Consider the following generic reaction: $$ \mathrm{Y}_{2}+2 \mathrm{XY} \longrightarrow 2 \mathrm{XY}_{2} $$ In a limiting reactant problem, a certain quantity of each reactant is given and you are usually asked to calculate the mass of product formed. If \(10.0 \mathrm{~g}\) of \(\mathrm{Y}_{2}\) is reacted with \(10.0 \mathrm{~g}\) of \(\mathrm{XY}\), outline two methods you could use to determine which reactant is limiting (runs out first) and thus determines the mass of product formed.

1. Calculate the number of moles of each reactant using their given masses and molecular weights: \(\text{moles of Y}_2 = \frac{\text{mass of Y}_2}{\text{molecular weight of Y}_2}\) \(\text{moles of XY} = \frac{\text{mass of XY}}{\text{molecular weight of XY}}\) 2. Determine the mole ratio between the two reactants according to the balanced equation. In this case, the mole ratio of Y₂ to XY is 1:2. 3. Divide the calculated moles of each reactant by their corresponding mole ratio: \(\text{Ratio of Y}_2 = \frac{\text{moles of Y}_2}{1}\) \(\text{Ratio of XY} = \frac{\text{moles of XY}}{2}\) 4. Compare the calculated mole ratios. The reactant with the lowest mole ratio is the limiting reactant. 5. Use the limiting reactant and the stoichiometry of the reaction to calculate the mass of the product (XY₂) formed: \(\text{moles of XY}_{2} = \text{moles of limiting reactant}\) \(\text{mass of XY}_{2} = \text{moles of XY}_{2} \times \text{molecular weight of XY}_{2}\)

1. Assume each reactant is the limiting reactant separately and calculate the corresponding theoretical yields (masses of the product) from each. This means disregarding the other reactant’s mass momentarily and considering only the given mass of the reactant under consideration. 2. When Y₂ is assumed as the limiting reactant: \(\text{moles of Y}_{2} = \frac{\text{mass of Y}_{2}}{\text{molecular weight of Y}_{2}\) Calculate moles of XY₂ formed: \(\text{moles of XY}_{2} = \text{moles of Y}_{2}\) Calculate mass of XY₂ formed: \(\text{mass of XY}_{2} = \text{moles of XY}_{2} \times \text{molecular weight of XY}_{2}\) 3. When XY is assumed as the limiting reactant: \(\text{moles of XY} = \frac{\text{mass of XY}}{\text{molecular weight of XY}}\) Calculate moles of XY₂ formed: \(\text{moles of XY}_{2} = \frac{1}{2} \times \text{moles of XY}\) Calculate mass of XY₂ formed: \(\text{mass of XY}_{2} = \text{moles of XY}_{2} \times \text{molecular weight of XY}_{2}\) 4. The reactant that yields the least amount of product mass (XY₂) when assumed as the limiting reactant is the actual limiting reactant. The corresponding mass of product formed is the actual mass of product formed in this scenario.