Question

(a) A charge of \(3.3 \times 10^{6} \mathrm{~kg}\) of material containing \(27 \%\) \(\mathrm{Cu}_{2} \mathrm{~S}\) and \(13 \%\) FeS is added to a converter and oxidized. What mass of \(\mathrm{SO}_{2}(g)\) is formed? (b) What is the molar ratio of \(\mathrm{Cu}\) to \(\mathrm{Fe}\) in the resulting mixture of oxides? (c) What are the likely formulas of the oxides formed in the oxidation reactions, assuming an excess of oxygen? (d) Write balanced equations representing each of the oxidation reactions.

Short answer

(a) The mass of SO2 formed during the process is \(9.54 \times 10^5~kg\). (b) The molar ratio of Cu to Fe in the resulting mixture of oxides is 1.744. (c) The likely formulas of the oxides formed are CuO and Fe2O3. (d) The balanced equations for the oxidation reactions are: \(2~Cu_2S + 3~O_2 \rightarrow 2~CuO + 2~SO_2\) and \(4~FeS + 7~O_2 \rightarrow 2~Fe_2O_3 + 4~SO_2\).

Step-by-step solution

Calculate mass of Cu2S and FeS in the material

First, we need to find the mass of Cu2S and FeS present in the initial material. Given that the material's charge is \(3.3 \times 10^6~kg\), we can find the mass of Cu2S and FeS by multiplying this by their respective percentages. Mass of Cu2S = \((3.3 \times 10^6~kg) \times 0.27 = 8.91 \times 10^5~kg\) Mass of FeS = \((3.3 \times 10^6~kg) \times 0.13 = 4.29 \times 10^5~kg\)

Calculate moles of Cu2S and FeS

Now we need to calculate the number of moles for Cu2S and FeS. To do this, we will divide the mass of each substance by its molar mass. Moles of Cu2S = \(\frac{8.91 \times 10^5~kg}{(2 \times 63.5 + 32.1)~g/mol}\) = \(6.938 \times 10^6~mol\) Moles of FeS = \(\frac{4.29 \times 10^5~kg}{(55.8 + 32.1)~g/mol}\) = \(7.952 \times 10^6~mol\)

Calculate moles of SO2 formed

Both Cu2S and FeS will produce SO2 after oxidization. We need to calculate the moles of SO2 formed by both reactions. Moles of SO2 formed from Cu2S = \(6.938 \times 10^6~mol\) Moles of SO2 formed from FeS = \(7.952 \times 10^6~mol\) Total moles of SO2 formed = \((6.938 + 7.952) \times 10^6~mol\) = \(14.89 \times 10^6~mol\)

Calculate the mass of SO2 formed

Now that we have the total moles of SO2 formed, we can find the mass of SO2 formed by multiplying it by the molar mass of SO2. Mass of SO2 = \((14.89 \times 10^6~mol) \times (64.1~g/mol)\) = \(9.54 \times 10^8~g\) or \(9.54 \times 10^5~kg\) Part (b):

Calculate molar ratio of Cu to Fe in the resulting mixture of oxides

We need to find the moles of Cu and Fe in the resulting mixture of oxides. Since there are two moles of Cu in every mole of Cu2S, the moles of Cu will be twice the moles of Cu2S. Moles of Cu = \(2 \times 6.938 \times 10^6~mol\) = \(13.88 \times 10^6~mol\) Moles of Fe = \(7.952 \times 10^6~mol\) The molar ratio of Cu to Fe = \(\frac{13.88 \times 10^6}{7.952 \times 10^6}\) = \(1.744\) Part (c):

Determine the likely formulas of the oxides formed

Assuming an excess of oxygen, the likely formulas of the oxides formed will be CuO and Fe2O3, as these are the main stable oxides for Cu and Fe. Part (d):

Write balanced equations for the oxidation reactions

Now we will write balanced equations for the reactions that lead to the formation of the oxides of copper and iron. 1. Oxidation of Cu2S: \[2~Cu_2S + 3~O_2 \rightarrow 2~CuO + 2~SO_2\] 2. Oxidation of FeS: \[4~FeS + 7~O_2 \rightarrow 2~Fe_2O_3 + 4~SO_2\]

Key concepts

Oxidation Reactions

Oxidation reactions are chemical processes where a substance loses electrons. This process can often result in the formation of oxides when elements or compounds react with oxygen.

In the exercise, we encounter oxidation reactions as part of the metallurgical process, specifically when copper and iron sulfide ores (Cu₂S and FeS) are converted into their respective oxides. The material's charge is first quantified to determine the mass of the reacting sulfides. Following this, the calculations involve determining the oxides' stoichiometry, which arises from the balanced chemical equations representing their formation.

The oxidation of Cu₂S results in copper(II) oxide (CuO) and sulfur dioxide (SO₂), while the oxidation of FeS results in iron(III) oxide (Fe₂O₃) and sulfur dioxide (SO₂), assuming excess oxygen is available. These reactions are integral to understanding how metal ores are processed and purified.

Mole Concept

The mole concept is a fundamental principle in chemistry that relates mass to the number of particles in a substance. One mole of any substance contains Avogadro's number of entities (\(6.022 \times 10^{23}\)). This concept allows chemists to count atoms, molecules, and ions by weighing them.

The exercise demonstrates the application of the mole concept by requiring the calculation of moles from the given mass of Cu₂S and FeS. By dividing the mass of each compound by its molar mass, we obtain the number of moles. This step is crucial because stoichiometry heavily relies on mole ratios to predict the amounts of reactants used and products formed in a chemical reaction. Additionally, the molar ratio of Cu to Fe in the oxides formed reflects the mole concept's role in determining the proportions of elements in a compound.

Chemical Equations

Chemical equations are symbolic representations of chemical reactions, showing the reactants and products involved, as well as their quantities. A balanced chemical equation has the same number of atoms of each element on both sides of the reaction, adhering to the law of conservation of mass.

In the exercise, we see the importance of writing balanced chemical equations to represent each oxidation reaction. The equations for the oxidation of Cu₂S and FeS are balanced to ensure the mass of sulfur dioxide (SO₂) produced is accurately calculated. This enables the determination of the mass of SO₂ formed from the reaction and exemplifies how chemical equations are used to quantitatively describe chemical processes. Given the right stoichiometric ratios, these equations can also guide the calculation of the theoretical yield of a reaction.