# Finding the sum of coefficients of the reaction

What is the sum of the coefficients $$(a + b + c)$$ in the following reaction?

$$\ce{x Zn + y HNO3} -> {a Zn(NO3)2 + b H2O + c NH4NO3}$$

Here if the equation is balanced we get 1 mol of $$\ce{Zn}$$ and 4 mol of $$\ce{HNO3}$$. As $$x + y = a + b + c$$ we get sum of coefficients $$a + b + c = 5$$. According to me, this is the correct answer, but in the actual answer key the answer is 8.

I may be wrong, but can someone help me clarify the right answer?

• So for the nonsensical reaction what is your balanced chemical formula? In other words the Zn, H, N, and O atoms have to balance on both sides of the reaction. // Obviously $x = a$, so $$\ce{aZn + yHNO3 -> aZn(NO3)2 + bH2O + cNH4NO3}$$
– MaxW
Apr 27 '19 at 18:45
• It's 4 ,10,4,1,3 . I was wrong earlier . The answer is 4+3+1 which is eight Apr 27 '19 at 18:56
• Curious, did you pound your head on the wall guessing, or did you use the set of linear equations for the atoms?
– MaxW
Apr 27 '19 at 19:02
• Linear equations Apr 27 '19 at 19:19
• I sincerely don't understand why the question is downvoted. The question itself looks reasonable, the reaction is chemically correct, and OP demonstrated their efforts and thoughts (partially in the comments, but still). Apr 27 '19 at 22:17

Linear equations aside, note that this is a redox reaction and you can use half-reactions method as well (BTW the reaction looks fine to me):

$$\ce{x \overset{0}{Zn} + y H\overset{+5}{N}O3 -> a \overset{+2}{Zn}(NO3)2 + b H2O + c \overset{-3}{N}H4NO3}$$

\begin{align} \ce{\overset{+5}{N} + 8 e- &→ \overset{-3}{N}} \tag{red}\\ \ce{\overset{0}{Zn} &→ \overset{+2}{Zn} + 2 e-} &|\cdot 4 \tag{ox}\\ \hline \ce{4 \overset{0}{Zn} + \overset{+5}{N} &→ 4 \overset{+2}{Zn} + \overset{-3}{N}} \tag{redox} \end{align}

So that the complete balanced equation is

$$\ce{4 Zn + 10 HNO3 -> 4 Zn(NO3)2 + 3 H2O + NH4NO3}$$

leaving $$a = 4$$, $$b = 3$$, $$c = 1$$ and the sum $$a + b + c = 4 + 3 + 1 = 8$$.

• I don't understand why it was commented that this is a nonsensical reaction? Nitrate ion can be easily reduced to ammonium ions. Apr 28 '19 at 5:36
• @M.Farooq You should ask the one who commented. As I mentioned in the comments and in answer itself the reaction looks completely fine to me. Apr 28 '19 at 5:37

What is the sum of the coefficients $$(a + b + c)$$ in the following reaction?

$$\ce{x Zn + y HNO3 -> a Zn(NO3)2 + b H2O + c NH4NO3}$$

This is a redox reaction. During OP's comments, it was clear that he/her got the correct answer, but it wasn't clear that OP understand this is a redox reaction. To balance the equation, it may be better work on with two relevant half reactions. It is also easier to work with ionic equations and add counter ions at the last step. First consider reduction half reaction: $$\ce{NO3- + d e- -> NH4+}$$ Now, balance $$\ce{O}$$ with $$\ce{H2O}$$, $$\ce{H}$$ with $$\ce{H+}$$ (since this is in acidic medium), and lastly, charge with $$\ce{e-}$$ (now you see $$d=8$$). $$\ce{NO3- + 10 H+ + 8e- -> NH4+ + 3H2O} \:\text{---} (1)$$ Now, consider oxidation half reaction: $$\ce{Zn -> Zn^2+ + 2 e- } \:\text{---} (2)$$ Now, solve equation (1) and (2) by cancelling the electrons: $$\ce{4Zn + NO3- + 10 H+ -> 4 Zn^2+ + NH4+ + 3H2O}$$ Now, to balance by counter ion, add $$\ce{9NO3-}$$ to both side of last equation so it keep balanced: $$\ce{4Zn + NO3- + 10 H+ + 9NO3- -> 4 Zn^2+ + NH4+ + 3H2O + 9NO3-}$$ Rewrite the equation with tight pair ions: $$\ce{4Zn + 10 HNO3 -> 4 Zn(NO3)2 + NH4NO3 + 3H2O }$$ Now you see: $$x=4; y=10; a=4; b=3;$$ and $$c=1$$. $$\therefore a+b+c=4+3+1=8$$