Balance the following redox equations by the half-reaction...

Balance the following redox equations by the half-reaction method: (a) $\mathrm{H}_{2} \mathrm{O}_{2}+\mathrm{Fe}^{2+} \longrightarrow \mathrm{Fe}^{3+}+\mathrm{H}_{2} \mathrm{O}$ (in acidic solution) (b) $\mathrm{Cu}+\mathrm{HNO}_{3} \longrightarrow \mathrm{Cu}^{2+}+\mathrm{NO}+\mathrm{H}_{2} \mathrm{O}$ (in acidic solution) (c) $\mathrm{CN}^{-}+\mathrm{MnO}_{4}^{-} \longrightarrow \mathrm{CNO}^{-}+\mathrm{MnO}_{2}$ (in basic solution) (d) $\mathrm{Br}_{2} \longrightarrow \mathrm{BrO}_{3}^{-}+\mathrm{Br}^{-}$ (in basic solution) (e) $\mathrm{S}_{2} \mathrm{O}_{3}^{2-}+\mathrm{I}_{2} \longrightarrow \mathrm{I}^{-}+\mathrm{S}_{4} \mathrm{O}_{6}^{2-}$ (in acidic solution)

Balance the following redox equations by the half-reaction method:
(a) $\mathrm{H}_{2} \mathrm{O}_{2}+\mathrm{Fe}^{2+} \longrightarrow \mathrm{Fe}^{3+}+\mathrm{H}_{2} \mathrm{O}$ (in acidic solution)
(b) $\mathrm{Cu}+\mathrm{HNO}_{3} \longrightarrow \mathrm{Cu}^{2+}+\mathrm{NO}+\mathrm{H}_{2} \mathrm{O}$ (in acidic solution)
(c) $\mathrm{CN}^{-}+\mathrm{MnO}_{4}^{-} \longrightarrow \mathrm{CNO}^{-}+\mathrm{MnO}_{2}$ (in basic solution)
(d) $\mathrm{Br}_{2} \longrightarrow \mathrm{BrO}_{3}^{-}+\mathrm{Br}^{-}$ (in basic solution)
(e) $\mathrm{S}_{2} \mathrm{O}_{3}^{2-}+\mathrm{I}_{2} \longrightarrow \mathrm{I}^{-}+\mathrm{S}_{4} \mathrm{O}_{6}^{2-}$ (in acidic solution)

Key Concepts

Conservation of Mass and Charge

In any chemical reaction, the total mass and total charge must remain constant. When balancing redox equations using the half-reaction method, it is essential to ensure that both the number of atoms and the total charge are balanced in each half-reaction before they are recombined.

Half-Reaction Method

The half-reaction method involves breaking a redox equation into two separate equations—one for the oxidation process and one for the reduction process. Each half-reaction is balanced individually for atoms and charges, and then they are combined in such a way that the electrons cancel out, yielding the balanced overall reaction.

Balancing in Acidic and Basic Media

Balancing redox reactions varies with the medium in which the reaction occurs. In acidic solutions, H+ ions and water molecules are used to balance hydrogen and oxygen atoms, respectively. In basic solutions, OH– ions and water are used instead. Recognizing the reaction environment is crucial for selecting the proper balancing agents.

Redox Reactions

Redox reactions involve the transfer of electrons between species, where one species is oxidized (loses electrons) and another is reduced (gains electrons). This concept is central to understanding various chemical processes including corrosion, energy production, and metabolic pathways.

Oxidation Numbers

Oxidation numbers are assigned to atoms in molecules and ions to help track electron transfer during chemical reactions. By identifying changes in oxidation numbers, one can determine which substances are oxidized and which are reduced.

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