For each of the following balanced oxidation-reduction...

For each of the following balanced oxidation-reduction reactions, (i) identify the oxidation numbers for all the elements in the reactants and products and (ii) state the total number of electrons transferred in each reaction. (a) $14 \mathrm{H}^{+}(a q)+2 \mathrm{Mn}^{2+}(a q)+5 \mathrm{NaBiO}_{3}(s)$ $\quad \longrightarrow 7 \mathrm{H}_{2} \mathrm{O}(l)+2 \mathrm{MnO}_{4}^{-}+5 \mathrm{Bi}^{3+}(a q)+5 \mathrm{Na}^{+}(a q)$ (b) $2 \mathrm{KMnO}_{4}(a q)+3 \mathrm{Na}_{2} \mathrm{SO}_{3}(a q)+\mathrm{H}_{2} \mathrm{O}(l)$ $\quad \longrightarrow 2 \mathrm{MnO}_{2}(s)+3 \mathrm{Na}_{2} \mathrm{SO}_{4}(a q)+2 \mathrm{KOH}(a q)$ (c) $\mathrm{Cu}(s)+2 \mathrm{AgNO}_{3}(a q) \longrightarrow 2 \mathrm{Ag (s)+\mathrm{Cu}\left(\mathrm{NO}_{3}\right)_{2}(a q)$

For each of the following balanced oxidation-reduction reactions, (i) identify the oxidation numbers for all the elements in the reactants and products and (ii) state the total number of electrons transferred in each reaction.
(a) $14 \mathrm{H}^{+}(a q)+2 \mathrm{Mn}^{2+}(a q)+5 \mathrm{NaBiO}_{3}(s)$ $\quad \longrightarrow 7 \mathrm{H}_{2} \mathrm{O}(l)+2 \mathrm{MnO}_{4}^{-}+5 \mathrm{Bi}^{3+}(a q)+5 \mathrm{Na}^{+}(a q)$
(b) $2 \mathrm{KMnO}_{4}(a q)+3 \mathrm{Na}_{2} \mathrm{SO}_{3}(a q)+\mathrm{H}_{2} \mathrm{O}(l)$ $\quad \longrightarrow 2 \mathrm{MnO}_{2}(s)+3 \mathrm{Na}_{2} \mathrm{SO}_{4}(a q)+2 \mathrm{KOH}(a q)$
(c) $\mathrm{Cu}(s)+2 \mathrm{AgNO}_{3}(a q) \longrightarrow 2 \mathrm{Ag (s)+\mathrm{Cu}\left(\mathrm{NO}_{3}\right)_{2}(a q)$

Key Concepts

Oxidation Numbers

Oxidation numbers (or oxidation states) are assigned to atoms in a compound or ion to reflect the hypothetical charge the atom would have if all bonds were completely ionic. This concept is essential for determining which species are oxidized and which are reduced in a redox reaction. It involves following standard rules, such as assigning oxygen usually -2, hydrogen +1 (with exceptions), and the overall charge of a molecule or ion being the sum of the oxidation numbers of its atoms.

Redox Reactions

Redox (oxidation-reduction) reactions are a class of chemical reactions involving the transfer of electrons between chemical species. In these reactions, one species undergoes oxidation (loss of electrons) while another undergoes reduction (gain of electrons). Understanding this concept is crucial for analyzing the changes in oxidation numbers for each element involved in the reaction.

Electron Transfer

The electron transfer concept quantifies the number of electrons lost by the oxidized species (and gained by the reduced species) in a redox reaction. Determining the total number of electrons transferred is important for verifying the conservation of charge in the reaction and for understanding the extent of oxidation and reduction processes.

Balancing Redox Reactions and the Half-Reaction Method

Balancing redox reactions requires ensuring that both mass and charge are conserved. The half-reaction method facilitates this by separately balancing the oxidation and reduction processes before combining them. This method involves identifying the change in oxidation numbers, balancing the atoms (often using water, hydrogen ions, or hydroxide ions, depending on the reaction medium), and finally ensuring that the electrons lost in the oxidation half equal the electrons gained in the reduction half.

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