91Ó°ÊÓ

Redox reactions are essential processes in electrochemistry where electrons are transferred between chemical species. These reactions consist of two parts: oxidation and reduction. Oxidation refers to the loss of electrons, while reduction denotes the gain of electrons.
In the original exercise provided, we have two half-reactions. The first half-reaction involves the reduction of manganese ions from a trivalent state (\(\mathrm{Mn}^{3+} \)) to bivalent (\(\mathrm{Mn}^{2+} \)), signifying a gain of one electron. The second, when reversed, represents the oxidation process of forming \(\mathrm{MnO}_2\) from \(\mathrm{Mn}^{3+}\). Together, these half-reactions generate the complete redox reaction.

• Oxidation: \(\mathrm{Mn}^{3+}(aq) + 2 \mathrm{H}_2 \mathrm{O}(l) \rightarrow \mathrm{MnO}_2(s) + 4 \mathrm{H}^{+}(aq) + \mathrm{e}^{-} \)
• Reduction: \(\mathrm{Mn}^{3+}(aq) + \mathrm{e}^{-} \rightarrow \mathrm{Mn}^{2+}(aq) \)

Understanding redox reactions requires examining electrons' movement and ensuring the balance of both mass and charge. In practice, this balance is achieved by combining the half-reactions such that the electrons on both sides cancel out. This results in the formation of new products without any unaccounted electrons.

Standard electrode potential (\(E^{\circ}\)) is a measure of the inherent potential difference of a half-reaction under standard conditions, which include a temperature of 25°C, a concentration of 1 M for solutions, and a pressure of 1 atm for gases. The \(E^{\circ}\) values indicate the tendency of a species to lose or gain electrons.
In electrochemical cells, \(E^{\circ}\) is used to determine the voltage of the cell. For the given half-reactions, the standard electrode potentials are provided as \(1.54\, \mathrm{V}\) for the reduction of \(\mathrm{Mn}^{3+} \,\mathrm{to} \, \mathrm{Mn}^{2+} \), and \(0.95\, \mathrm{V}\) for the reduction of \(\mathrm{MnO}_2\).
When reversing the second half-reaction to facilitate oxidation, the sign of \(E^{\circ}\) is changed. In this case, it becomes \(-0.95\, \mathrm{V}\), illustrating that energy is required for oxidation. The cell potential for the overall reaction is found by adding the standard electrode potentials: i.e., \(E^{\circ}_{cell} = 1.54\, \mathrm{V} + (-0.95\, \mathrm{V}) = 0.59\, \mathrm{V}\).
This combined potential reveals the energy changes as electrons are transferred in the redox reaction.

The spontaneity of a chemical reaction in electrochemistry depends on the overall standard cell potential \(E^{\circ}_{cell}\). A reaction is deemed spontaneous if \(E^{\circ}_{cell}\) is positive. This implies that the reaction can proceed without any external energy input.
In the context of the problem, we compute and examine the overall \(E^{\circ}_{cell}\) as \(0.59\, \mathrm{V}\). A positive value like this indicates a spontaneous reaction under standard conditions.

• Positive \(E^{\circ}_{cell}\) → Spontaneous reaction
• Negative \(E^{\circ}_{cell}\) → Non-spontaneous reaction

Therefore, because the calculated potential is positive, we conclude that the redox reaction involving the formation of \(\mathrm{Mn}^{2+}\) and \(\mathrm{MnO}_2\) from \(\mathrm{Mn}^{3+}\) proceeds spontaneously, highlighting its feasibility without external forces.