Question

A plot of Gibbs energy of a reaction mixture against the extent of the reaction is : (a) minimum at equilibrium (b) zero at equilibrium (c) maximum at equilibrium (d) None of these

Short answer

The Gibbs energy of a reaction mixture at equilibrium is minimum, so the correct answer is (a) minimum at equilibrium.

Step-by-step solution

Understanding Gibbs Free Energy

Gibbs free energy (\( G \) ) is a thermodynamic potential that can be used to calculate the maximum amount of work that may be performed by a thermodynamically closed system at constant temperature and pressure. The Gibbs free energy is used to determine the spontaneity of a process. A negative change in Gibbs free energy (\( \triangle G < 0 \) ) indicates that a process is spontaneous, while a positive change (\( \triangle G > 0 \) ) indicates a non-spontaneous process. At equilibrium, the free energy is at its lowest possible value for the system, and there is no net change in the system as the forward and reverse reactions occur at equal rates.

Identifying the State of Equilibrium

At equilibrium, the system has reached a state where the chemical potential, and thus the Gibbs free energy, is minimized. This means that the change in Gibbs free energy relative to the reaction (\( \triangle G \) ) is zero because the system is at its lowest energy state and there are no further tendencies for a reaction to proceed in either direction.

Choosing the Correct Answer

Given that at equilibrium the Gibbs free energy of the reaction mixture is at a minimum, the correct answer must reflect this state. We can eliminate option (b) and (c) because they suggest the Gibbs energy is either zero or at a maximum at equilibrium, which is incorrect. Option (d) is also incorrect because it implies none of the presented options are true. Therefore, the correct answer is option (a), which states that the Gibbs energy is minimum at equilibrium.

Key concepts

Thermodynamics

Thermodynamics is the study of heat, work, and energy within a system. It is a branch of physics that looks at how energy is transferred and transformed, guiding us in understanding how different processes occur. Specifically, thermodynamics deals with the principles of energy conservation and the tendency of systems to reach a state of equilibrium. A key aspect of this field is the understanding of thermodynamic potentials, such as internal energy, enthalpy, entropy, and Gibbs free energy. Each of these quantities provides crucial insights into the energy dynamics of a system under various constraints, such as constant temperature, constant pressure, or both. Gibbs free energy (\( G \)) in particular, plays a central role in predicting the direction and spontaneity of chemical reactions.

Chemical Spontaneity

Chemical spontaneity refers to the natural tendency of a chemical reaction to occur without the need for additional energy. This concept is tied deeply to the second law of thermodynamics, which states that the total entropy of an isolated system can never decrease over time. In practical terms, a spontaneous reaction is one that can proceed on its own under a given set of conditions such as temperature and pressure. The Gibbs free energy change (\( \triangle G \)) is the decisive factor for chemical spontaneity. If \( \triangle G \) is negative, the process is spontaneous, meaning it releases energy and moves towards equilibrium. Conversely, if \( \triangle G \) is positive, the process is non-spontaneous and will require energy to proceed. Zero change in Gibbs free energy indicates a system is at equilibrium, which is a state of balance where the forward and reverse reactions occur at an equal rate, resulting in no net change.

Thermodynamical Systems

A thermodynamical system encompasses any material or collection of materials that we can analyze with the principles of thermodynamics. Systems are classified based on their interactions with the surroundings: isolated (no exchange of energy or matter), closed (energy exchange but no matter exchange), and open (both energy and matter exchange). The state of a thermodynamic system is defined by properties such as temperature, pressure, volume, and composition, which can describe the system's condition at a particular time. Thermodynamic processes change the state of the system, often described by paths on pressure-volume or temperature-entropy diagrams. For chemical reactions, Gibbs free energy provides a quantitative measure of the system’s capacity to do work at constant temperature and pressure, and it plays a crucial role in predicting the evolution of the system towards equilibrium.

Equilibrium State

An equilibrium state is a condition where a dynamic balance exists in a system, with no net change over time. In the context of chemical reactions, this means that the rates of the forward and reverse reactions are equal, leading to constant concentrations of reactants and products. A system in equilibrium is at its lowest Gibbs free energy for the given conditions. At this point, \( \triangle G \) equals zero, signifying that there is no thermodynamic driving force for the reaction to proceed in either direction. Understanding this state is crucial in chemistry and engineering because it determines the maximum yield of a reaction and dictates the conditions needed to shift the equilibrium, which is essential for the design of industrial processes. As brought out in the exercise, the Gibbs energy graph of a reaction is at a minimum at equilibrium, a critical concept that helps understand the balance a system reaches when no external work is done on or by the system.