Question

Write equations for the half-reactions that occur in the electrolysis of a mixture of molten potassium bromide and molten lithium bromide.

Short answer

Anode half-reaction: 2Br- - 2e- -> Br2 (g); Cathode half-reaction for potassium: K+ + e- -> K (s); Cathode half-reaction for lithium: Li+ + e- -> Li (s).

Step-by-step solution

Identify the Cations and Anions

Determine the cations and anions present in the electrolyte. For a mixture of molten potassium bromide (KBr) and lithium bromide (LiBr), the cations are potassium (K+) and lithium (Li+), while the anion is bromide (Br-).

Write the Half-Reaction for the Anode

At the anode, oxidation occurs. The anion, bromide (Br-), loses electrons to form bromine (Br2). The half-reaction is: 2Br- - 2e- -> Br2 (g)

Write the Half-Reaction for the Cathode (Potassium)

At the cathode, reduction occurs. Potassium ions (K+) gain electrons to form potassium metal (K). The half-reaction for potassium is: K+ + e- -> K (s)

Write the Half-Reaction for the Cathode (Lithium)

Similarly, lithium ions (Li+) also gain electrons to form lithium metal (Li). The half-reaction for lithium is: Li+ + e- -> Li (s)

Verify the Electrons Balance in Each Half-Reaction

Check that the number of electrons lost in the anode half-reaction equals the number of electrons gained in the cathode half-reactions. To balance the reduction of one mole of bromide ions (which produces half a mole of Br2), one mole of potassium or lithium ions must be reduced.

Key concepts

Half-Reactions in Electrolysis

In electrolysis, compounds are decomposed into their constituent elements through the application of an electric current. This process takes place in a setup called an electrolytic cell, which has two electrodes: an anode (positive) and a cathode (negative). The decomposition reactions occur in two parts, known as half-reactions: one at the anode and the other at the cathode.

During the electrolysis of molten salts, like a mixture of potassium bromide (KBr) and lithium bromide (LiBr), cations (positively charged ions) migrate to the cathode and anions (negatively charged ions) to the anode. At the anode, an oxidation half-reaction occurs where anions release electrons, and at the cathode, a reduction half-reaction takes place where cations gain electrons.

For example, the anode half-reaction for the bromide ion (Br^-) losing electrons to form bromine (Br₂) gas can be written as:
\[\begin{equation} 2Br^- - 2e^- \rightarrow Br_2 \text{(g)} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \text{} \ \end{equation}\]\

It's important that students understand both half-reactions to grasp the full electrochemical process. This also forms a foundation for more complex topics in electrochemistry. For clarity, diagrams or illustrations of the electrolytic cell setup can be helpful. They can visualize the movement of ions towards the respective electrodes and the change that occurs as electrons are transferred.

Oxidation and Reduction

Oxidation and reduction are two key concepts in the study of redox reactions, which are essential in processes like electrolysis.

Oxidation

In an oxidation half-reaction, a species loses electrons and increases its oxidation state. Returning to our example, bromide ions (Br^-) undergo oxidation when they lose electrons to form bromine gas (Br₂). This process occurs at the anode, the positively charged electrode, where electrons are pulled away from the bromide ions due to the electric potential.

Reduction

Conversely, in a reduction half-reaction, a species gains electrons and reduces its oxidation state. In our molten salt electrolysis example, potassium (K⁺) and lithium (Li⁺) ions each gain an electron to become the neutral atoms of potassium (K) and lithium (Li), respectively. These reduction processes occur at the cathode, the negatively charged electrode, where electrons from the power supply reduce the cations to their elemental forms.

It's crucial for students to understand that in every redox reaction, oxidation and reduction occur simultaneously; electrons lost by one species are gained by another. This complementary nature is often described by the mnemonic 'LEO the lion says GER': 'Lose Electrons Oxidation, Gain Electrons Reduction.' Understanding the concepts of oxidation and reduction helps in identifying which electrode is the anode or cathode and predicting the products of an electrolysis reaction.

Balancing Redox Reactions

Balancing redox reactions is essential to ensure that the number of electrons lost in the oxidation half-reaction is equal to the number of electrons gained in the reduction half-reaction. The process of balancing involves making sure that the number of atoms of each element, and the total charge, is the same on both sides of the reaction equation.

Considering our previous example with the mixture of potassium bromide and lithium bromide, here's how to check for balance:

• For the oxidation half-reaction at the anode: 2Br^- becomes Br₂ along with the loss of 2 electrons.
• For the reduction half-reaction at the cathode with potassium: K⁺ gains 1 electron to form K.
• For the reduction half-reaction at the cathode with lithium: Li⁺ gains 1 electron to form Li.

For every 2 moles of Br^- that become 1 mole of Br₂, 2 moles of K⁺ or 2 moles of Li⁺ must be reduced to balance the electrons. This means the reduction of 1 mole of Br₂ requires the reduction of 2 moles of either K⁺ or Li⁺ ions. If the reduction half-reactions with potassium and lithium are happening simultaneously, balancing may require summing the reactions or using a common multiple to ensure the overall electron transfer is equal.

Students should practice balancing redox reactions by identifying the oxidation states of elements before and after the reaction, ensuring electron transfer is equal, and checking that mass and charge are conserved. Through this, one develops a strong foundation for understanding redox behavior in electrochemistry and other applications.