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I need to balance the following reaction:

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

I assigned all oxidation numbers:

$$\ce{\overset{0}{Zn} + \overset{+1}{H}\overset{+5}{N}\overset{-2}{O_3}\longrightarrow \overset{2+}{Zn}(\overset{+5}{N}\overset{-2}{O_3})2 +\overset{-3}{N}\overset{+1}{H_4}\overset{+5}{N}\overset{-2}{O_3} +\overset{+1}{H2}\overset{-2}{O}},$$

but I'm having troubles finding the half reactions. I know

$$\ce{Zn -> Zn^{2+} + 2 e-}$$

is one half reaction, but what about the other? Since ammonium nitrate has nitrogen atoms in two different oxidation states, what do I do with them? Do I add them to see if the nitrogen is or it is not balanced?

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    $\begingroup$ Think a bit: none of the hydrogens or oxygens change oxidation numbers. But some (not all, obviously) of the nitrogens drop from +5 to -3 in oxidation numbers. Those are in the ammonium ions. $\endgroup$
    – Ed V
    Apr 19 at 19:06
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    $\begingroup$ You just need to know that 4*2=1*8, so 4 Zn for 1 ammonium. That simple. $\endgroup$
    – Poutnik
    Apr 20 at 2:47
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The oxidation state of $\ce{Zn}$ as calculated by you is incorrect. The correct oxidation state of $\ce{Zn}$ is $+2$ as it is associated with two mono negatively charged $\ce{NO3-}$ ions.

Thus the unbalanced reaction with correct oxidation states would be:

$$\ce{\overset{0}{Zn} + \overset{+1}{H}\overset{+5}{N}\overset{-2}{O_3}\longrightarrow \overset{+2}{Zn}(\overset{+5}{N}\overset{-2}{O_3})2 +\overset{-3}{N}\overset{+1}{H_4}\overset{+5}{N}\overset{-2}{O_3} +\overset{+1}{H2}\overset{-2}{O}} $$

Now the half-cell reactions are as follows: $$ \ce{Zn -> Zn^{2+} + 2e-}\\ \ce{NO3- + 10H+ + 8e- -> NH4+ + 3H2O}\\ $$

Thus the balanced iconic reaction would be:

$$\ce{4Zn + NO3- + 10H+ -> 4Zn^{2+} + NH4+ + 3H2O}\\\\$$

Now adding nine $\ce{NO3-}$ spectator ions to the ionic reaction gives us the standard molecular reaction.

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

What did you learn from this?

Always try to write the half-cell reaction in ionic form and only involve the ions which undergo oxidation state change. Don't bother yourself with the spectator ions at first. After you balance the equation in an ionic form adjust it to the molecular form by adding relevantly needed ions. Identify the oxidizing and the reducing species is the key.

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