There are two steps in the extraction of copper metal from chalcocite, a copper ore. In the first step, copper(I) sulfide and oxygen react to form copper(I) oxide and sulfur dioxide:
2Cu2S(s) + 3O2(g) --> 2Cu2O(s)+ 2SO2(g)
In the second step, copper(I) oxide and carbon react to form copper and carbon monoxide:
Cu2O(s) + C(s) --> 2Cu(s) + CO(g)
Suppose the yield of the first step is 65% and the yield of the second step is 93%. Calculate the mass of copper(I) sulfide required to make 6.0 kg of copper.
Be sure your answer has a unit symbol, if needed, and is rounded to 2 significant digits.
First, we need to calculate the moles of copper produced in the second step. We can use the formula:
moles of Cu = mass / molar mass
The molar mass of copper is 63.55 g/mol.
moles of Cu = 6000 g / 63.55 g/mol = 94.38 mol
Next, we need to calculate the moles of copper(I) oxide produced in the second step. According to the balanced equation, 2 moles of copper(I) oxide are formed for every 1 mole of copper.
moles of Cu2O = (94.38 mol * 2) / 1 = 188.76 mol
Since the yield of the second step is given as 93%, we need to adjust the moles of copper(I) oxide accordingly.
Adjusted moles of Cu2O = 188.76 mol * 0.93 = 175.47 mol
According to the balanced equation, 2 moles of copper(I) oxide are formed for every 2 moles of copper(I) sulfide.
moles of Cu2S = moles of Cu2O = 175.47 mol
Finally, we can calculate the mass of copper(I) sulfide required using its molar mass. The molar mass of copper(I) sulfide is 159.15 g/mol.
mass of Cu2S = moles of Cu2S * molar mass = 175.47 mol * 159.15 g/mol = 27.92 kg
Therefore, the mass of copper(I) sulfide required to make 6.0 kg of copper is 27.92 kg (rounded to 2 significant digits).