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 of copper.
Be sure your answer has a unit symbol, if needed, and is rounded to significant digits.
To calculate the mass of copper(I) sulfide required to make a certain amount of copper, we need to work backwards from the desired amount of copper.
Let's assume we want to make 1 gram of copper (Cu).
Step 1: Calculate the mass of copper(I) oxide (Cu2O) formed in the second step.
From the balanced equation, we know that 2 moles of Cu2O are formed for every 2 moles of Cu.
The molar mass of Cu2O is 143.1 g/mol.
So, the mass of Cu2O formed is (2/2) x 143.1 g/mol = 143.1 g.
Step 2: Calculate the mass of Cu2O required to get 143.1 g of Cu2O, taking into account the yield of the second step.
Since the second step has a yield of 93%, the actual mass of Cu2O required would be (143.1 g) / (0.93) = 153.9 g.
Step 3: Calculate the mass of copper(I) sulfide (Cu2S) required to get 153.9 g of Cu2O, taking into account the yield of the first step.
Since the first step has a yield of 65%, the actual mass of Cu2S required would be (153.9 g) / (0.65) = 237.2 g.
Therefore, to make 1 gram of copper, approximately 237.2 grams of copper(I) sulfide is required.