Question

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

Short answer

The correct reaction is either copper(II) sulfate (aq) + iron (s) → copper (s) + iron(II) sulfate (aq) or copper(II) sulfate (aq) + iron (s) → copper (s) + iron(III) sulfate (aq), as the experimental yield of copper (2.27 g) is very close to the theoretical yield (2.276 g) calculated using the moles of the limiting reactant, iron.

Step-by-step solution

Calculate the moles of copper(II) sulfate and iron

Given the volume and concentration of copper(II) sulfate solution, moles of copper(II) sulfate can be calculated using the formula: Moles of copper(II) sulfate = volume (L) × concentration (M) Given mass of iron and its molar mass, moles of iron can be calculated as: Moles of iron = mass (g) ÷ molar mass (g/mol) First, let's convert volume into liters and calculate moles for both reactants: Volume of copper(II) sulfate solution = \(87.7 ml = \frac{87.7}{1000} L = 0.0877 L\) Moles of copper(II) sulfate = \(0.0877 L \times 0.500 M = 0.04385 mol\) Mass of iron = 2.00 g Molar mass of iron = 55.85 g/mol Moles of iron = \(\frac{2.00 g}{55.85 g/mol} = 0.03581 mol\)

Determine the limiting reactant for each reaction

For both reactions, the equation has a 1:1 stoichiometric ratio. Thus, the limiting reactant is the one with fewer moles. Since \(0.03581 mol < 0.04385 mol\), the limiting reactant is iron.

Calculate the theoretical yield of copper for each reaction

According to stoichiometry, one mole of iron reacts with one mole of copper(II) sulfate and produces one mole of copper in both of the reactions. Using the moles of the limiting reactant (iron) and molar mass of copper, we can calculate the theoretical yield as: Theoretical yield of copper (g) = moles of limiting reactant × molar mass of copper Molar mass of copper = 63.55 g/mol Theoretical yield of copper = \(0.03581 mol \times 63.55 g/mol = 2.276 g\)

Compare the theoretical yield with the experimental yield

The experimental yield is given as 2.27 g of copper. Comparing this with our calculated theoretical yield: Experimental yield = 2.27 g Theoretical yield = 2.276 g Since the experimental yield is very close to the theoretical yield, we can conclude that the reaction occurred as per the given stoichiometry. Therefore, both reactions can be represented as: copper(II) sulfate (aq) + iron (s) → copper (s) + iron(II) sulfate (aq) OR iron(III) sulfate (aq)

Key concepts

Copper(II) Sulfate

Copper(II) sulfate is a chemical compound with the formula CuSO₄. It is widely used in chemistry for various applications, such as in the preparation of catalysts and as a fungicide. In a lab setting, it often appears as a bright blue crystalline solid when anhydrous, or as blue pentahydrate crystals when hydrated, commonly known as blue vitriol. When dissolved in water, copper(II) sulfate dissociates into copper ions (Cu²⁺) and sulfate ions (SO₄²⁻), forming a blue solution. This solution acts as the starting reactant in the reactions we are discussing.

Iron Filings

Iron filings are tiny particles of iron used often in chemical reactions and studies involving magnetism. Composed of pure iron, they have high reactivity with other substances. In our exercise, the iron filings react with the copper(II) sulfate solution. During the reaction, iron (Fe) displaces copper from its salt, demonstrating a single displacement reaction, a subset of redox reactions. Iron, being more reactive than copper, replaces the copper ions in solution, leading to the formation of solid copper and iron sulfate.

Stoichiometry

Stoichiometry is a branch of chemistry that deals with the quantitative relationships between reactants and products in a chemical reaction. It allows us to predict how much product will form from given amounts of reactants. Breaking down stoichiometry makes it easier to solve problems like the one in this exercise. When iron filings react with copper(II) sulfate, we can use the balanced chemical equations to determine the mole ratios of reactants and products. This helps us calculate the number of moles, which in turn allows us to estimate the theoretical amount of copper produced and identify the limiting reactant.

Limiting Reactant

In a chemical reaction, the limiting reactant is the substance that is completely consumed first, stopping the reaction from continuing because there is no more to react with other substances. It dictates the maximum yield of product. In the provided example, after calculating moles of each reactant, iron filings were found to have fewer moles compared to copper(II) sulfate. Thus, iron is the limiting reactant. Knowing the limiting reactant is crucial for calculating the theoretical yield of the product—in this case, copper. This step ensures precise predictions of product formation and helps in determining which reaction equation most closely fits the experimental data.