Chapter 4, Problem 27P

The dissolution of copper sulfide in aqueous nitric acid is described by the following chemical equation:

$a\text{CuS}+b{\text{NO}}^{-}{}_{\text{3}}+{\text{cH}}^{+}\to dC{u}^2{}^{+}{\text{eSO}}^{\text{2}-}{}_{\text{4}}+f\text{NO}+{\text{gH}}_{\text{2}}\text{O}$

where the coefficients a, b, c, d, e, f, and gare the numbers of the various molecules participating in the reaction and are unknown. The unknown coefficients are determined by balancing each atom on left and right and then balancing the ionic charge. The resulting equations are:

$a=d,a=e,b=f,3b=4e+f+g,c=2g,-b+c=2d-2e$

There are seven unknowns and only six equations. A solution can still be obtained, however, by taking advantage of the fact that all the coefficients must be positive integers. Add a seventh equation by guessing a = 1 and solve the system of equations. The solution is valid if all the coefficients are positive integers. If this is not the case, take a= 2 and repeat the solution. Continue the process until all the coefficients in the solution are positive integers.