Question

what is the minimum mass of chalcopyrite (cufes₂), a copper ore, from which 1.0 kg of pure copper could be extracted? be sure your answer has a unit symbol, if necessary, and is rounded to the correct number of significant digits.

Explanation:

Step1: Calculate molar masses

The molar mass of $Cu$ is $M_{Cu}=63.55\ g/mol$. The molar mass of $CuFeS_{2}$ is $M_{CuFeS_{2}}=63.55 + 55.85+2\times32.07=183.52\ g/mol$.

Step2: Determine mole - ratio

In $CuFeS_{2}$, there is 1 mole of $Cu$ per 1 mole of $CuFeS_{2}$, so the mole - ratio of $Cu$ to $CuFeS_{2}$ is 1:1.

Step3: Calculate moles of $Cu$

Given the mass of $Cu$, $m_{Cu}=1.0\ kg = 1000\ g$. The number of moles of $Cu$, $n_{Cu}=\frac{m_{Cu}}{M_{Cu}}=\frac{1000\ g}{63.55\ g/mol}\approx15.74\ mol$.

Step4: Calculate moles of $CuFeS_{2}$

Since the mole - ratio of $Cu$ to $CuFeS_{2}$ is 1:1, $n_{CuFeS_{2}} = n_{Cu}=15.74\ mol$.

Step5: Calculate mass of $CuFeS_{2}$

The mass of $CuFeS_{2}$, $m_{CuFeS_{2}}=n_{CuFeS_{2}}\times M_{CuFeS_{2}}=15.74\ mol\times183.52\ g/mol\approx2889\ g = 2.9\ kg$ (rounded to 2 significant digits).

Answer:

$2.9\ kg$