Balance the following redox reactions using the oxidation number and ion-electron method:
$(1) H_2S + Fe^{3+} \to Fe^{2+} + S + H^{+}$
$(2) Cu + NO_3^{-} \to Cu^{2+} + NO_2$
$(3) Sn + NO_3^{-} + H^{+} \to Sn^{2+} + NH_4^{+} + H_2O$
$(4) As + NO_3^{-} + H^{+} \to AsO_4^{3-} + NO_2 + H_2O$

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$(1) H_2S + 2Fe^{3+} \to 2Fe^{2+} + S + 2H^{+}$
$(2) Cu + 2NO_3^{-} + 4H^{+} \to Cu^{2+} + 2NO_2 + 2H_2O$
$(3) 4Sn + NO_3^{-} + 10H^{+} \to 4Sn^{2+} + NH_4^{+} + 3H_2O$
$(4) As + 5NO_3^{-} + 2H_2O \to AsO_4^{3-} + 5NO_2 + 4H^{+}$

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