Questions: The mineral chalcocite, Cu2S, has been mined for centuries and is one of the most profitable copper ores because of its high copper content. How many grams of chalcocite must be mined to obtain 312 g of pure Cu? Express your answer in grams to 3 significant figures. mass of chalcocite = g

Solution Steps

First, we need to calculate the molar mass of chalcocite (\(\mathrm{Cu}_2\mathrm{S}\)). The molar mass is the sum of the atomic masses of all the atoms in the formula.

• The atomic mass of copper (Cu) is approximately 63.55 g/mol.
• The atomic mass of sulfur (S) is approximately 32.07 g/mol.

The formula for chalcocite is \(\mathrm{Cu}_2\mathrm{S}\), which contains 2 copper atoms and 1 sulfur atom. Therefore, the molar mass of chalcocite is:

\[ \text{Molar mass of } \mathrm{Cu}_2\mathrm{S} = 2 \times 63.55 + 32.07 = 159.17 \, \text{g/mol} \]

Next, we need to determine how many moles of copper are in 312 g of pure copper.

\[ \text{Moles of Cu} = \frac{312 \, \text{g}}{63.55 \, \text{g/mol}} \approx 4.910 \, \text{mol} \]

In the formula \(\mathrm{Cu}_2\mathrm{S}\), there are 2 moles of copper for every 1 mole of chalcocite. Therefore, the moles of chalcocite required are:

\[ \text{Moles of } \mathrm{Cu}_2\mathrm{S} = \frac{4.910 \, \text{mol Cu}}{2} = 2.455 \, \text{mol} \]

Finally, we calculate the mass of chalcocite needed using its molar mass:

\[ \text{Mass of } \mathrm{Cu}_2\mathrm{S} = 2.455 \, \text{mol} \times 159.17 \, \text{g/mol} \approx 390.7 \, \text{g} \]

Final Answer