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Copper exists in the form of \(\mathrm{CuFeS}_{2}\) in copper ore. Copper is isolated in a two-step process. First, CuFeS \(_{2}\) is heated with \(\mathrm{SiO}_{2}\) in the presence of oxygen to form copper(I) sulfide, \(\mathrm{CuS:} 2 \mathrm{CuFeS}_{2}+2 \mathrm{SiO}_{2}(s)+4 \mathrm{O}_{2}(g) \longrightarrow \mathrm{Cu}_{2} \mathrm{~S}(s)+\) \(2 \mathrm{FeSiO}_{3}(s)+3 \mathrm{SO}_{2}(g) . \mathrm{Cu}_{2} \mathrm{~S}\) is then heated with oxygen to form copper and \(\mathrm{SO}_{2}(g)\). (a) Write the balanced chemical equation for the second reaction. (b) Which atoms from which compounds are being oxidized, and which atoms from which compounds are being reduced? (c) How many grams of copper would be isolated from \(85.36 \mathrm{~g}\) of \(\mathrm{CuFeS}_{2}\) in copper ore?

Short Answer

Expert verified
The balanced chemical equation for the second reaction is: 2 Cu₂S(s) + 3 O₂(g) → 4 Cu(s) + 2 SO₂(g). In this process, Cu is being reduced, while Fe and S are being oxidized. From 85.36 g of CuFeS₂ in copper ore, 59.13 g of copper can be isolated.

Step by step solution

01

Write the balanced chemical equation for the second reaction

We are given that Cu₂S is heated with oxygen to form copper and SO₂. To write the balanced chemical equation, we need to balance all atoms on both sides of the equation. Since there are 2 copper atoms and 1 sulfur atom on the left-hand side, we require 2 copper atoms and 1 sulfur atom on the right-hand side as well: 2 Cu₂S(s) + 3 O₂(g) → 4 Cu(s) + 2 SO₂(g)
02

Identify the atoms being oxidized and reduced

In the first reaction, CuFeS₂ is heated with SiO₂ in the presence of oxygen to form Cu₂S, FeSiO₃, and SO₂. The species being oxidized and reduced can be identified by analyzing the change in their oxidation states: - Cu: goes from +1 in CuFeS₂ to 0 in Cu (reduced) - Fe: goes from +2 in CuFeS₂ to +3 in FeSiO₃ (oxidized) - S: goes from -2 in CuFeS₂ to +4 in SO₂ (oxidized) Thus, Cu is being reduced, while Fe and S are being oxidized.
03

Calculate the amount of copper isolated

We are given that 85.36 g of CuFeS₂ is used in copper ore. To determine the amount of copper isolated, we need to convert the mass of CuFeS₂ to mole and then use stoichiometry to convert moles of CuFeS₂ to moles of copper. Finally, we will convert moles of copper back to mass (grams). 1. Calculate the molar mass of CuFeS₂: M(CuFeS₂) = Atomic Mass of Cu + Atomic Mass of Fe + 2 * Atomic Mass of S M(CuFeS₂) = 63.55 g/mol + 55.85 g/mol + 2 * 32.07 g/mol = 183.54 g/mol 2. Convert mass of CuFeS₂ to moles: moles of CuFeS₂ = (mass of CuFeS₂) / (molar mass of CuFeS₂) moles of CuFeS₂ = 85.36 g / 183.54 g/mol = 0.4649 mol 3. Convert moles of CuFeS₂ to moles of Cu using stoichiometry (from the balanced chemical equation in Step 1): moles of Cu = 2 * moles of CuFeS₂ (since coefficent of Cu₂S is 2 and coefficent of Cu is 4 in the balanced chemical equation) moles of Cu = 2 * 0.4649 mol = 0.9298 mol 4. Convert moles of Cu back to mass in grams: mass of Cu = moles of Cu * Atomic Mass of Cu mass of Cu = 0.9298 mol * 63.55 g/mol = 59.13 g Hence, 59.13 g of copper would be isolated from 85.36 g of CuFeS₂ in copper ore.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Chemical Reactions
In the realm of chemistry, a chemical reaction is a process where substances, called reactants, transform into different substances known as products. In the context of copper extraction, chemical reactions are pivotal. The initial chemical equations given in the problem demonstrate the transformation of copper in its ore form \(\text{CuFeS}_{2}\) to eventually refine pure copper metal. Here, different reactants like \(\text{SiO}_{2}\) and \(\text{O}_{2}\) partake in this conversion.
  • First Reaction: Involves heating \(\text{CuFeS}_{2}\) with \(\text{SiO}_{2}\) and \(\text{O}_{2}\) to form \(\text{Cu}_{2}\text{S}\).
  • Second Reaction: \(\text{Cu}_{2}\text{S}\) is heated with \(\text{O}_{2}\) resulting in copper and \(\text{SO}_{2}\).
To balance these reactions, ensure each type of atom appears equally on both sides of the reaction arrow. This conservation of mass is crucial for the proper understanding of the reaction dynamics. Visualizing these changes, a balanced equation ensures that chemical identity and reaction stoichiometry are accurately represented.
Stoichiometry
Stoichiometry involves the calculations of reactants and products in chemical reactions. It is a powerful tool to predict yields and guide experimentations.
In the context of copper extraction:
  • The initial ore \(\text{CuFeS}_{2}\) yields copper through a series of reactions where stoichiometric ratios determine how much copper can be extracted from a given ore mass.
  • Stoichiometry allows us to convert grams of \(\text{CuFeS}_{2}\) to moles using its molar mass and then relate these moles to moles of copper produced using the balanced equation.
For instance, if 85.36 g of \(\text{CuFeS}_{2}\) is available, stoichiometry helps us calculate how many grams of copper can be isolated. This involves converting between mass and moles, using the equation coefficients to relate reactants and products.
Oxidation and Reduction
Oxidation and reduction (redox) reactions are key aspects of many chemical processes, including copper extraction.
  • Oxidation involves the loss of electrons, while reduction involves the gain of electrons.
  • In the given context, copper \(\text{(Cu)}\) is reduced from +1 in \(\text{CuFeS}_{2}\) to 0 in elemental copper, indicating it gains electrons.
  • Conversely, iron \(\text{(Fe)}\) is oxidized from +2 in \(\text{CuFeS}_{2}\) to +3 in \(\text{FeSiO}_{3}\).
  • Sulfur \(\text{(S)}\) also undergoes oxidation from -2 in \(\text{CuFeS}_{2}\) to +4 in \(\text{SO}_{2}\).
It's important to grasp how oxidation states change during the reaction. This helps identify the substance that acts as a reducing agent (provides electrons) and the oxidizing agent (accepts electrons), which is essential for understanding the chemical mechanism behind copper extraction.
Molar Mass Calculation
Calculating molar mass is vital for converting between mass and moles, a foundational step in stoichiometric calculations.
  • The molar mass of a compound is the sum of the atomic masses of its constituent elements in appropriate proportions.
  • For \(\text{CuFeS}_{2}\):
    • Copper (Cu): 63.55 g/mol
    • Iron (Fe): 55.85 g/mol
    • Sulfur (S): 32.07 g/mol (two sulfur atoms are present, so \(2 \times 32.07\) g/mol)
  • Total molar mass: \(63.55 + 55.85 + 2 \times 32.07 = 183.54 \text{ g/mol}\)
Using the molar mass allows direct conversion of grams to moles, setting the stage for further stoichiometric analysis. This precise conversion ensures accuracy when predicting the amount of product formed in a reaction—like determining the mass of copper extracted from an ore sample.

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