Question

The following "cycle of copper" experiment is performed in some general chemistry laboratories. The series of reactions starts with copper and ends with metallic copper. The steps are as follows: (1) A piece of copper wire of known mass is allowed to react with concentrated nitric acid [the products are copper(II) nitrate, nitrogen dioxide, and water]. (2) The copper(II) nitrate is treated with a sodium hydroxide solution to form copper(II) hydroxide precipitate. (3) On heating, copper(II) hydroxide decomposes to yield copper(II) oxide. (4) The copper(II) oxide is combined with concentrated sulfuric acid to yield copper(II) sulfate. (5) Copper(II) sulfate is treated with an excess of zinc metal to form metallic copper. (6) The remaining zinc metal is removed by treatment with hydrochloric acid, and metallic copper is filtered, dried, and weighed. (a) Write a balanced equation for each step and classify the reactions. (b) Assuming that a student started with \(65.6 \mathrm{~g}\) of copper, calculate the theoretical yield at each step. (c) Considering the nature of the steps, comment on why it is possible to recover most of the copper used at the start.

Short answer

Balanced equations ensure consistent mass of copper in each cycle step, allowing for potential full recovery.

Step-by-step solution

Balance Reaction Equation for Step 1

The reaction of copper with nitric acid is represented as \( \text{Cu} + 4\text{HNO}_3 \rightarrow \text{Cu(NO}_3\text{)}_2 + 2\text{NO}_2 + 2\text{H}_2\text{O} \). This reaction is classified as a redox reaction, where copper is oxidized and nitric acid acts as an oxidizing agent.

Balance Reaction Equation for Step 2

Copper(II) nitrate reacts with sodium hydroxide to form copper(II) hydroxide and sodium nitrate: \( \text{Cu(NO}_3\text{)}_2 + 2\text{NaOH} \rightarrow \text{Cu(OH)}_2 + 2\text{NaNO}_3 \). This is a double displacement reaction.

Balance Reaction Equation for Step 3

Copper(II) hydroxide decomposes upon heating: \( \text{Cu(OH)}_2 \rightarrow \text{CuO} + \text{H}_2\text{O} \). This is a decomposition reaction.

Balance Reaction Equation for Step 4

Copper(II) oxide reacts with sulfuric acid: \( \text{CuO} + \text{H}_2\text{SO}_4 \rightarrow \text{CuSO}_4 + \text{H}_2\text{O} \). This is a neutralization reaction.

Balance Reaction Equation for Step 5

Copper(II) sulfate reacts with zinc: \( \text{CuSO}_4 + \text{Zn} \rightarrow \text{Cu} + \text{ZnSO}_4 \). This is a single displacement reaction.

Balance Reaction Equation for Step 6

Remaining zinc is removed with hydrochloric acid: \( \text{Zn} + 2\text{HCl} \rightarrow \text{ZnCl}_2 + \text{H}_2 \). This is a single displacement reaction.

Calculate Theoretical Yields

For each step, calculate the theoretical yield using molar masses. Start with 65.6 g of Cu: - Step 1: Molar mass of Cu is 63.55 g/mol, calculate moles of Cu as \( \frac{65.6}{63.55} = 1.032 \text{ mol Cu} \). - Subsequent reactions consume and produce copper, maintaining 1.032 mol of Cu throughout since every reaction is 1:1. - The mass of copper recovered theoretically should remain 65.6 g.

Comment on Copper Recovery

Each step in the reaction involves reversible transformations that theoretically preserve the total moles of copper throughout the process. The sequence eliminates side reactions and helps maintain the copper mass, reinforcing a closed cycle where most copper reverts to its initial metallic state.

Key concepts

Redox Reaction

A redox reaction, short for reduction-oxidation reaction, involves the transfer of electrons between two species. This type of chemical reaction plays a crucial role in various chemical processes and is prominently featured in the initial step of the copper cycle experiment. Here, copper and nitric acid interact, where copper undergoes oxidation by losing electrons, while nitric acid acts as the oxidizing agent, gaining the electrons lost by copper. This reaction results in the formation of copper(II) nitrate, nitrogen dioxide, and water. In essence, the redox reaction is characterized by the change in oxidation states of the substances involved.
Understanding redox reactions is fundamental for grasping how different compounds can transform during chemical interactions. It also serves as a foundation for studying more complex processes in chemistry, including energy production and metabolic pathways in biology. The copper gaining and losing electrons throughout the cycle reflects the dynamic nature of redox reactions in chemistry.

Decomposition Reaction

Decomposition reactions involve a single compound breaking down into two or more simpler substances. These reactions often require energy, typically in the form of heat, to proceed. In Step 3 of the copper cycle experiment, copper(II) hydroxide is heated, causing it to decompose into copper(II) oxide and water. This step is quintessential to changing the chemical form of copper, facilitating its journey back to a metallic state.
Decomposition reactions are important in various scientific processes and industrial applications. For instance, they play a vital role in breaking down substances in chemical manufacture and in biological decomposition, where complex organic materials are broken down into simpler compounds by living organisms. Understanding how compounds decompose can provide insight into predicting product formation and energy changes in a reaction.

Single Displacement Reaction

A single displacement reaction, or single replacement reaction, involves one element being replaced by another in a compound. In the copper cycle experiment, single displacement is evident in Step 5 when zinc is introduced to a copper(II) sulfate solution. Here, zinc displaces copper, forming metallic copper and zinc sulfate. This reaction is pivotal in regenerating copper from its compound form.
These reactions are significant in the field of metallurgy and in the extraction of metals from ores. They are also used in galvanic cells where a more reactive metal displaces a less reactive one, producing electric current. The zinc displacing copper showcases the reactivity series of metals, which predicts which metals can displace others based on their relative reactivities.

Theoretical Yield

Theoretical yield refers to the maximum amount of product that can be generated from a given amount of reactants under optimal conditions, assuming complete conversion with no loss. In the context of the copper cycle experiment, starting with 65.6 g of copper demands the calculation of theoretical yield at each step, expecting to retrieve all original copper in its metal form.
To calculate the theoretical yield, knowledge of the molar masses of the reactants and products, along with balanced equations, is required. This involves converting mass to moles using the molar mass of copper (63.55 g/mol) and predicting the product amounts through stoichiometry. Each reaction in the cycle maintains the amount of copper, theoretically allowing for full recovery of the starting mass.
Understanding theoretical yield helps in gauging the efficiency of chemical processes and is indispensable in research and industrial chemistry for designing optimized reactions with minimal waste. It also offers insight into the limitations and directions for process improvements in practical scenarios.