ is needed to fully react with 0.383 mol of Fe. But we have 0.502 mol of O₂ available, which is more than enough.
So iron is not the limiting reactant.
Step 2: How much Fe is needed to react with 0.502 mol of O₂?
Fe needed=43×0.502=0.6693 mol\text{Fe needed} = \frac{4}{3} \times 0.502 = 0.6693 \text{ mol}
But we only have 0.383 mol of Fe, which is less than required. So Fe runs out first if we try to use up all the oxygen.
Oops! That means our earlier conclusion is incorrect. Let’s correct it:
✅ Correct Limiting Reactant: Iron (Fe)
Iron is the limiting reactant because you need 0.669 mol of Fe to react with all the oxygen, but you only have 0.383 mol.
Thus, Fe is the limiting reactant, not O₂.