Problem 4 - An Introduction to Thermal Physics

Question

In a hydrogen fuel cell, the steps of the chemical reaction are at - electrode: \(\mathrm{H}_{2}+2 \mathrm{OH}^{-} \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}+2 \mathrm{e}^{-}\)at \(+\) electrode: \(\frac{1}{2} \mathrm{O}_{2}+\mathrm{H}_{2}\mathrm{O}+2 \mathrm{e}^{-} \longrightarrow 2 \mathrm{OH}^{-}\) Calculate the voltage of the cell. What is the minimum voltage required for electrolysis of water? Explain briefly.

Step-by-Step Solution

Answer

The cell voltage is 1.23 V. The minimum voltage for water electrolysis is 1.23 V.

Step 1: Identify Overall Reaction

To find the overall reaction for the hydrogen fuel cell, we need to combine the two electrode reactions given: the anode reaction \[\mathrm{H}_{2} + 2 \mathrm{OH}^{-} \longrightarrow 2 \mathrm{H}_{2} \mathrm{O} + 2 \mathrm{e}^{-}\]and the cathode reaction \[\frac{1}{2} \mathrm{O}_{2} + \mathrm{H}_{2} \mathrm{O} + 2 \mathrm{e}^{-} \longrightarrow 2 \mathrm{OH}^{-}.\]Combining both reactions and cancelling the electrons, we get the overall cell reaction:\[\mathrm{H}_{2} + \frac{1}{2} \mathrm{O}_{2} \longrightarrow \mathrm{H}_{2} \mathrm{O}.\]

Step 2: Calculate Standard Cell Potential

Use the standard electrode potential values from a standard reduction potential table. The standard potential for the water formation reaction can be determined. For the reaction:\[\mathrm{H}_2 + \frac{1}{2}\mathrm{O}_2 \longrightarrow \mathrm{H}_2\mathrm{O},\]the standard cell potential \(E^0_{cell}\) is given as 1.23 V.

Step 3: Minimum Voltage for Electrolysis

For the electrolysis of water, the reaction is the reverse of the fuel cell reaction,\[\mathrm{H}_2\mathrm{O} \longrightarrow \mathrm{H}_2 + \frac{1}{2}\mathrm{O}_2.\]The standard potential required for electrolysis is equal in magnitude to the fuel cell's potential, but since energy is required to drive the electrolysis, losses like overpotential and efficiency need consideration. However, the theoretical minimum voltage required for the electrolysis under ideal conditions is also 1.23 V.

Key Concepts

Hydrogen Fuel Cell

A hydrogen fuel cell is a device that converts chemical energy into electrical energy through an electrochemical reaction between hydrogen and oxygen. It works similarly to a battery but does not run down or need recharging. Instead, it continuously produces electricity as long as hydrogen and oxygen are supplied.

A key aspect of hydrogen fuel cells is that the only by-product of this energy conversion process is water, making it an environmentally friendly energy source. Fuel cells find applications in various fields, including transportation, portable power systems, and stationary power generation, offering a clean and efficient alternative to fossil fuels.

Electrode Reactions

Electrode reactions are the chemical processes that occur at the electrodes in an electrochemical cell. In the case of a hydrogen fuel cell, there are two primary reactions occurring at the electrodes.

• Anode Reaction: This is the oxidation reaction where hydrogen gas (\( \mathrm{H}_{2} + 2 \mathrm{OH}^{-} \rightarrow 2 \mathrm{H}_{2} \mathrm{O} + 2 \mathrm{e}^{-} \)) is oxidized to form water and release electrons.
• Cathode Reaction: This is the reduction reaction where oxygen gas (\( \frac{1}{2}\mathrm{O}_{2} + \mathrm{H}_{2}\mathrm{O} + 2 \mathrm{e}^{-} \rightarrow 2 \mathrm{OH}^{-}\)) combines with electrons and water to form hydroxide ions.

Combining these reactions gives the overall cell reaction, where hydrogen and oxygen react to form water. Each reaction contributes to the flow of electrons through an external circuit, thus generating electricity.

Standard Cell Potential

The standard cell potential (\(E^0_{cell}\)) is a measure of the voltage difference between two half-cells in an electrochemical cell under standard conditions. It indicates the energy available from the cell and depends on the particular reactions occurring at the electrode.

For the overall reaction in a hydrogen fuel cell (\(\mathrm{H}_2 + \frac{1}{2}\mathrm{O}_2 \rightarrow \mathrm{H}_2\mathrm{O},\)), the standard cell potential is calculated from standard reduction potential values, which for this reaction is 1.23 V. This value represents the maximum voltage the cell can produce and guides the design and efficiency of the cell.

Electrolysis of Water

Electrolysis of water is the process of using electricity to decompose water into hydrogen and oxygen gases. This process is the reverse of the reaction that occurs in a hydrogen fuel cell.

To achieve electrolysis, energy must overcome the stability of water molecules, requiring a minimum voltage equal to the standard cell potential of the reverse reaction (\(1.23 \text{V}\)). In practice, the required voltage is higher because of inefficiencies like overpotential, which accounts for additional energy needed due to resistance and other losses in the system. Despite these challenges, electrolysis remains a vital method for producing clean hydrogen fuel from renewable sources.