Problem 111 - Chemistry An Atoms First Approach

Question

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

Step-by-Step Solution

Answer

The reactions occurring at the electrodes during the electrolysis of each solution are: a. NiBr\(_2\) solution - Cathode: Ni\(^{2+}\) + 2e\(^{-}\) → Ni - Anode: 2Br\(^{-}\) → Br\(_2\) + 2e\(^{-}\) b. AlF solution - Cathode: Al\(^{3+}\) + 3e\(^{-}\) → Al - Anode: 2F\(^{-}\) → F\(_2\) + 2e\(^{-}\) c. MnI\(_2\) solution - Cathode: Mn\(^{2+}\) + 2e\(^{-}\) → Mn - Anode: 2I\(^{-}\) → I\(_2\) + 2e\(^{-}\)

Step 1: Understanding Electrolysis

Electrolysis is a process that uses an electric current to drive a non-spontaneous redox reaction. In electrolysis, the anode is the positive electrode, where oxidation takes place, and the cathode is the negative electrode, where reduction takes place.

Step 2: Look up the Reduction Potentials

For each of the given electrolyte solutions, we will need to look up their reduction potentials from a standard reduction potentials table. These values will help us identify which species are most likely to be reduced or oxidized at the electrodes. For the cases in question: a. NiBr\(_2\): Ni\(^{2+}\) and Br\(^{-}\) will be the ions in solution. -Ni\(^{2+}\) reduction potential: Ni\(^{2+}\) + 2e\(^{-}\) → Ni ; E° = -0.25V -Br\(^{-}\) reduction potential: 2Br\(^{-}\) → Br\(_2\) + 2e\(^{-}\) ; E° = +1.09V b. AlF: Al\(^{3+}\) and F\(^{-}\) will be the ions in solution. -Al\(^{3+}\) reduction potential: Al\(^{3+}\) + 3e\(^{-}\) → Al ; E° = -1.66V -F\(^{-}\) reduction potential: 2F\(^{-}\) → F\(_2\) + 2e\(^{-}\) ; E° = +2.87V c. MnI\(_2\): Mn\(^{2+}\) and I\(^{-}\) will be the ions in solution. -Mn\(^{2+}\) reduction potential: Mn\(^{2+}\) + 2e\(^{-}\) → Mn ; E° = -1.18V -I\(^{-}\) reduction potential: 2I\(^{-}\) → I\(_2\) + 2e\(^{-}\) ; E° = +0.54V

Step 3: Determine the Electrode Reactions

To determine the reactions occurring at the electrodes, we will choose the species with the highest reduction potential to be reduced at the cathode and the species with the lowest reduction potential to be oxidized at the anode. For each solution, do the following: a. NiBr\(_2\) solution -Cathode reaction (reduction): Ni\(^{2+}\) + 2e\(^{-}\) → Ni ; E° = -0.25V -Anode reaction (oxidation): 2Br\(^{-}\) → Br\(_2\) + 2e\(^{-}\) ; E° = +1.09V b. AlF solution -Cathode reaction (reduction): Al\(^{3+}\) + 3e\(^{-}\) → Al ; E° = -1.66V -Anode reaction (oxidation): 2F\(^{-}\) → F\(_2\) + 2e\(^{-}\) ; E° = +2.87V c. MnI\(_2\) solution -Cathode reaction (reduction): Mn\(^{2+}\) + 2e\(^{-}\) → Mn ; E° = -1.18V -Anode reaction (oxidation): 2I\(^{-}\) → I\(_2\) + 2e\(^{-}\) ; E° = +0.54V So the reactions occurring at the electrodes during the electrolysis of each solution are: a. NiBr\(_2\) solution -Cathode: Ni\(^{2+}\) + 2e\(^{-}\) → Ni -Anode: 2Br\(^{-}\) → Br\(_2\) + 2e\(^{-}\) b. AlF solution -Cathode: Al\(^{3+}\) + 3e\(^{-}\) → Al -Anode: 2F\(^{-}\) → F\(_2\) + 2e\(^{-}\) c. MnI\(_2\) solution -Cathode: Mn\(^{2+}\) + 2e\(^{-}\) → Mn -Anode: 2I\(^{-}\) → I\(_2\) + 2e\(^{-}\)

Key Concepts

Redox Reaction

A redox reaction, short for reduction-oxidation reaction, involves the transfer of electrons between two species. In these reactions, one substance undergoes oxidation, losing electrons, while the other undergoes reduction, gaining electrons. This electron transfer is what enables the reaction to take place. Redox reactions are fundamental to electrolysis, a process used to drive a non-spontaneous chemical change. During electrolysis, an external voltage is applied using electrodes to compel ions within a solution to undergo oxidation or reduction at their respective anodes or cathodes.

• Oxidation: Involves the loss of electrons by a molecule, atom, or ion.
• Reduction: Involves the gain of electrons by a molecule, atom, or ion.

A crucial aspect of redox reactions is that they must occur simultaneously — one reaction cannot happen without the other, as electrons need to be transferred. In the context of electrolysis, understanding these reactions helps in determining which ions will move to the cathode and anode to become reduced or oxidized.

Reduction Potential

Reduction potential, also known as electrode potential, is a measure of the tendency of a chemical species to be reduced, measured in volts under standard conditions. It tells us how easily a given ion or molecule gains electrons during a redox reaction. When conducting electrolysis, we refer to standard reduction potential values to predict and determine the direction of electron flow. This helps identify which ions are more likely to gain or lose electrons at the electrodes.

• Higher Reduction Potential: Species with higher reduction potentials are more likely to gain electrons and be reduced.
• Lower Reduction Potential: Species with lower reduction potentials are more likely to lose electrons and be oxidized.

Comparing the reduction potentials of ions present in a solution helps determine the favorable reactions at the cathode and anode. For example, in the electrolysis of NiBr\(_2\): Ni\(^{2+}\) has a reduction potential of \(-0.25\, V\) while Br\(^-\) has a potential of \(+1.09\, V\). Thus, Br\(^-\) would oxidize at the anode, and Ni\(^{2+}\) would reduce at the cathode.

Cathode and Anode Reactions

In electrolysis, reactions at the cathode and anode are determined based on the oxidation and reduction potentials of the involved species. The cathode is where reduction, the gain of electrons, occurs, while the anode is the site of oxidation, the loss of electrons.

• Cathode Reactions: At the cathode, cations (positively charged ions) are attracted to the negative electrode. These ions gain electrons to form their elemental state. For instance, in MnI\(_2\) electrolysis, Mn\(^{2+}\)+2e\(^{-}\) → Mn occurs at the cathode.
• Anode Reactions: Conversely, the anode attracts anions (negatively charged ions) which lose electrons and often form diatomic or polyatomic molecules. In the case of the same electrolysis, 2I\(^-\) → I\(_2\) + 2e\(^{-}\) happens at the anode.

These reactions provide a clear picture of how ions in solution transform during electrolysis. By assessing the reduction potentials, the reactions at each electrode can be accurately predicted, facilitating the desired chemical transformations.