Problem 117 - General Chemistry: Principles and Modern Applications

Question

If a chemical reaction is carried out in a fuel cell, the maximum amount of useful work that can be obtained is (a) \(\Delta G ;\) (b) \(\Delta H ;\) (c) \(\Delta G / \Delta H ;\) (d) \(T \Delta S\).

Step-by-Step Solution

Answer

The correct answer is (a) \(\Delta G\). The maximum work other than expansion work that can be achieved from a chemical reaction (at constant temperature and pressure) is equivalent to the Gibbs Free Energy change.

Step 1: Evaluate each option

Examine each provided choice: \(\Delta G\), \(\Delta H\), \(\Delta G / \Delta H\), and \(T \Delta S\). These represent different thermodynamic properties. \(\Delta G\) is the change in Gibbs Free Energy, \(\Delta H\) is the change in enthalpy, \(\Delta G / \Delta H\) is a ratio of these two changes, and \(T \Delta S\) denotes the change in entropy times the absolute temperature. However, the maximum amount of useful work that can be obtained from a chemical reaction is given by the Gibbs Free Energy Change, not by the Enthalpy change, their ratio or the term related to entropy.

Key Concepts

Fuel Cell Reactions

Fuel cell reactions are fascinating chemical processes that directly convert the chemical energy from a fuel into electricity through electrochemical reactions. A typical example is the hydrogen-oxygen fuel cell, where hydrogen gas and oxygen gas react to form water, generating electricity in the process. This occurs through separate half-reactions at the anode and cathode, where electrons are transferred between the electrodes, allowing the generation of electric current.

Fuel cells are lauded for their efficiency and environmentally friendly nature. They produce power with minimal pollution since their only by-product, in many cases, is water. However, understanding what limits the useful work obtainable from these reactions is key.

An important aspect of fuel cell reactions is that they operate at a constant temperature and pressure. Under these conditions, the Gibbs Free Energy ( ΔG ) change of the reaction is crucial, as it represents the maximum amount of non-PV (pressure-volume) work that can be done by the system.

Key points about fuel cell reactions include:

• They involve redox reactions happening in separate compartments.
• Efficiency is based on converting chemical energy directly to electrical energy.
• The reactions are environmentally friendly and sustainable power sources.

Thermodynamic Properties

Thermodynamic properties help us determine the feasibility and extent of chemical reactions. If we consider reactions within a fuel cell or beyond, thermodynamics plays a crucial role in defining how and why these reactions occur.

Key thermodynamic properties include:

• **Gibbs Free Energy ( ΔG ):** It indicates the amount of energy available to do work under constant temperature and pressure conditions. The sign and magnitude of ΔG tell us whether a reaction will occur spontaneously.
• **Enthalpy ( ΔH ):** This is the total heat content of a system. It gives a measure of energy absorbed or released during a reaction but does not account for work done, which makes it less useful than ΔG in determining the maximum work extractable.
• **Entropy ( ΔS ):** This describes the disorder or randomness of a system. TΔS , the product of temperature and entropy change, represents the energy unavailable for work. It plays a significant role in spontaneous reaction prediction.

All these properties are interrelated by the relationship: ΔG = ΔH - TΔS , making it possible to predict the direction and capability of reactions in terms of energy changes.

Useful Work in Chemistry

In chemistry, especially in processes like fuel cells, the concept of "useful work" is essential to understand efficiency and energy utilization. Useful work refers to the part of total energy change that can be harnessed to perform tasks, like generating electricity or powering machines.

With a focus on thermodynamics, Gibbs Free Energy ( ΔG ) is the cornerstone for calculating this useful work. It gives the maximum reversible work obtainable from a thermodynamic system at constant temperature and pressure, excluding any work done by expansion or contraction of the volume (PV work).

Why is Gibbs Free Energy so crucial for useful work?

• It indicates the fraction of energy that can be transformed into non-PV work, such as electrical work in fuel cells.
• If ΔG is negative, the process releases free energy that can perform useful work, indicating a spontaneous, exergonic reaction.
• If ΔG is positive, it indicates an input of energy is required for the reaction to proceed, signifying an endergonic reaction.

Thus, Gibbs Free Energy serves as a guiding parameter for assessing and optimizing energy efficiency in fuel cell technology and other chemical processes.