Question

Write a balanced equation for the overall cell reaction in the following galvanic cell, and tell why inert electrodes are required at the anode and cathode. $$ \operatorname{Pt}(s)\left|\operatorname{Br}^{-}(a q)\right| \mathrm{Br}_{2}(l) \| \mathrm{Cl}_{2}(g)\left|\mathrm{Cl}^{-}(a q)\right| \mathrm{Pt}(s) $$

Short answer

Inert electrodes are required because neither Br nor Cl are solid conductors.

Step-by-step solution

Identify Half-Reactions

Identify the half-reactions that occur at each electrode. For the bromine solution, the half-reaction is:\[\text{Cathode: } \ \text{Br}_2 (l) + 2e^- \rightarrow 2 \text{Br}^- (aq)\]For the chlorine solution, the half-reaction is:\[\text{Anode: } \ \text{Cl}_2 (g) + 2e^- \rightarrow 2 \text{Cl}^- (aq)\]

Key concepts

Galvanic Cell

A galvanic cell, also known as a voltaic cell, is an electrochemical cell that converts chemical energy into electrical energy through spontaneous redox reactions. This is achieved in a setup consisting of two different half-cells. Each half-cell contains an electrode and an electrolyte, where the electrode serves as a site for oxidation or reduction reactions. In the given example, the galvanic cell consists of a bromine half-cell and a chlorine half-cell.

• The purpose of a galvanic cell is to create electrical energy from chemical reactions.
• It consists of two half-cells, each with its own electrode and electrolyte.
• The overall energy generated is the sum of the energies produced in each half-cell.

Electrons flow from the anode, where oxidation occurs, to the cathode, where reduction takes place, via an external circuit. Bridging the solutions in each half-cell is a salt bridge, which maintains electrical neutrality. In our specific example, platinum electrodes are used in both half-cells as inert electrodes to facilitate the reaction.

Inert Electrodes

Inert electrodes play a crucial role in electrochemical reactions, especially in the context of galvanic cells, where they act as a surface for the redox reactions without participating in the reaction itself. In many cases, the desired reactions involve non-conductive compounds or gases, which require a conductor for electron transfer.

• Inert electrodes, like platinum, do not react with the substances in the cell.
• They serve as a medium for electron transfer from the external circuit to the solution.
• In our galvanic cell, inert electrodes are used because neither bromine nor chlorine are conductive.

Platinum is a common choice for inert electrodes due to its excellent conductivity and resistance to corrosion. This prevents side reactions and ensures that only the intended redox processes occur within the cell.

Half-Reactions

Half-reactions are a vital part of understanding electrochemical cells, as they divide the redox reactions into two processes: oxidation and reduction. Each half-reaction occurs in separate half-cells in a galvanic cell:

• Reduction occurs at the cathode, where gain of electrons takes place.
• Oxidation happens at the anode, where loss of electrons occurs.

For the cell in question:

At the Cathode:

• The half-reaction is for bromine: \[\text{Br}_2 (l) + 2e^- \rightarrow 2 \text{Br}^- (aq)\]This equation indicates that bromine molecules gain electrons to form bromide ions.

At the Anode:

• The half-reaction for chlorine is:\[\text{Cl}_2 (g) + 2e^- \rightarrow 2 \text{Cl}^- (aq)\]Here, chlorine molecules gain electrons to become chloride ions, representing the reduction process.

Understanding these reactions allows us to calculate the cell's overall potential and gauge the feasibility of the cell reaction.

Balanced Equation

Balancing the overall cell reaction is crucial for making sure that the number of electrons gained in the reduction equals the number lost in oxidation. This ensures the reaction abides by the law of conservation of mass and charge. To achieve a balanced equation:

• Combine the half-reactions while ensuring the number of electrons on both sides cancels out.
• From our examples, balance the electrons transferred in each half-reaction.

Thus, the final balanced equation for the overall cell reaction is expressed as:\[\text{Br}_2 (l) + ext{Cl}_2 (g) \rightarrow 2\text{Br}^- (aq) + 2\text{Cl}^- (aq)\]This equation represents both the reactants and the products accurately, taking into account electron transfer between them. Balanced equations are essential for predictions about reaction quantities and the generation of electric current in galvanic cells.