Question

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

Short answer

The reaction that best fits the provided data is: $$\operatorname{copper}(\mathrm{II}) \text { sulfate }(a q)+\mathrm{iron}(s) \longrightarrow (s)+\operatorname{iron}(\mathrm{II}) \text { sulfate }(a q)$$ This conclusion is based on the stoichiometry, limiting reactant concept, and the observed amount of copper, indicating that reaction 1 is the most likely reaction to have occurred.

Step-by-step solution

Calculate the moles of copper(II) sulfate and iron

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

Determine the moles of copper produced

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

Calculate the mole ratios for each reaction

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: \(1 : 1 : 1\)

Deciding the correct reaction

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: $$\operatorname{copper}(\mathrm{II}) \text { sulfate }(a q)+\mathrm{iron}(s) \longrightarrow (s)+\operatorname{iron}(\mathrm{II}) \text { sulfate }(a q)$$

Key concepts

Copper(II) Sulfate

Copper(II) sulfate, often abbreviated as CuSO extsubscript{4}, is a widely used chemical compound in various fields, including chemistry labs and industrial applications. In this exercise, Copper(II) sulfate plays a crucial role as a reactant that interacts with iron. Copper(II) sulfate's role is pivotal because it can undergo different chemical reactions depending on the conditions and the amount of reactant it interacts with.

This compound can be observed in solutions as a blue liquid due to the presence of hydrated copper ions, which appear blue due to their specific absorption of light. In solid form, it might be seen as blue crystals of pentahydrate when mixed with water.

When copper(II) sulfate reacts with iron, a redox reaction occurs. This means there is an exchange of electrons where copper is reduced and iron is oxidized. By measuring the amount of copper that is produced as a result of this reaction, we can determine the original chemical reaction pathway. This makes copper(II) sulfate a key player in stoichiometry problems where determining the mole ratios is essential to understanding the outcome of the reaction.

Mole Ratios

Mole ratios are fundamental in understanding chemical reactions. They represent the proportions of reactants and products that participate in a reaction, as indicated by the coefficients in a balanced chemical equation. In our reaction with copper(II) sulfate and iron, the mole ratios are crucial.

In the given reactions, both potential equations involve a 1:1:1 mole ratio. This means for every mole of copper(II) sulfate that reacts, we get one mole of iron and produce one mole of copper. This simple ratio helps in determining how much of each substance will be consumed or produced in a reaction.

Determining mole ratios involves balancing chemical equations to ensure the law of conservation of mass is upheld. The coefficients in a balanced equation tell us not only the relative quantities but also help identify how many molecules of one substance will react to form a certain quantity of another.

• Equation for Reaction 1: Copper(II) sulfate + Iron → Copper + Iron(II) sulfate has a 1:1:1 ratio.
• Equation for Reaction 2: Copper(II) sulfate + Iron → Copper + Iron(III) sulfate also displays a 1:1:1 stoichiometric ratio.

Understanding these ratios is necessary for predicting product amounts based on starting reactants.

Limiting Reactant

The concept of a limiting reactant is significant in stoichiometry, dictating the extent to which a reaction can proceed. The limiting reactant is the substance that gets completely consumed first, thus determining the maximum amount of product formed.

In our exercise featuring copper(II) sulfate and iron, identifying the limiting reactant is crucial. By calculating the moles of reactants present:

Copper(II) sulfate: 0.04385 moles

Iron: 0.03582 moles

we can assess which reactant limits the formation of copper. Since the mole ratio is 1:1 for both potential reactions, iron, with lesser moles, acts as the limiting reactant. It gets used up completely before all of the copper(II) sulfate is consumed.

The presence of excess copper(II) sulfate after all iron has reacted ensures the reaction's constraints are dictated by the available iron, thus confirming it as the limiting reactant. This helps in verifying the stoichiometry of the reaction and the amount of copper we observe as a product.

Reaction Analysis

Analyzing a chemical reaction involves comparing theoretical predictions with actual experimental data. For the exercise involving copper(II) sulfate and iron, reaction analysis helps us pinpoint which of the two possible reactions occurred. Initially, we established reactions for both Copper(II) sulfate to form two different sulfates of Iron: Iron(II) sulfate and Iron(III) sulfate. By considering the experimentally obtained amount of copper, which is 2.27 g, we turn this mass into moles (0.03573 moles). This value is compared to theoretical calculations of moles from each reaction's stoichiometry.

The key to reaction analysis is in the reality check:

• For Reaction 1 (yielding Iron(II) sulfate), the moles of copper closely match, ensuring that 0.03582 moles of iron leads to a similar 0.03573 moles of copper.
• For Reaction 2 (yielding Iron(III) sulfate), the stoichiometry still offers a 1:1:1 ratio, but the available iron doesn't allow completion under given conditions.

The actual outcome aligns with Reaction 1, confirming that the formed product is in harmony with the limiting reactant and predicted mole ratios, ensuring the reaction proceeds as expected.