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:
In the second step, copper(I) oxide and carbon react to form copper and carbon monoxide:
Suppose the yield of the first step is and the yield of the second step is . 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.
First, we need to calculate the mass of copper(I) oxide produced in the first step. To do this, we can use the molar mass of copper(I) oxide (Cu2O) to convert from moles to grams:
Mass of copper(I) oxide = (yield of the first step) × (molar mass of copper(I) oxide)
Next, we need to calculate the mass of copper(I) sulfide required to produce that amount of copper(I) oxide. Since the reaction between copper(I) sulfide (Cu2S) and oxygen (O2) is in a 1:1 molar ratio to produce copper(I) oxide, we can use the molar mass of copper(I) sulfide to convert from grams to moles:
Moles of copper(I) sulfide = (mass of copper(I) oxide) × (1 mol of Cu2S / molar mass of Cu2S)
Finally, we need to convert the moles of copper(I) sulfide to grams using the molar mass of copper(I) sulfide:
Mass of copper(I) sulfide = (moles of copper(I) sulfide) × (molar mass of copper(I) sulfide)
Note: To find the molar mass of copper(I) sulfide and copper(I) oxide, you can look up their atomic masses on the periodic table:
Cu2S: copper (Cu) has a molar mass of 63.55 g/mol, and sulfur (S) has a molar mass of 32.07 g/mol.
Cu2O: copper (Cu) has a molar mass of 63.55 g/mol, and oxygen (O) has a molar mass of 16.00 g/mol.