Question

Balance the following reaction in acidic aqueous solution: \(\left(\mathrm{ClO}^{-}_{3}\right)+\mathrm{Fe}^{2+} \rightarrow\left(\mathrm{Cl}^{-}\right)+\mathrm{Fe}^{3+}\)

Short answer

The balanced equation in acidic solution for the given reaction is: \(6\mathrm{Fe}^{2+} + \mathrm{ClO}_{3}^{-} + 6\mathrm{H}^{+} \rightarrow 6\mathrm{Fe}^{3+} + \mathrm{Cl}^{-} + 3\mathrm{H}_{2}\mathrm{O}\).

Step-by-step solution

Identify the Oxidation and Reduction Half-Reactions

In the given reaction, oxidation is occurring in the iron Fe(II) atom as it is being oxidized to Fe(III). This is accompanied by the reduction of the chlorate ion ClO3- to chloride ion Cl-. Therefore, the two half-reactions are: Oxidation: Fe²⁺→Fe³⁺ Reduction: ClO³⁻→ Cl⁻

Balance Atoms other than H and O

Balancing the atoms (except H and O) in each of these half reaction gives: Oxidation: Fe²⁺→Fe³⁺ (already balanced) Reduction: ClO³⁻→ Cl⁻ (already balanced)

Balance the Oxygen Atoms

In the reduction half-reaction, there are 3 oxygen atoms on the left side and none on the right side. Oxygen atoms can be balanced by adding water molecules to the right side: Reduction: ClO³⁻→ Cl⁻ + 3H₂O

Balance the Hydrogen Atoms

In the new reduction rubric, there exists a balance of 6 hydrogen atoms in the water molecules on the right side and none on the left side. This unbalance of hydrogen atoms can be corrected by adding hydrogen ions (H⁺) to the left side: Reduction: ClO³⁻ + 6H⁺→ Cl⁻ + 3H₂O

Balance the Charges

For the reduction half-reaction, there is a total positive charge of +6 on the left and a total charge of -1 on the right. To balance the charges, 6 electrons must be added to the right side: Reduction: ClO³⁻ + 6H⁺ → Cl⁻ + 3H₂O + 6e⁻ In the oxidation half-reaction, there is a +2 charge on the left and a +3 charge on the right, so one electron should be placed on the left side: Oxidation: Fe²⁺ → Fe³⁺ + e⁻

Balance the Two Half-Reactions

To balance the half-reactions, they should involve the same number of electrons. Multiply the oxidation half-reaction by 6 and add it to the reduction half-reaction which yields: Oxidation: 6Fe²⁺ → 6Fe³⁺ + 6e⁻ Reduction: ClO³⁻ + 6H⁺ + 6e⁻ → Cl⁻ + 3H₂O Overall reaction: 6Fe²⁺ + ClO³⁻ + 6H⁺ → 6Fe³⁺ + Cl⁻ +3H₂O This is the final balanced equation in an acidic solution.

Key concepts

Oxidation Half-Reaction

Oxidation is a process that involves the loss of electrons or an increase in oxidation state by a molecule, atom, or ion. In an oxidation half-reaction, we witness the transformation of a substance as it loses electrons. This is a critical component in redox reactions, which are at the heart of electrochemistry. Diving into our specific example, the oxidation half-reaction can be represented as:
\( \text{Fe}^{2+} \rightarrow \text{Fe}^{3+} + \text{e}^- \).
Here, the iron (II) ion losses an electron to become an iron (III) ion. The half-reaction is already balanced concerning the atoms; what we need to ensure is that the number of electrons lost is the same as those gained in the reduction half-reaction to maintain charge balance.

Reduction Half-Reaction

Any reduction half-reaction conversely demonstrates gain of electrons, or a decrease in oxidation state. When looking at the reduction process occurring within our example, we see that the chlorate ion (\( \text{ClO}_3^- \)) gains electrons to become a chloride ion (\( \text{Cl}^- \)).
The balanced reduction half-reaction in our exercise is:
\( \text{ClO}_3^- + 6\text{H}^+ \rightarrow \text{Cl}^- + 3\text{H}_2\text{O} + 6\text{e}^- \).
In this half-reaction, the addition of water molecules and hydrogen ions was necessary for balancing oxygen and hydrogen atoms, respectively, with electrons being added at the end to equalize charge.

Acidic Solution Balance

The balance of redox reactions in an acidic solution requires a special approach. Acidic solutions provide an abundance of hydrogen ions (\( \text{H}^+ \)), which we may use to balance hydrogen atoms in reduction half-reactions as shown in our exercise.
The steps in balancing redox reactions in an acidic medium typically involve:

• Identifying and writing separate oxidation and reduction half-reactions.
• Adjusting coefficients to balance atoms other than hydrogen and oxygen.
• Adding water molecules to balance oxygen atoms when needed.
• Introducing \( \text{H}^+ \) ions to balance hydrogen atoms.
• Addition of electrons to balance the overall charge and subsequent equalization of electron exchange between oxidation and reduction.

Our balanced final reaction well reflects each of these steps, resulting in a harmonious equation that respects both mass and charge balance within an acidic context.

Electrochemistry

Electrochemistry is the study of chemical processes that cause electrons to move. This movement of electrons provides a bridge between chemical reactions and electrical energy. Balancing redox reactions is fundamental in electrochemistry, as it provides insights into the electron transfer mechanisms fundamental to batteries, corrosion, and electrolysis.
Our textbook problem showcased the importance of understanding the transfer of electrons in electrochemical reactions, demonstrating the harmony required between oxidation and reduction processes. Grasping the art of balancing these reactions can reveal much about the energy changes and dynamics involved in electrochemical systems and has vast applications spanning from industrial processes to biological systems.