Question

What are the anode and cathode reactions during the discharge of a lead storage battery? How can a battery produce a potential of \(12 \mathrm{~V}\) if the cell reaction has a standard potential of only \(2 \mathrm{~V}\) ?

Short answer

The anode reaction is \(Pb + SO4^{2-} \to PbSO4 + 2e^-\), and the cathode reaction is \(PbO2 + 4H^+ + SO4^{2-} + 2e^- \to PbSO4 + 2H2O\). A battery produces a potential of 12V by connecting six cells, each with a standard potential of 2V, in series.

Step-by-step solution

Identify the Anode Reaction

During the discharge of a lead storage battery, the anode reaction involves the conversion of lead (Pb) to lead sulfate (PbSO4), releasing electrons in the process. The anode half-reaction can be written as: \(Pb(s) + SO4^{2-}(aq) \rightarrow PbSO4(s) + 2e^-\).

Identify the Cathode Reaction

At the cathode, lead dioxide (PbO2) reacts with lead sulfate (PbSO4) and hydrogen ions (H+) from the sulfuric acid electrolyte to produce water (H2O) and release more lead sulfate (PbSO4). The cathode half-reaction is: \(PbO2(s) + 4H^+(aq) + SO4^{2-}(aq) + 2e^- \rightarrow PbSO4(s) + 2H2O(l)\).

Explain Battery Voltage Output

A lead storage battery consists of multiple cells connected in series. Each cell has a standard potential of approximately \(2 \mathrm{~V}\). To achieve a potential of \(12 \mathrm{~V}\), six cells are connected in series, where the voltage of the individual cells adds up to the total voltage of the battery: \(6 \times 2 \mathrm{~V} = 12 \mathrm{~V}\).

Key concepts

Anode and Cathode Reactions

In lead storage batteries, the reactions at the anode and cathode during discharging are key to their operation. The anode reaction involves the oxidation of lead (Pb) to lead sulfate (PbSO4). Specifically, the lead gives up electrons to become lead sulfate, as shown in the equation:
\(Pb(s) + SO4^{2-}(aq) \rightarrow PbSO4(s) + 2e^-\).
During this process, the lead at the anode loses two electrons per atom in what is called an oxidation reaction.

At the cathode, lead dioxide (PbO2) is reduced. It gains electrons, which are supplied by the anode, and reacts with hydrogen ions and sulfate ions to form lead sulfate and water, described by the equation:
\(PbO2(s) + 4H^+(aq) + SO4^{2-}(aq) + 2e^- \rightarrow PbSO4(s) + 2H2O(l)\).
This reduction reaction at the cathode complements the oxidation at the anode, maintaining the balance of the electrochemical process.

Electrochemical Cells

An electrochemical cell is the basic unit of a battery where the chemical reactions occur that generate electricity. It consists of an anode and a cathode submerged in an electrolyte solution. In the context of a lead storage battery, the cell contains a lead anode, a lead dioxide cathode, and a sulfuric acid electrolyte.

The electrolyte enables the flow of ions between the electrodes, while the circuit outside the battery allows electrons to flow from the anode to the cathode. This movement of electrons through the external circuit is what we use as electricity. When multiple electrochemical cells are connected together, such as in a lead storage battery, we can increase the overall voltage and power capacity.

Standard Potential

Standard potential is a measure of the tendency of a chemical species to be reduced or oxidized at standard conditions, which translates to the potential (voltage) of each electrochemical cell at standard conditions. For a lead storage battery, the standard potential for the cell reaction is about \(2 \text{ V}\).

The standard potential is determined by the specific electrode materials and electrolyte used in the cell, and represents the voltage that can be achieved under ideal conditions. This standard potential is a critical factor in determining how the battery will perform, as it defines the maximum energy per charge unit that can be drawn from the cell.

Battery Voltage Output

The voltage output of a battery correlates directly with the number of electrochemical cells connected in series within it. For a lead storage battery producing a voltage of \(12 \text{ V}\), six individual cells, each with a standard potential of approximately \(2 \text{ V}\), are connected in a series.

This series connection is crucial since it sums up the voltage of each cell, allowing for a higher total voltage output from the battery. In other words, each cell contributes its own standard potential to the total, so with six cells, you get:
\(6 \times 2 \text{ V} = 12 \text{ V}\).
The battery's ability to produce the required voltage output for applications such as starting a car or powering an emergency light system relies on this principle of series connection, as well as the chemistry of the lead-acid reactions.