Problem 28 - Chemistry: An Atoms-Focused Approach

Question

Copper was one of the first metals used by humans because it can be recovered from several copper minerals, including cuprite (Cu \(_{2} \mathrm{O}\) ), chalcocite (Cu \(_{2} \mathrm{S}\) ), and malachite \(\left[\mathrm{Cu}_{2} \mathrm{CO}_{3}(\mathrm{OH})_{2}\right] .\) Balance the following reactions for converting these minerals into copper metal: a. \(\mathrm{Cu}_{2} \mathrm{O}(s)+\mathrm{C}(s) \rightarrow \mathrm{Cu}(s)+\mathrm{CO}_{2}(g)\) b. \(\mathrm{Cu}_{2} \mathrm{O}(s)+\mathrm{Cu}_{2} \mathrm{S}(s) \rightarrow \mathrm{Cu}(s)+\mathrm{SO}_{2}(g)\) c. \(\mathrm{Cu}_{2} \mathrm{CO}_{3}(\mathrm{OH})_{2}(s)+\mathrm{C}(s) \rightarrow \mathrm{Cu}(s)+\mathrm{CO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(g)\)

Step-by-Step Solution

Answer

Question: Balance the following chemical reactions involved in the conversion of copper minerals into copper metal: a) Cu2O(s) + C(s) → Cu(s) + CO2(g) b) Cu2O(s) + Cu2S(s) → Cu(s) + SO2(g) c) Cu2CO3(OH)2(s) + C(s) → Cu(s) + CO2(g) + H2O(g) Answer: a) Balanced reaction: 2Cu2O(s) + C(s) → 4Cu(s) + 2CO2(g) b) Balanced reaction: Cu2O(s) + Cu2S(s) → 4Cu(s) + 2SO2(g) c) Balanced reaction: 2Cu2CO3(OH)2(s) + 2C(s) → 4Cu(s) + 2CO2(g) + 4H2O(g)

Step 1: Balancing Reaction (a)

We are given the following reaction: Cu2O(s) + C(s) → Cu(s) + CO2(g) First, let's balance the copper atoms: 2Cu2O(s) + C(s) → 4Cu(s) + CO2(g) Now, balance the oxygen atoms: 2Cu2O(s) + C(s) → 4Cu(s) + 2CO2(g) Finally, let's check the carbon atoms: 2Cu2O(s) + C(s) → 4Cu(s) + 2CO2(g) The balanced reaction is: 2Cu2O(s) + C(s) → 4Cu(s) + 2CO2(g)

Step 2: Balancing Reaction (b)

We are given the following reaction: Cu2O(s) + Cu2S(s) → Cu(s) + SO2(g) First, let's balance the copper atoms: Cu2O(s) + Cu2S(s) → 4Cu(s) + SO2(g) Now, balance the oxygen atoms: Cu2O(s) + Cu2S(s) → 4Cu(s) + O2SO2(g) Finally, let's check the sulfur atoms: Cu2O(s) + Cu2S(s) → 4Cu(s) + 2SO2(g) The balanced reaction is: Cu2O(s) + Cu2S(s) → 4Cu(s) + 2SO2(g)

Step 3: Balancing Reaction (c)

We are given the following reaction: Cu2CO3(OH)2(s) + C(s) → Cu(s) + CO2(g) + H2O(g) First, let's balance the copper atoms: 2Cu2CO3(OH)2(s) + C(s) → 4Cu(s) + CO2(g) + H2O(g) Now, balance the carbon atoms: 2Cu2CO3(OH)2(s) + 2C(s) → 4Cu(s) + 2CO2(g) + H2O(g) Next, let's balance the hydrogen atoms: 2Cu2CO3(OH)2(s) + 2C(s) → 4Cu(s) + 2CO2(g) + 4H2O(g) Finally, check the balance of the oxygen atoms: 2Cu2CO3(OH)2(s) + 2C(s) → 4Cu(s) + 2CO2(g) + 4H2O(g) The balanced reaction is: 2Cu2CO3(OH)2(s) + 2C(s) → 4Cu(s) + 2CO2(g) + 4H2O(g)

Key Concepts

Copper Minerals

Copper minerals are naturally occurring compounds from which we can extract the valuable metal copper. These minerals include:

• Cuprite (Cu₂O): This reddish mineral is an important source of copper and contains both copper and oxygen.
• Chalcocite (Cu₂S): Recognizable by its dark gray to black color, chalcocite is rich in copper sulfidic content.
• Malachite [Cu₂CO₃(OH)₂]: Known for its vibrant green hue, malachite is a copper carbonate hydroxide mineral widely used in jewelry and for copper extraction.

Each mineral requires specific processes to obtain copper efficiently. While malachite undergoes a calcination process to liberate its carbon, cuprite and chalcocite necessitate reduction or smelting with other elements to release copper from their mineral structures. Understanding these differences helps in optimizing the extraction process.

Copper Extraction

Copper extraction from its minerals is a process that involves chemical reactions to extract pure copper metal. The methods vary based on the mineral type:

• From Cuprite: Cuprite reacts with carbon in a reduction process to form copper metal and carbon dioxide, as seen in the equation:
  \[ 2\, \text{Cu}_2\text{O}(s) + \text{C}(s) \rightarrow 4\, \text{Cu}(s) + 2\, \text{CO}_2(g) \]
• From Chalcocite: Chalcocite undergoes a reaction with cuprite, whereby sulfur in chalcocite is oxidized, emitting sulfur dioxide, resulting in copper metal:
  \[ \text{Cu}_2\text{O}(s) + \text{Cu}_2\text{S}(s) \rightarrow 4\, \text{Cu}(s) + 2\, \text{SO}_2(g) \]
• From Malachite: Malachite decomposes in a multi-step process. Initially, it breaks down with carbon, producing carbon dioxide, water vapor, and copper:
  \[ 2\, \text{Cu}_2\text{CO}_3(\text{OH})_2(s) + 2\, \text{C}(s) \rightarrow 4\, \text{Cu}(s) + 2\, \text{CO}_2(g) + 4\, \text{H}_2\text{O}(g) \]

Each process highlights the necessity of using specific reactants like carbon to achieve the desired reaction. These methods ultimately reduce the mineral compounds to obtain pure copper for utilization.

Stoichiometry

Stoichiometry involves the calculation and balancing of chemical equations to ensure mass conservation, meaning that the number of atoms of each element is the same on both sides of the equation. This concept is crucial in converting copper minerals to pure copper effectively.

• Balancing Chemical Reactions: To extract copper correctly, balancing each reaction is vital. For example, starting with the initial equation \(\text{Cu}_2\text{O}(s) + \text{C}(s) \rightarrow \text{Cu}(s) + \text{CO}_2(g)\), it must be balanced to ensure the same number of atoms of copper, oxygen, and carbon are present. That results in the balanced equation:
  \[ 2\, \text{Cu}_2\text{O}(s) + \text{C}(s) \rightarrow 4\, \text{Cu}(s) + 2\, \text{CO}_2(g) \]
• Mole Ratios: Stoichiometry requires understanding the mole ratios, which indicate how many moles of one substance react with moles of another. Using the balanced equation, we know that two moles of cuprite react with one mole of carbon to produce four moles of copper.

By employing stoichiometric principles, chemists accurately predict the amounts of reactants needed and products formed. This allows for efficient extraction processes and minimal waste in copper production.