Complete and balance the following equations, and identify...

Complete and balance the following equations, and identify the oxidizing and reducing agents. Recall that the $\mathrm{O}$ atoms in hydrogen peroxide, $\mathrm{H}_{2} \mathrm{O}_{2}$, have an atypical oxidation state. (a) $\mathrm{NO}_{2}^{-}(a q)+\mathrm{Cr}_{2} \mathrm{O}_{7}^{2-}(a q)-\cdots$ $\mathrm{Cr}^{3+}(a q)+\mathrm{NO}_{3}^{-}(a q)$ (acidic solution) (b) $\mathrm{S}(s)+\mathrm{HNO}_{3}(a q) \rightarrow-\rightarrow \mathrm{H}_{2} \mathrm{SO}_{3}(a q)+\mathrm{N}_{2} \mathrm{O}(g)$ (acidic solution) (c) $\mathrm{Cr}_{2} \mathrm{O}_{7}^{2-}(a q)+\mathrm{CH}_{3} \mathrm{OH}(a q) \longrightarrow$ $\mathrm{HCO}_{2} \mathrm{H}(a q)+\mathrm{Cr}^{3+}(a q)$ (acidic solution) (d) $\mathrm{MnO}_{4}^{-}(a q)+\mathrm{Cl}^{-}(a q) \longrightarrow \mathrm{Mn}^{2+}(a q)+\mathrm{Cl}_{2}(a q)$ (acidic solution) (e) $\mathrm{NO}_{2}^{-}(a q)+\mathrm{Al}(s) \longrightarrow \mathrm{NH}_{4}{ }^{+}(a q)+\mathrm{AlO}_{2}^{-}(a q)$ (basic solution) (f) $\mathrm{H}_{2} \mathrm{O}_{2}(a q)+\mathrm{ClO}_{2}(a q) \longrightarrow \mathrm{ClO}_{2}^{-}(a q)+\mathrm{O}_{2}(g)$ (basic solution)

Complete and balance the following equations, and identify the oxidizing and reducing agents. Recall that the $\mathrm{O}$ atoms in hydrogen peroxide, $\mathrm{H}_{2} \mathrm{O}_{2}$, have an atypical oxidation state.
(a) $\mathrm{NO}_{2}^{-}(a q)+\mathrm{Cr}_{2} \mathrm{O}_{7}^{2-}(a q)-\cdots$
$\mathrm{Cr}^{3+}(a q)+\mathrm{NO}_{3}^{-}(a q)$ (acidic solution)
(b) $\mathrm{S}(s)+\mathrm{HNO}_{3}(a q) \rightarrow-\rightarrow \mathrm{H}_{2} \mathrm{SO}_{3}(a q)+\mathrm{N}_{2} \mathrm{O}(g)$
(acidic solution)
(c) $\mathrm{Cr}_{2} \mathrm{O}_{7}^{2-}(a q)+\mathrm{CH}_{3} \mathrm{OH}(a q) \longrightarrow$
$\mathrm{HCO}_{2} \mathrm{H}(a q)+\mathrm{Cr}^{3+}(a q)$ (acidic solution)
(d) $\mathrm{MnO}_{4}^{-}(a q)+\mathrm{Cl}^{-}(a q) \longrightarrow \mathrm{Mn}^{2+}(a q)+\mathrm{Cl}_{2}(a q)$
(acidic solution)
(e) $\mathrm{NO}_{2}^{-}(a q)+\mathrm{Al}(s) \longrightarrow \mathrm{NH}_{4}{ }^{+}(a q)+\mathrm{AlO}_{2}^{-}(a q)$
(basic solution)
(f) $\mathrm{H}_{2} \mathrm{O}_{2}(a q)+\mathrm{ClO}_{2}(a q) \longrightarrow \mathrm{ClO}_{2}^{-}(a q)+\mathrm{O}_{2}(g)$
(basic solution)

Key Concepts

Balancing Equations in Acidic and Basic Solutions

Balancing redox equations requires different approaches depending on whether the reaction occurs in an acidic or basic solution. In acidic conditions, H+ ions and water are used to balance hydrogen and oxygen atoms, while in basic conditions, OH? ions and water are employed. This adaptation ensures that both mass and charge are conserved in the final balanced equation.

Oxidizing Agent and Reducing Agent

In a redox reaction, the oxidizing agent is the species that accepts electrons and is therefore reduced, whereas the reducing agent is the species that donates electrons and is oxidized. Identifying these agents is crucial for understanding the direction of electron flow and the overall transformation in the reaction.

Half-Reactions Method

The half-reactions method is a systematic technique used to balance redox reactions by dividing the overall reaction into its oxidation and reduction components. Each half-reaction is balanced separately for atoms and charge, especially by adding H2O, H+, or OH? depending on the solution conditions, and then recombined to ensure that electrons are canceled out.

Oxidation States

Oxidation states or numbers assign a hypothetical charge to atoms in a compound, allowing chemists to track electron transfer during redox processes. They are particularly useful in identifying which species undergo oxidation (increase in oxidation state) or reduction (decrease in oxidation state), even when elements manifest unusual oxidation states in specific compounds.

Redox Reactions

Redox reactions involve a simultaneous process of oxidation and reduction, where one species loses electrons (oxidation) and another gains electrons (reduction). This electron transfer is the fundamental aspect of these reactions and underlies many chemical processes including energy generation and corrosion.

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