Limiting Reagent In Multi-step Context
Consider the reaction: (\text{Fe}_2\text{O}_3 + 3\text{CO} \rightarrow 2\text{Fe} + 3\text{CO}_2). If 160 g of (\text{Fe}_2\text{O}_3) and 84 g of CO are mixed, what is the maximum mass of iron that can be produced? (Molar masses: (\text{Fe}_2\text{O}_3 = 160) g/mol, CO (= 28) g/mol, Fe (= 56) g/mol)
Select the correct option:
Solution
112 g
Identifying the limiting reagent is the critical first step in any yield calculation. Moles of (\text{Fe}_2\text{O}_3 = 160/160 = 1.0) mol. Moles of CO (= 84/28 = 3.0) mol. From the balanced equation, 1 mol (\text{Fe}_2\text{O}_3) requires 3 mol CO. Available CO (= 3.0) mol, which is exactly the stoichiometric requirement for 1 mol (\text{Fe}_2\text{O}_3). Both reactants are consumed in exact stoichiometric amounts, so neither is in excess. From 1 mol (\text{Fe}_2\text{O}_3), the equation gives 2 mol Fe. Mass of Fe (= 2 \times 56 = 112) g. Option 56 g corresponds to only 1 mol Fe, which would arise from assuming 1:1 stoichiometry instead of 1:2 for (\text{Fe}_2\text{O}_3):(\text{Fe}). Option 168 g would require 3 mol Fe, but the equation yields only 2 mol per mol of (\text{Fe}_2\text{O}_3). Option 224 g would require 4 mol Fe, which would need 2 mol (\text{Fe}_2\text{O}_3), but only 1 mol is available. This is an NCERT-pattern stoichiometry question embedded in an industrially significant context (blast furnace iron extraction) common in JEE. Plausibility check: 112 g of Fe from 160 g of (\text{Fe}_2\text{O}_3) represents (2 \times 56/160 = 70%) yield by mass, consistent with Fe being (2 \times 56/160 \times 100 = 70%) of (\text{Fe}_2\text{O}_3).
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About This Question
- Subject
- chemistry
- Chapter
- some basic concepts in chemistry
- Topic
- limiting reagent in multi-step context
- Difficulty
- Hard
- Year
- 2025
Solution
Correct Answer:
112 g
Identifying the limiting reagent is the critical first step in any yield calculation. Moles of (\text{Fe}_2\text{O}_3 = 160/160 = 1.0) mol. Moles of CO (= 84/28 = 3.0) mol. From the balanced equation, 1 mol (\text{Fe}_2\text{O}_3) requires 3 mol CO. Available CO (= 3.0) mol, which is exactly the stoichiometric requirement for 1 mol (\text{Fe}_2\text{O}_3). Both reactants are consumed in exact stoichiometric amounts, so neither is in excess. From 1 mol (\text{Fe}_2\text{O}_3), the equation gives 2 mol Fe. Mass of Fe (= 2 \times 56 = 112) g. Option 56 g corresponds to only 1 mol Fe, which would arise from assuming 1:1 stoichiometry instead of 1:2 for (\text{Fe}_2\text{O}_3):(\text{Fe}). Option 168 g would require 3 mol Fe, but the equation yields only 2 mol per mol of (\text{Fe}_2\text{O}_3). Option 224 g would require 4 mol Fe, which would need 2 mol (\text{Fe}_2\text{O}_3), but only 1 mol is available. This is an NCERT-pattern stoichiometry question embedded in an industrially significant context (blast furnace iron extraction) common in JEE. Plausibility check: 112 g of Fe from 160 g of (\text{Fe}_2\text{O}_3) represents (2 \times 56/160 = 70%) yield by mass, consistent with Fe being (2 \times 56/160 \times 100 = 70%) of (\text{Fe}_2\text{O}_3).
This hard difficulty chemistry question is from the chapter some basic concepts in chemistry, covering the topic of limiting reagent in multi-step context. It appeared in the 2025 exam.
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