Question

Balance each of the following oxidation-reduction reactions, which take place in acidic solution, by using the "half-reaction" method. a. \(\mathrm{I}^{-}(a q)+\mathrm{MnO}_{4}^{-}(a q) \rightarrow \mathrm{I}_{2}(a q)+\mathrm{Mn}^{2+}(a q)\) b. \(\mathrm{S}_{2} \mathrm{O}_{8}^{2-}(a q)+\mathrm{Cr}^{3+}(a q) \rightarrow \mathrm{SO}_{4}^{2-}(a q)+\mathrm{Cr}_{2} \mathrm{O}_{7}^{2-}(a q)\) c. \(\mathrm{BiO}_{3}^{-}(a q)+\mathrm{Mn}^{2+}(a q) \rightarrow \mathrm{Bi}^{3+}(a q)+\mathrm{MnO}_{4}^{-}(a q)\)

Short answer

The balanced equations for the reactions are: (a) \(10I^-(aq) + 2MnO_4^-(aq) + 16H^+(aq) \rightarrow 5I_2(aq) + 2Mn^{2+}(aq) + 8H_2O(l)\) (b) \(2S_2O_8^{2-}(aq) + 6Cr^{3+}(aq) + 10H_2O(l) \rightarrow 4SO_4^{2-}(aq) + 3Cr_2O_7^{2-}(aq) + 20H^+(aq)\) (c) \(2BiO_3^-(aq) + 3Mn^{2+}(aq) + 7H_2O(l) \rightarrow 2Bi^{3+}(aq) + 3MnO_4^-(aq) + 14H^+(aq)\)

Step-by-step solution

Write the oxidation and reduction half-reactions

: Oxidation half-reaction: \(I^{-}(aq) \rightarrow I_{2}(aq)\) Reduction half-reaction: \(MnO_{4}^{-}(aq) \rightarrow Mn^{2+}(aq)\)

Balance the atoms other than oxygen and hydrogen in each half-reaction

: Oxidation half-reaction: \(2I^{-}(aq) \rightarrow I_{2}(aq)\) Reduction half-reaction: No changes needed, as the manganese is already balanced.

Balance the oxygen atoms in each half-reaction by adding water molecules

: Oxidation half-reaction: No changes needed, as there are no oxygen atoms. Reduction half-reaction: \(MnO_{4}^{-}(aq) \rightarrow Mn^{2+}(aq) + 4H_2O(l)\)

Balance the hydrogen atoms in each half-reaction by adding hydrogen ions

: Oxidation half-reaction: No changes needed, as there are no hydrogen atoms. Reduction half-reaction: \(MnO_{4}^{-}(aq) + 8H^{+}(aq) \rightarrow Mn^{2+}(aq) + 4H_2O(l)\)

Balance the charges in each half-reaction by adding electrons

: Oxidation half-reaction: \(2I^{-}(aq) \rightarrow I_{2}(aq) + 2e^{-}\) Reduction half-reaction: \(MnO_{4}^{-}(aq) + 8H^{+}(aq) + 5e^{-} \rightarrow Mn^{2+}(aq) + 4H_2O(l)\)

Make the number of electrons the same in each half-reaction and combine the half-reactions

: Oxidation half-reaction: \(2I^{-}(aq) \rightarrow I_{2}(aq) + 2e^{-}\) (x5) Total: \(10I^{-}(aq) \rightarrow 5I_{2}(aq) + 10e^{-}\) Reduction half-reaction: \(MnO_{4}^{-}(aq) + 8H^{+}(aq) + 5e^{-} \rightarrow Mn^{2+}(aq) + 4H_2O(l)\) (x2) Total: \(2MnO_{4}^{-}(aq) + 16H^{+}(aq) + 10e^{-} \rightarrow 2Mn^{2+}(aq) + 8H_2O(l)\) Combined Reaction: \(10I^{-}(aq) + 2MnO_{4}^{-}(aq) + 16H^{+}(aq) \rightarrow 5I_{2}(aq) + 2Mn^{2+}(aq) + 8H_2O(l)\) The balanced equation for the reaction (a) is: \(10I^-(aq) + 2MnO_4^-(aq) + 16H^+(aq) \rightarrow 5I_2(aq) + 2Mn^{2+}(aq) + 8H_2O(l)\) Balance the remaining reactions (b and c) using the same method.

Key concepts

Half-Reaction Method

When balancing redox reactions, the half-reaction method helps organize the oxidation and reduction parts separately. This method is particularly useful in breaking down complex reactions into simpler individual steps.
The procedure involves the following steps:

• Identify the oxidation and reduction components: Determine which species undergoes oxidation (loss of electrons) and which one undergoes reduction (gain of electrons).
• Balance each half-reaction: Start by ensuring that the number of atoms, excluding oxygen and hydrogen, is the same on both sides of the half-reaction.
• Balance oxygens with water (H₂O): Add water molecules to balance oxygen atoms in each half-reaction.
• Balance hydrogens with hydrogen ions (H⁺): Use hydrogen ions to balance hydrogen atoms in the equation.
• Balance charge with electrons (e^-): Add electrons to one side of the half-reaction to equalize the charges on each side.
• Equalize electrons: Ensure that the number of electrons lost in the oxidation half-reaction equals the electrons gained in the reduction half-reaction, and then combine them.

This comprehensive approach not only helps in balancing complex redox equations but also provides a clear view of the redox processes occurring.

Balancing Chemical Equations

Balancing chemical equations is crucial for reliable predictions of reactions and their outcomes. It ensures that matter is neither created nor destroyed during a chemical reaction, abiding by the principle of conservation of mass.
Here’s a simple guide:

• Write the unbalanced equation: Start from the chemical formulas of the reactants and products.
• Count atoms of each element: Count the number of atoms for each element on both the reactant and product sides.
• Balance atoms one at a time: Choose an element to balance, and use coefficients to balance the number of atoms of this element on both sides.
• Iterate through elements: Repeat for all elements in the reaction. It's often useful to start with elements that appear in only one reactant and one product, saving complex molecules for last.
• Verify the balance: Re-check the equation to ensure that the same number of each type of atom appears on both sides.

This process might seem systematic, but it is essential for accurately describing what takes place in a chemical reaction. Sometimes multiple trials are needed to achieve the perfectly balanced equation, especially in complex reactions.

Acidic Solutions

Some redox reactions occur in acidic solutions, which influence the balancing process. Acidic solutions have an abundance of hydrogen ions (H⁺), which are crucial when balancing redox reactions, particularly with the half-reaction method.
Key points to remember:

• Presence of H⁺ ions: In acidic conditions, hydrogen ions are readily available to aid in balancing hydrogen atoms after balancing oxygen atoms with water.
• Affects equation coefficients: The availability of H⁺ ions may change how the equation coefficients are adjusted during balancing.
• Impacts redox reaction dynamics: Acidic environments can alter the ease and speed of redox reactions, influencing which species is oxidized or reduced.

When working in acidic solutions, balance the reaction using water to balance oxygen and then apply H⁺ to balance hydrogen atoms. Understanding these conditions leads to a more straightforward balancing process and a deeper grasp of reaction specifics.