Consider reacting copper(II) sulfate with iron. Two possible reactions can occur, as represented by the following equations. $$\operatorname{copper}(\mathrm{II}) \text { sulfate }(a q)+\mathrm{iron}(s) \longrightarrow (s)+\operatorname{iron}(\mathrm{II}) \text { sulfate }(a q)$$ $$\operatorname{copper}(\mathrm{II}) \text { sulfate }(a q)+\mathrm{iron}(s) \longrightarrow (s)+\text { iron (III) sulfate }(a q) $$ You place 87.7 mL of a 0.500-M solution of copper(II) sulfate in a beaker. You then add 2.00 g of iron filings to the copper(II) sulfate solution. After one of the above reactions occurs, you isolate 2.27 g of copper. Which equation above describes the reaction that occurred? Support your answer

Using the provided copper(II) sulfate solution volume and molarity, we find out the moles of copper(II) sulfate: moles of Copper(II) Sulfate = molarity × volume = 0.500 mol/L × 0.0877 L = 0.04385 mol We also find out the moles of iron using the given mass: moles of Iron = mass / molar mass = 2.00 g / (55.85 g/mol) = 0.03582 mol

We can calculate the moles of copper produced from the given mass of copper: moles of Copper = mass / molar mass = 2.27 g / (63.55 g/mol) = 0.03573 mol

Check if any reaction's stoichiometry can lead to given moles of copper. For both reactions, the balanced equation gives a mole ratio of 1:1:1 for copper(II) sulfate, iron, and copper. For reaction 1: Mole ratio of copper(II) sulfate to iron to copper: \(1 : 1 : 1\) For reaction 2: Mole ratio of copper(II) sulfate to iron to copper: \(1 : 1 : 1\)

For each reaction, find out which reactant is the limiting reactant and determine whether their mole ratios could result in the observed amount of copper. Reaction 1: Since CuSO4 : Fe : Cu or \(1 : 1 : 1\), for each mole of CuSO4 and Fe reacting, we will get 1 mole of Cu. If CuSO4 reacts completely with Fe, we would have 0.03582 moles of Cu while in reality, we obtained 0.03573 moles of Cu which is closer to Iron availability. Reaction 2: Reaction 2 has the same stoichiometry for reactants as Reaction 1. Considering the amount of Cu produced and the given amounts of reactants, this reaction appears incompatible with the given data. So, based on the limiting reactant concept and the observed amount of copper, Reaction 1 is the most likely reaction that occurred: $$\operatorname{copper}(\mathrm{II}) \text { sulfate }(a q)+\mathrm{iron}(s) \longrightarrow (s)+\operatorname{iron}(\mathrm{II}) \text { sulfate }(a q)$$