Question 3.17: Writing an Overall Equation for a Reaction Sequence Problem ......

Plan To obtain the overall equation, we write the individual equations in sequence, adjust coefficients to cancel the common substance (or substances), and add the equations together. In this case, only Cu_2O appears as a product in one equation and a reactant in the other, so it is the common substance.
Solution Writing the individual balanced equations:

   2Cu_2S(s)  +  3O_2(g)  ⟶  2Cu_2O(s)  +  2SO_2(g)      [equation 1; see Sample Problem 3.14]
     Cu_2O(s)  +  C(s)  ⟶  2Cu(s)  +  2CO(g)         [equation 2]

Adjusting the coefficients: Since 2 mol of Cu_2O form in equation 1 but 1 mol of Cu_2O reacts in equation 2, we double all the coefficients in equation 2 to use up the Cu_2O:

          2Cu_2S(s)  +  3O_2(g)  ⟶  2Cu_2O(s)  +  2SO_2(g)       [equation 1]
            2Cu_2O(s)  +  2C(s)  ⟶  4 Cu(s)  +  2CO(g)         [equation 2, doubled]

Adding the two equations and canceling the common substance: We keep the reactants of both equations on the left and the products of both equations on the right:

    2Cu_2S(s)  +  3 O_2(g)  +  \cancel{2Cu_2O(s)}  +  2C(s)  ⟶  \cancel{2Cu_2O(s)}  +  2 SO_2(g)  +  4Cu(s)  +  2 CO(g)
or,            2Cu_2S(s)  +  3O_2(g)  +  2C(s)  ⟶  2SO_2(g)  +  4Cu(s)  +  2CO(g)

Check Reactants (4 Cu, 2 S, 6 O, 2 C) ⟶ products (4 Cu, 2 S, 6 O, 2 C)

Comment 1. Even though Cu_2O does participate in the chemical change, it is not involved in the reaction stoichiometry. An overall equation may not show which substances actually react; for example, C(s) and Cu_2S(s) do not interact directly in this reaction sequence, even though both are shown as reactants.
2. The SO_2 formed in copper recovery contributes to acid rain, so chemists have devised microbial and electrochemical methods to extract metals without roasting sulfide ores. Such methods are examples of green chemistry, a topic discussed further at the end of this section.
3. These reactions were shown to explain how to obtain an overall equation. The actual extraction of copper is more complex, as you’ll see in Chapter 22.