The limiting reagent for a given reaction can be recognized because it is the reagent that

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First, restating the question helps frame the problem: The limiting reagent for a given reaction can be recognized because it is the reagent that
Option 1: has the smallest coefficient in the balanced equation for the reaction. This is a common misconception; the coefficient in a balanced equation reflects the stoichiometric ratio, not which reagent runs out first. The actual limiting reagent depends on the amounts of reactants present, not the coefficients alone.
Option 2: has the smallest mass in the reaction mixture. Mass alone is not the determinant of limiting reagent, because a substance with small mass could still be present in excess if its molar quantity relative to its required amount is sufficient; conversely a larger mass of another reactant could be limiting if its molar amount is too small. Therefore, mass is not a reliable indicator by itself.
Option 3: is present in the smallest molar quantity. While the limiting reagent must be capable of limiting the reaction due to insufficient amount, simply being the smallest quantity in moles is not enough, because you must compare to the stoichiometric needs of the reaction. A smaller amount of a reactant with a large coefficient could still be less limiting than a reactant present in the required stoichiometric proportion in a larger amount. This option captures part of the idea but is not a complete criterion by itself.
Option 4: would be used up first. This option correctly identifies that the limiting reagent is the one that is consumed completely first during the reaction, thus preventing the reaction from continuing because there is no more of this reactant to sustain the stoichiometric proportions. This is the standard chemical definition of the limiting reagent.
In summary, options 1, 2, and 3 each misstate a criterion or fail to capture the full condition for a reagent to be limiting, whereas option 4 directly expresses the defining property of the limiting reagent: it would be used up first, stopping the reaction once it is exhausted.

The limiting reagent for a given reaction can be recognized because it is the reagent that

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