Given the following reduction half-reactions:
Fe³⁺(aq) + e^- → Fe²⁺(aq) E°_red = +0.77 V
S₂O₆^2-(aq) + 4 H⁺(aq) + 2 e^- → 2 H₂SO₃(aq) E°_red = +0.60 V
N₂O(g) + 2 H⁺(aq) + 2 e^- → N₂(g) + H₂O(l) E°_red = -1.77 V
VO²⁺(aq) + 2 H⁺(aq) + e^- → VO²⁺ + H₂O(l) E°_red = +1.00 V
(a) Write balanced chemical equations for the oxidation of Fe²⁺(aq) by S₂O₆^2-(aq), by N₂O(aq), and by VO²⁺(aq).

Verified step by step guidance

1. Identify the reduction half-reactions given in the problem and their respective standard reduction potentials (E°).
2. Determine the oxidation half-reaction for Fe^{2+} by reversing the given reduction half-reaction: Fe^{2+} \(\rightarrow\) Fe^{3+} + e^{-}.
3. For each oxidizing agent (S_2O_6^{2-}, N_2O, VO_2^{+}), write the corresponding reduction half-reaction as given in the problem.
4. Combine the oxidation half-reaction of Fe^{2+} with each reduction half-reaction to form a balanced redox equation. Ensure that the number of electrons lost in the oxidation half-reaction equals the number of electrons gained in the reduction half-reaction.
5. Balance the overall chemical equation for each reaction by ensuring that the number of atoms and the charge are balanced on both sides of the equation.

Key Concepts

Oxidation-Reduction Reactions

Oxidation-reduction (redox) reactions involve the transfer of electrons between species, where oxidation refers to the loss of electrons and reduction refers to the gain of electrons. In these reactions, the species that loses electrons is oxidized, while the one that gains electrons is reduced. Understanding the roles of oxidizing and reducing agents is crucial for balancing redox equations.

Standard Electrode Potentials (E°)

Standard electrode potentials (E°) are measured under standard conditions and indicate the tendency of a species to be reduced. A higher E° value means a greater likelihood of reduction occurring. In redox reactions, comparing the E° values of the half-reactions helps determine which species will oxidize and which will reduce, guiding the balancing of the overall reaction.

Balancing Redox Reactions

Balancing redox reactions involves ensuring that both mass and charge are conserved. This typically requires separating the reaction into half-reactions for oxidation and reduction, balancing each for atoms and charge, and then combining them. The use of coefficients and the adjustment of electrons transferred are essential steps in achieving a balanced equation.