Concept:The coefficients in a balanced chemical equation dictate the stoichiometric ratio of moles needed for reactants to form products.
Formula:$$ \frac{\text{Moles of N}_2}{\text{Coefficient of N}_2} = \frac{\text{Moles of NH}_3}{\text{Coefficient of NH}_3} $$
Solution:- Analyze the balanced Haber process equation: \( \text{N}_2 + 3\text{H}_2 \rightleftharpoons 2\text{NH}_3 \).
- This explicitly shows a ratio: 1 mole of Nitrogen (\( \text{N}_2 \)) is required to synthesize exactly 2 moles of Ammonia (\( \text{NH}_3 \)).
- The question asks for the amount of Nitrogen needed to synthesize 4 moles of Ammonia.
- Since the required product amount is doubled (from 2 to 4), the required reactant amount must also be doubled.
- \( 1 \times 2 = 2 \text{ moles of N}_2 \).
Why other options are incorrect:- 4 moles: This assumes an incorrect 1:1 stoichiometric ratio between Nitrogen and Ammonia.
- 3 & 4.5 moles: These values do not align with the strict 1:2 molar proportionality.
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