# How to balance the reaction equation between copper (I) sulfide and nitric acid?

What is the sum of stoichiometric coefficients of redox reaction: $$\ce{Cu2S + HNO3 -> S + NO2 + Cu(NO3)2 + H2O}$$?

This exercise is from a multiple choice exam. I have balanced the equation: $$\ce{1 Cu2S + 4 HNO3 -> 1 S + 2 NO2 + 1 Cu(NO3)2 + 2 H2O.}$$

Therefore I have calculated the sum of coefficients as $$\sum a = 11$$. This has not been offered as an answer and the correct answer is 20.

• The exact equation is : $\ce{Cu2S + 8 HNO3 -> 2 Cu(NO3)2 + 4 NO2 + S + 4 H2O}$ May 16 at 12:55
• It'd be beneficial if you show how you balanced the equation. That way we'd see where you make the error. May 16 at 14:29
• At first glance, your $\ce{Cu}$ is not balanced. May 16 at 15:24

$$\ce{Cu2S + HNO3 -> S + NO2 + Cu(NO3)2 + H2O}$$

Let's balance this reaction using the half-reaction method.

The oxidation half reaction (O.H.R) would be:

$$\ce{\overset{+1}{Cu}_2\overset{-2}{S} -> 2Cu^2+ + S^0 + 4e-}\tag{O.H.R}\label{ohr}$$

The reduction half reaction (R.H.R) here is:

$$\ce{H\overset{+5}{N}O3 +e- -> \overset{+4}{N}O2} \tag{R.H.R}\label{rhr}$$

The final reaction would be $$4\times\eqref{rhr} + 1\times\eqref{ohr}$$.

Therefore the reaction would be partially balanced as:

$$\ce{Cu2S + 4HNO3 -> 2 Cu^2+ + S + 4NO2}$$

Now, we have $$\ce{Cu(NO3)2}$$ and not $$\ce{Cu^2+}$$, so we need to add the 4 more nitrate ions which implies 4 more molecules of $$\ce{HNO3}$$

So now, we have the equation as:

$$\ce{Cu2S + 8HNO3 -> 2 Cu(NO3)2 + S + 4NO2}$$

Now, we balance the hydrogens and oxygens, the left has 8 hydrogens and 24 oxygens, whereas the right has no hydrogens and 20 oxygens. Therefore, we need to add 4 water molecules to the right. Therefore, the final reaction becomes:

$$\ce{Cu2S + 8 HNO3 -> S + 4 NO2 + 2Cu(NO3)2 + 4 H2O}$$

Now, $$\sum a = 1 + 8 + 1 + 4 + 2 + 4 = 20$$ and not 23.

• RHR = right hand reaction? OHR = other hand reaction? Use \label{something} and \eqref{something} to make clear what you mean. May 19 at 22:18
• @Martin-マーチン label{} and \eqref{} seems to break in my answer when it is displayed, i've modified the answer to fix the issues you have pointed out. May 20 at 2:15
• Works like a charm; MathJax usually requires an update/refresh though. May 20 at 18:26