What is (a) the electrolyte and (b) the oxidizing agent during discharge in a lead-acid battery? (c) Write the reaction that takes place at the cathode during the charging of the lead-acid battery.

Understanding the role of the electrolyte is crucial when examining the functionality of lead-acid batteries. The electrolyte acts as the medium for ion transfer, vital for the electrochemical reactions that power devices. In lead-acid batteries, the electrolyte composition is a dilute solution of sulfuric acid (H2SO4) and water (H2O).

The specificity of this solution lies in its ability to conduct electricity through the movement of ions. In technical terms, when the battery discharges, hydrogen ions (H+) move towards the cathode, and sulfate ions (SO4 2-) move towards the anode. This ion exchange is what allows current to flow out of the battery, providing power to the connected circuit.

It's interesting to note that the concentration of the sulfuric acid in the electrolyte changes during the battery's charge and discharge cycles. A dense electrolyte usually indicates a fully charged battery, while a more dilute one suggests it's discharged, effectively making the electrolyte's specific gravity a measure of the battery's charge state.

The oxidizing agent plays a pivotal role in the discharge process of a battery, accepting electrons and facilitating the flow of electricity. In lead-acid batteries, the oxidizing agent is lead dioxide (PbO2), found at the positive electrode, or anode, during discharge.

During discharge, PbO2 reacts with the sulfuric acid electrolyte to form lead sulfate (PbSO4) and water (H2O) in a process that involves the transfer of electrons from the external circuit. This exchange is central to the battery's ability to generate electrical energy, as the electrons flow through the circuit, doing the work needed to power the device to which the battery is connected. The chemical dynamics of lead dioxide as the oxidizing agent are integral to the reversible reactions that allow for the recharging of lead-acid batteries.

It's this reversibility that enables lead-acid batteries to be used over and over again, making them suitable for a range of applications including vehicle starting, power backup, and energy storage systems.

When it comes to recharging a lead-acid battery, the reactions at the cathode and anode reverse from the discharge process. At the cathode, lead sulfate (PbSO4) formed during discharge undergoes a chemical transformation back into lead dioxide (PbO2).

The reaction during charging that occurs at the cathode can be written as: \[ PbSO_4 + 2H_2O \rightarrow PbO_2 + 2H_2SO_4 + 2e^- \]. This indicates that water and lead sulfate, through the supply of energy, are converted into lead dioxide, sulfuric acid, and electrons. The lead dioxide reforms on the cathode plate, and the sulfuric acid adds to the concentration of the electrolyte, thereby restoring the battery's potential to provide power on the next discharge.

This rechargeability of the cathode is a vital aspect of lead-acid battery operation, offering the practicality of multiple cycles of use. Understanding this reaction is key for students not only to grasp how batteries are charged but also to infer how the restored concentration of sulfuric acid affects the overall capacity and health of the battery.