Answer:
The net chemical equation is:
[tex]2Cu_2S + 3O_2 + 2C -> 2SO_2 + 2CO + 4Cu[/tex]
Explanation:
Condictions for extraction of copper metal allow the reaction ocurrs.
First step yield 2 moles of [tex]Cu_2O[/tex], that later reacts with C, to poduce the copper metal.
Necessarily, reactions has to be balanced to know the proportion of each element.
In the first step oxygen (O2) replace sulfur (S), yielding sulfur dioxide and copper(I) oxide:
[tex]2Cu_2S + 3O_2 -> 2Cu_2O + 2SO_2\\[/tex]
Next, copper(I) oxide reacts with carbon (C), yielding copper (Cu) and carbon monoxide:
[tex]Cu_2O + C -> 2Cu + CO[/tex]
At the end, to complete the net chemical reaction, it is necessary multiply second step for 2, since it is obtained two moles of [tex]Cu_2O[/tex] from the first step. Then, we can sum both steps, reminding that species present in both terms are canceled.
[tex]2Cu_2S + 3O_2 -> 2Cu_2O + 2SO_2\\2Cu_2O + 2C -> 4Cu + 2CO\\2Cu_2S+ 3O_2 + 2C -> 2SO_2 + 2CO + 4Cu[/tex]