Write the balanced chemical equation for the following reaction:
$Cl_2O_7$ in the gaseous state combines with an aqueous solution of hydrogen peroxide $(H_2O_2)$ in an acidic medium to give chlorite ion $(ClO_2^-)$ and oxygen gas $(O_2)$. (Balance by the ion-electron method)

(N/A) Step $1$: Identify the oxidation and reduction half-reactions.
Reduction Half-Reaction $(R.H.E.)$: $Cl_2O_7(g) \rightarrow ClO_2^-(aq)$
Oxidation Half-Reaction $(O.H.E.)$: $H_2O_2(aq) \rightarrow O_2(g)$
Step $2$: Balance atoms and charges in each half-reaction in an acidic medium.
$R.H.E.$: $Cl_2O_7 + 6H^+ + 8e^- \rightarrow 2ClO_2^- + 3H_2O$
$O.H.E.$: $H_2O_2 \rightarrow O_2 + 2H^+ + 2e^-$
Step $3$: Multiply the $O.H.E.$ by $4$ to equalize the number of electrons $(8e^-)$.
$4H_2O_2 \rightarrow 4O_2 + 8H^+ + 8e^-$
Step $4$: Add the two half-reactions and simplify.
$Cl_2O_7(g) + 6H^+(aq) + 8e^- + 4H_2O_2(aq) \rightarrow 2ClO_2^-(aq) + 3H_2O(l) + 4O_2(g) + 8H^+(aq) + 8e^-$
Final Balanced Equation:
$Cl_2O_7(g) + 4H_2O_2(aq) \rightarrow 2ClO_2^-(aq) + 4O_2(g) + 3H_2O(l) + 2H^+(aq)$