Question

Apply Concepts A mining company has two possible sources of copper: chalcopyrite (CuFeS \(_{2} )\) and chalcocite \(\left(\mathrm{Cu}_{2} \mathrm{S}\right) .\) If the mining conditions and the extraction of copper from the ore were identical for each of the ores, which ore would yield the greater quantity of copper? Explain your answer.

Short answer

Chalcocite (\( Cu_{2}S \)) would provide a larger quantity of copper. The mole ratio of copper in chalcopyrite and chalcocite was determined and compared. It was found that in chalcopyrite, copper amounts to 34.4% of the compound. In contrast, copper accounts for 79.8% of chalcocite. Therefore, under identical mining conditions and extraction processes, chalcocite would yield more copper than chalcopyrite.

Step-by-step solution

Calculate the molar mass of each compound

Compute the molar mass of chalcopyrite and chalcocite by adding the atomic masses of each element in the compounds. For chalcopyrite \(CuFeS_2\): the molar mass is calculated as the sum of the molar mass of Copper (63.55 g/mol), Iron (55.85 g/mol), and Sulfur (32.07 g/mol * 2) which equals 184.64 g/mol. For chalcocite \(Cu_2S\): the molar mass is calculated as the sum of the molar mass of Copper (63.55 g/mol * 2) and Sulfur (32.07 g/mol) which equals 159.17 g/mol.

Calculate the mole ratio of copper in each compound

For this step, divide the molar mass of copper by the molar mass of the compound. For chalcopyrite: \( CuFeS_2\), the mole ratio of copper is \( \frac{63.55 g/mol}{184.54 g/mol} = 0.344 \) (or 34.4% of the compound is copper). For chalcocite: \( Cu_2S\), the mole ratio of copper is \( \frac{63.55 g/mol * 2}{159.17 g/mol} = 0.798 \) (or 79.8% of the compound is copper).

Compare the copper content of each ore

Finally, compare the copper content in each compound. Chalcocite, with 79.8% copper content, yields a greater quantity of copper when compared to chalcopyrite, which has 34.4% copper content. Therefore, chalcocite (\(Cu_2S\)) would yield more copper than chalcopyrite (\(CuFeS_2\)) under identical mining conditions and extraction processes.

Key concepts

Molar Mass Calculation

Understanding how to calculate molar mass is fundamental when delving into the world of copper extraction chemistry. Molar mass refers to the mass of one mole of a substance, measured in grams per mole (g/mol). A mole is a standard unit in chemistry representing Avogadro's number of particles, molecules, or atoms, which is approximately 6.022 x 10²³.

To calculate the molar mass, you need to know the atomic masses of each element involved, which can be found on the periodic table. The atomic mass of an element is usually located below its symbol and represents the mass of a single mole of atoms of that element. For compounds, you'll add the atomic masses of all atoms in the molecule’s formula.

Let’s apply this to the provided exercise. For chalcopyrite, the molar mass is computed by adding the molar mass of one copper atom, one iron atom, and two sulfur atoms together. For chalcocite, it's the sum of two copper atoms and a single sulfur atom. This step is critical because it provides the foundation for understanding the composition and potential yield from mining ores.

Mole Ratio

The mole ratio is a critical component in mining chemistry and dictates the efficiency of copper extraction. In essence, the mole ratio is the ratio of the number of moles of one substance compared to the number of moles of another in a chemical equation, or in this context, within a compound.

For practical purposes, in the exercise on copper extraction, the mole ratio is used to determine the proportion of copper in relation to the entire compound. Calculating the mole ratio of copper involves dividing the molar mass of copper present in the compound by the total molar mass of the compound. This gives us insight into what percentage of the compound is copper, regarded as its copper content.

Why is the Copper Percentage Important?

Understanding this proportion is crucial for a mining company looking to maximize its copper yield. If extraction methods and conditions are constant, the ore with a higher mole ratio of copper will predictably provide more copper per unit of ore extracted.

Mining Chemistry

The process of extracting copper from its ores is all about applying fundamental principles of mining chemistry. Extraction begins with mining the ore from the earth's crust and then separating the copper minerals from the rest of the ore. Mining companies must make a choice between different sources of copper ore based on efficiency and economic factors.

When companies assess potential mining sources, they must consider factors such as the type of mineral, the composition of the ore, and the geographical location. In this scenario, the choice between chalcopyrite and chalcocite is informed by the copper content and the easiness of the copper to be separated from other elements. By examining these factors, mining companies can decide which ore will provide the most copper with the least effort and cost.

Environmental Impact

Additionally, the choice of what ore to mine influences the environmental footprint. Methods for processing high-grade ores like chalcocite often require less energy and generate fewer byproducts than those with a lower ratio of copper like chalcopyrite, potentially reducing the environmental impact.

Percent Composition

Percent composition is a term that's commonly used in chemistry to describe the percentage by mass of each element within a compound. For metallurgy and mining, understanding the percent composition is essential for evaluating the potential yield of metal from an ore.

To calculate the percent composition, you divide the total mass of each element in one mole of the compound by the molar mass of the compound and then multiply by 100%. This reveals the concentration of each element, providing a clear picture of what a specific source of ore contains.

In the exercise, the calculation of percent composition allows us to compare the amount of copper in chalcopyrite and chalcocite. Chalcocite’s higher percentage means that, per unit of ore, there is more copper available for extraction, making it the more lucrative option for mining operations seeking to maximize their production of copper.