Question

What is the maximum work that can be obtained from a hydrogen-oxygen fuel cell at standard conditions that produces \(1.00 \mathrm{kg}\) water at \(25^{\circ} \mathrm{C} ?\) Why do we say that this is the maximum work that can be obtained? What are the advantages and disadvantages in using fuel cells rather than the corresponding combustion reactions to produce electricity?

Short answer

The maximum work that can be obtained from a hydrogen-oxygen fuel cell producing 1.00 kg of water at standard conditions (25°C, 1 atm) is about 13,116 kJ. This is the maximum work because it represents the ideal situation where all energy conversion is 100% efficient, which is not possible in real-world systems due to inefficiencies and losses. Fuel cells have advantages like higher efficiency, less pollution, and quiet operation compared to combustion reactions. However, they also have disadvantages such as higher cost, limited availability of hydrogen, and challenges in storing hydrogen.

Step-by-step solution

Write the balanced chemical equation for the hydrogen-oxygen fuel cell reaction

The balanced chemical equation for the hydrogen-oxygen fuel cell reaction is: H₂(g) + ½O₂(g) → H₂O(l)

Determine the number of moles of water produced

We are given that 1.00 kg of water is produced by the fuel cell. First, we need to convert the mass of water into moles: 1.00 kg = 1000 g Molar mass of water (H₂O) = 18.015 g/mol Number of moles = mass / molar mass = 1000 g / 18.015 g/mol = 55.5 mol (approximately) So, 55.5 moles of water are produced in the reaction.

Find the change in Gibbs free energy for the reaction

At standard conditions (25°C, 1 atm), the change in Gibbs free energy (ΔG) for the formation of one mole of liquid water from hydrogen and oxygen is -237.2 kJ/mol.

Calculate the maximum work that can be obtained from the reaction using Gibbs free energy change

To find the maximum work that can be obtained from the reaction, we can use the following formula for a system at constant temperature (T) and constant pressure (P): Wmax = -ΔG * n Where Wmax is the maximum work, ΔG is the Gibbs free energy change, and n is the number of moles of water produced. In our case, ΔG = -237.2 kJ/mol, and n = 55.5 mol. Wmax = -(-237.2 kJ/mol) * 55.5 mol = 13116 kJ (approximately) The maximum work that can be obtained is about 13,116 kJ.

Discuss the reasons why this is the maximum work obtainable

The maximum work that can be obtained from a chemical reaction is directly related to the change in Gibbs free energy. It represents the upper limit of how much energy can be converted into useful work. Any potential energy not converted into work will be lost as heat. The maximum work represents the ideal situation where all energy conversion is 100% efficient, which is not possible in real-world systems due to inefficiencies and losses. Thus, we say that 13,116 kJ is the maximum work that can be obtained.

Analyze the advantages and disadvantages of using fuel cells compared to combustion reactions to produce electricity

Advantages of fuel cells: 1. Higher efficiency: Fuel cells are typically more efficient at converting chemical energy into electrical energy as compared to combustion reactions. 2. Less pollution: Fuel cells produce only water as a byproduct, whereas combustion reactions release greenhouse gases and other pollutants. 3. Quiet operation: Fuel cells have no moving parts, which makes them very quiet compared to combustion engines. Disadvantages of fuel cells: 1. Cost: Fuel cells tend to be more expensive than combustion engines due to their complex and delicate components. 2. Availability: Hydrogen, which is a key fuel source for fuel cells, is not as readily available as fossil fuels. 3. Storage: Storing hydrogen for fuel cells can be challenging due to its low energy density and high pressure requirements.

Key concepts

Gibbs Free Energy

Gibbs free energy, often denoted as \( G \), plays a pivotal role in thermodynamics and chemistry, particularly in the analysis of energy changes during chemical reactions. It integrates the concepts of entropy and enthalpy to predict the direction of a chemical process. In essence, the change in Gibbs free energy \( (\Delta G) \) of a reaction at constant temperature and pressure indicates the spontaneous nature of the process. A negative \( \Delta G \) signifies that a reaction will proceed without the input of additional energy, thus it is exergonic.The maximum work obtainable from a reaction, under ideal conditions, is equal to the negative of the \( \Delta G \) for the reaction when no work is done against the atmosphere. In the context of a hydrogen-oxygen fuel cell, this corresponds to the electricity that can be harnessed as the fuel cell operates, converting chemical energy directly to electrical energy with water as the only byproduct. Therefore, the \( \Delta G \) provides not only thermodynamic insights but also practical predictions about the energy output of such electrochemical processes.

Electrochemical Cell Efficiency

The efficiency of an electrochemical cell, such as a hydrogen-oxygen fuel cell, is one of the central considerations when evaluating its performance. It is defined as the ratio of useful energy output to the total chemical energy available in the fuel—an indicator of how effectively the cell converts chemical energy into electrical energy. The theoretical efficiency is derived from the change in Gibbs free energy over the enthalpy change, with the underlying assumption of reversible reactions. However, in real-life scenarios, the presence of overpotentials, ohmic losses, and mass transport limitations lead to actual efficiencies that are lower than the theoretical maximum.

Understanding Real-Life Inefficiencies

In practice, issues such as slow reaction kinetics and resistance to ion flow in the electrolyte contribute to less than optimal performance. Therefore, pursuing advancements in cell materials and designs is crucial to mitigate these losses and improve the cell's operational efficiency. By enhancing efficiency, we can directly impact the viability and sustainability of fuel cell technologies as alternatives to traditional combustion engines.

Advantages and Disadvantages of Fuel Cells

Fuel cells possess a unique combination of features that make them a compelling choice for clean energy conversion. They offer several advantages over traditional combustion-based electricity generation.

Key Advantages

• Energy Efficiency: Fuel cells often have higher energy conversion efficiency, which means a greater proportion of the chemical energy in hydrogen is transformed into electrical energy, reducing waste.
• Environmental Impact: As fuel cells emit only water vapor, they have a minimal environmental footprint, particularly when the hydrogen source is also derived from renewable energy.
• Noise Pollution: The absence of moving parts in a fuel cell reduces noise pollution, providing a quieter alternative to internal combustion engines.

However, the technology is not without its drawbacks.

Considerable Challenges

• High Costs: Fuel cells currently bear high manufacturing costs due to the need for expensive catalysts like platinum, making them less economically competitive.
• Hydrogen Infrastructure: A significant challenge is the lack of a widespread infrastructure for distributing and storing hydrogen, which inhibits the widespread adoption of fuel cells.
• Energy Storage: Hydrogen's low energy density compared to fossil fuels necessitates complex and costly storage systems to maintain it at high pressures or low temperatures.

Weighing these advantages against the existing disadvantages is key in projecting the future role of fuel cells in the world's energy mix.