Question

What reactions take place at the cathode and the anode when each of the following is electrolyzed? (Assume standard conditions.) a. 1.0 \(M \mathrm{NiBr}_{2}\) solution b. 1.0 \(M \mathrm{AlF}_{3}\) solution c. 1.0 \(M \mathrm{MnI}_{2}\) solution

Short answer

For the electrolysis of the given solutions under standard conditions, the following half-reactions take place: a. 1.0 M NiBr₂ solution: Cathode: Ni²⁺ + 2e⁻ → Ni Anode: 2Br⁻ → Br₂ + 2e⁻ b. 1.0 M AlF₃ solution: Cathode: Al³⁺ + 3e⁻ → Al Anode: 2F⁻ → F₂ + 2e⁻ c. 1.0 M MnI₂ solution: Cathode: Mn²⁺ + 2e⁻ → Mn Anode: 2I⁻ → I₂ + 2e⁻

Step-by-step solution

Identify the ions in the solution

In a 1.0 M NiBr₂ solution, the ions present are Ni²⁺ and Br⁻.

Determine the reactions at the cathode and anode using reduction potentials

The standard reduction potentials for the relevant half-reactions are: Ni²⁺ + 2e⁻ → Ni (E° = -0.25 V) 2Br⁻ → Br₂ + 2e⁻ (E° = +1.09 V) Since the reaction with the more positive reduction potential occurs at the cathode, Ni²⁺ will be reduced to Ni, and Br⁻ will be oxidized to Br₂ at the anode.

Write balanced half-reactions

The balanced half-reactions for the electrolysis of 1.0 M NiBr₂ are: Cathode: Ni²⁺ + 2e⁻ → Ni Anode: 2Br⁻ → Br₂ + 2e⁻ #1.0 M AlF₃ solution#

Identify the ions in the solution

In a 1.0 M AlF₃ solution, the ions present are Al³⁺ and F⁻.

Determine the reactions at the cathode and anode using reduction potentials

The standard reduction potentials for the relevant half-reactions are: Al³⁺ + 3e⁻ → Al (E° = -1.66 V) 2F⁻ → F₂ + 2e⁻ (E° = +2.87 V) Since the reaction with the more positive reduction potential occurs at the cathode, Al³⁺ will be reduced to Al, and F⁻ will be oxidized to F₂ at the anode.

Write balanced half-reactions

The balanced half-reactions for the electrolysis of 1.0 M AlF₃ are: Cathode: Al³⁺ + 3e⁻ → Al Anode: 2F⁻ → F₂ + 2e⁻ #1.0 M MnI₂ solution#

Identify the ions in the solution

In a 1.0 M MnI₂ solution, the ions present are Mn²⁺ and I⁻.

Determine the reactions at the cathode and anode using reduction potentials

The standard reduction potentials for the relevant half-reactions are: Mn²⁺ + 2e⁻ → Mn (E° = -1.18 V) 2I⁻ → I₂ + 2e⁻ (E° = +0.54 V) Since the reaction with the more positive reduction potential occurs at the cathode, Mn²⁺ will be reduced to Mn, and I⁻ will be oxidized to I₂ at the anode.

Write balanced half-reactions

The balanced half-reactions for the electrolysis of 1.0 M MnI₂ are: Cathode: Mn²⁺ + 2e⁻ → Mn Anode: 2I⁻ → I₂ + 2e⁻

Key concepts

Reduction Potential

Reduction potential is a critical concept in understanding electrolysis. It tells us how likely a substance is to gain electrons, or reduce, in a chemical reaction. Each element or compound has a specific reduction potential, usually given in volts under standard conditions. A higher reduction potential means a higher likelihood of getting reduced.

To predict which ion gets reduced at the cathode during electrolysis, we look at the standard reduction potentials of the ions in solution.

• The ion with the higher reduction potential will be reduced at the cathode.
• For example, in a solution of NiBr₂, Ni²⁺ has a reduction potential of -0.25 V.
• The reaction at the cathode is Ni²⁺ gaining electrons to become Ni metal.

Understanding these potentials is crucial in predicting the outcomes of electrolysis reactions.

Cathode Reaction

The cathode is the electrode where reduction occurs in an electrolysis process. The ions in solution gain electrons to form atoms or molecules, a process termed reduction.

In our electrolysis examples:

• For NiBr₂, Ni²⁺ ions gain electrons to form nickel metal (Ni).
• For AlF₃, Al³⁺ ions receive electrons to produce aluminum metal (Al).
• For MnI₂, Mn²⁺ ions gain electrons and form manganese metal (Mn).

This reaction forms the solid elemental form of the metal present in the solution at the cathode.

Anode Reaction

The anode is where oxidation occurs during electrolysis and involves the loss of electrons.

When analyzing reactions at the anode, we look for the ion that wants to lose electrons the most. This is shown by the lower standard electrode potential value compared to the cathodic reaction. In these electrolysis examples:

• For NiBr₂ solution, Br⁻ ions are oxidized to form bromine gas (Br₂).
• In AlF₃ solution, F⁻ ions lose electrons to form fluorine gas (F₂).
• For MnI₂ solution, I⁻ ions are oxidized to produce iodine gas (I₂).

Anode reactions are essential as they release gaseous forms of the non-metal ions in the electrolytic cell.

Half-Reactions

Half-reactions provide detailed insight into the separate processes taking part in electrolysis – reduction and oxidation.

Half-reactions break down the overall electrolysis reaction into two simpler processes. You can see which species get reduced and which get oxidized.

• In a solution of NiBr₂, the half-reactions are:
  Reduction: Ni²⁺ + 2e⁻ → Ni
  Oxidation: 2Br⁻ → Br₂ + 2e⁻
• For AlF₃:
  Reduction: Al³⁺ + 3e⁻ → Al
  Oxidation: 2F⁻ → F₂ + 2e⁻
• With MnI₂:
  Reduction: Mn²⁺ + 2e⁻ → Mn
  Oxidation: 2I⁻ → I₂ + 2e⁻

Understanding and writing half-reactions helps in grasping the complete picture of electrochemical processes in a systematic manner.