Questions: The most common source of copper (Cu) is the mineral chalcopyrite (CuFeS2). How many kilograms of chalcopyrite must be mined to obtain 350 g of pure Cu? Express your answer to three significant figures and include the appropriate units.

Solution Steps

Chalcopyrite has the chemical formula \(\mathrm{CuFeS}_2\). To find the molar mass, we sum the molar masses of its constituent elements:

• Copper (Cu): \(63.55 \, \text{g/mol}\)
• Iron (Fe): \(55.85 \, \text{g/mol}\)
• Sulfur (S): \(32.07 \, \text{g/mol}\)

The molar mass of chalcopyrite is:

\[ 63.55 + 55.85 + 2 \times 32.07 = 183.55 \, \text{g/mol} \]

We need to obtain \(350 \, \text{g}\) of pure copper. First, calculate the moles of copper:

\[ \text{Moles of Cu} = \frac{350 \, \text{g}}{63.55 \, \text{g/mol}} \approx 5.507 \, \text{mol} \]

Since each mole of chalcopyrite contains one mole of copper, the moles of chalcopyrite required are the same as the moles of copper:

\[ \text{Moles of chalcopyrite} = 5.507 \, \text{mol} \]

Convert the moles of chalcopyrite to mass using its molar mass:

\[ \text{Mass of chalcopyrite} = 5.507 \, \text{mol} \times 183.55 \, \text{g/mol} \approx 1011.8 \, \text{g} \]

Convert grams to kilograms:

\[ 1011.8 \, \text{g} = 1.0118 \, \text{kg} \]

Final Answer