Problem 107 - Chemistry The Central Science In Si Units

Question

Copper exists in the form of \(\mathrm{CuFeS}_{2}\) in copper ore. Copper is isolated in a two-step process. First, \(\mathrm{CuFeS}_{2}\) 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?

Step-by-Step Solution

Answer

The balanced equation is \(\mathrm{Cu_2S} + \mathrm{O_2} \rightarrow 2\mathrm{Cu} + \mathrm{SO_2}\). \(\mathrm{Cu}\) is reduced and \(\mathrm{S}\) is oxidized. 59.055 grams of copper are isolated.

Step 1: Write the Balanced Equation for the Second Reaction

The second reaction involves the conversion of copper(I) sulfide, \(\mathrm{Cu_2S}\), to copper metal and sulfur dioxide in the presence of oxygen. The balanced equation is \(\mathrm{Cu_2S} + \mathrm{O_2} \rightarrow 2\mathrm{Cu} + \mathrm{SO_2}\).

Step 2: Identify Oxidation and Reduction

In the balanced equation from Step 1, identify the oxidation states of sulfur and copper. In \(\mathrm{Cu_2S}\), \(\mathrm{S}\) has an oxidation state of \(-2\) and in \(\mathrm{SO_2}\), \(\mathrm{S}\) has an oxidation state of \(+4\), indicating oxidation. Copper in \(\mathrm{Cu_2S}\) goes from \(+1\) to \(0\), indicating reduction. Thus, \(\mathrm{S}\) in \(\mathrm{Cu_2S}\) is oxidized and \(\mathrm{Cu}\) in \(\mathrm{Cu_2S}\) is reduced.

Step 3: Calculate Molar Mass of \(\mathrm{CuFeS_2}\)

Calculate the molar mass of \(\mathrm{CuFeS_2}\) for the conversion. \(\mathrm{Cu}\) has a molar mass of 63.5 g/mol, \(\mathrm{Fe}\) has a molar mass of 55.8 g/mol, and \(\mathrm{S}\) has a molar mass of 32.1 g/mol. Thus, the molar mass of \(\mathrm{CuFeS_2}\) is \(63.5 + 55.8 + 2 \times 32.1 = 183.5\) g/mol.

Step 4: Calculate Moles of \(\mathrm{CuFeS_2}\)

Given 85.36 g of \(\mathrm{CuFeS_2}\), find the moles by dividing by the molar mass calculated in Step 3. \(\text{Moles of } \mathrm{CuFeS_2} = \frac{85.36 \text{ g}}{183.5 \text{ g/mol}} \approx 0.465\) mol.

Step 5: Calculate Grams of Isolated Copper

From the first reaction, \(2 \text{ moles of } \mathrm{CuFeS_2}\) produce \(2 \text{ moles of } \mathrm{Cu_2S}\), which yields \(2 \text{ moles of } \mathrm{Cu}\). Thus, \(1 \text{ mole of } \mathrm{CuFeS_2}\) produces \(2 \text{ moles of } \mathrm{Cu}\), or \(\approx 0.93\) moles of \(\mathrm{Cu}\) for the given moles. With the molar mass of \(\mathrm{Cu}\) being 63.5 g/mol, mass of copper is \(0.93 \times 63.5 = 59.055\) grams.

Key Concepts

Copper Extraction

Copper extraction is a vital part of the mining industry, focusing on converting copper ores into pure copper metal. The starting material in copper ore processing is a mineral called chalcopyrite, represented as \(\mathrm{CuFeS}_{2}\). When copper is extracted, it undergoes a series of chemical reactions that isolate the metal from other components in the ore.

The initial stage of copper extraction involves heating chalcopyrite with silicon dioxide \((\mathrm{SiO}_{2})\) and oxygen. This process produces copper(I) sulfide \((\mathrm{Cu}_{2}\mathrm{S})\), iron silicate \((\mathrm{FeSiO}_{3})\), and sulfur dioxide \((\mathrm{SO}_{2})\). The reaction is as follows:

\[2 \mathrm{CuFeS}_{2} + 2 \mathrm{SiO}_{2} + 4 \mathrm{O}_{2} \rightarrow \mathrm{Cu}_{2} \mathrm{S} + 2 \mathrm{FeSiO}_{3} + 3 \mathrm{SO}_{2}.\]

The second step involves heating \(\mathrm{Cu}_{2}\mathrm{S}\) with oxygen to form pure copper and sulfur dioxide:

\[\mathrm{Cu}_{2}\mathrm{S} + \mathrm{O}_{2} \rightarrow 2\mathrm{Cu} + \mathrm{SO}_{2}.\]

This two-step method effectively transitions the copper within the ore from a combined state to metallic form, ready for further refining and use in various applications.

Oxidation and Reduction

Oxidation and reduction reactions, often referred to as redox reactions, are central to many chemical processes, including copper extraction. In the context of the given exercise, oxidation involves the loss of electrons while reduction involves the gain of electrons.

During the conversion of copper(I) sulfide \((\mathrm{Cu}_{2}\mathrm{S})\) to copper, there are changes in oxidation states for both copper and sulfur. Initially, copper has an oxidation state of \(+1\) in \(\mathrm{Cu}_{2}\mathrm{S}\) and is reduced to an oxidation state of \(0\) in elemental copper. This change signifies a gain of electrons, typical of a reduction process.

Conversely, sulfur starts with an oxidation state of \(-2\) in \(\mathrm{Cu}_{2}\mathrm{S}\) and moves to an oxidation state of \(+4\) in sulfur dioxide \((\mathrm{SO}_{2})\). This signifies a loss of electrons, which is characteristic of oxidation.

Understanding these transformations is crucial for appreciating how redox reactions facilitate the extraction and purification of elements like copper from their ores. Students should focus on how electron transfer underlies these processes to form new substances.

Stoichiometry

Stoichiometry involves the calculation of reactants and products in chemical reactions. It is a quantitative aspect of chemistry that allows us to predict the amounts of substances consumed and produced in reactions, like those involved in copper extraction.

For instance, with chalcopyrite \((\mathrm{CuFeS}_{2})\), its molar mass is essential to calculate how much pure copper can be extracted. From the problem, the molar mass of \(\mathrm{CuFeS}_{2}\) is calculated as \(183.5\) g/mol. Given \(85.36\) grams of chalcopyrite, we determine the number of moles:

\[\text{Moles of } \mathrm{CuFeS}_{2} = \frac{85.36 \text{ g}}{183.5 \text{ g/mol}} \approx 0.465\text{ mol}.\]

The stoichiometry of the extraction reactions shows that each mole of \(\mathrm{CuFeS}_{2}\) can yield two moles of copper. Therefore, \(0.465\) moles of \(\mathrm{CuFeS}_{2}\) would produce approximately \(0.93\) moles of copper.

Finally, using the molar mass of copper \((63.5 \text{ g/mol})\), the weight of copper extracted from our \(0.93\) moles is:

\[0.93 \times 63.5 = 59.055 \text{ grams of copper}.\]

This process highlights how stoichiometric coefficients help in deducing quantities for industrial applications and chemical research.