Question

(a) What is the meaning of the standard free-energy change, \(\Delta G^{\circ}\), as compared with \(\Delta G ?\) (b) For any process that occurs at constant temperature and pressure, what is the significance of \(\Delta G=0 ?(c)\) For a certain process, \(\Delta G\) is large and negative. Does this mean that the process necessarily occurs rapidly?

Short answer

(a) The standard free-energy change, ΔG°, represents the change in Gibbs free energy under standard conditions (1 atm pressure and 25 °C), determining the spontaneity of a reaction under those conditions. Free-energy change, ΔG, is the actual change in Gibbs free energy during a reaction at any given temperature and pressure, and determines whether a reaction will proceed spontaneously in the given conditions. (b) When ΔG = 0 at constant temperature and pressure, the reaction is at equilibrium, meaning the forward and reverse reaction rates are equal and there's no net change in the concentrations of reactants and products. (c) A large negative ΔG value signifies a thermodynamically favorable reaction but does not necessarily mean the reaction is rapid; the rate of a reaction is primarily determined by its activation energy.

Step-by-step solution

Part (a): Meaning of Standard Free-Energy Change and Free-Energy Change

Standard free-energy change, ΔG°, refers to the change in Gibbs free energy when a reaction occurs under standard conditions (1 atm pressure and usually 25 °C or 298 K temperature). It is a measure of the maximum available energy from a reaction that can be converted into work at constant temperature and pressure. ΔG° determines the spontaneity of a reaction under standard conditions. Free-energy change, ΔG, is the actual change in Gibbs free energy during a reaction at any given temperature and pressure. It depends on the concentrations of reactants and products, and is used to determine whether a reaction will proceed spontaneously under the given conditions. If ΔG is negative, the reaction is spontaneous; if ΔG is positive, the reaction is non-spontaneous; and if ΔG is zero, the reaction is at equilibrium.

Part (b): Significance of ΔG = 0 at Constant Temperature and Pressure

When ΔG = 0 at constant temperature and pressure, the reaction has reached equilibrium. This means that the forward and reverse rates of the reaction are equal, and there is no net change in the concentrations of reactants and products over time. At this point, the system has reached its lowest possible Gibbs free energy, and it is in a stable state.

Part (c): Relationship Between ΔG and Reaction Rate

A large negative value for ΔG indicates that the reaction is thermodynamically favorable, meaning that it can release a high amount of energy when it proceeds. However, a negative ΔG value does not necessarily mean the reaction will occur rapidly. The reaction rate is determined by the reaction's activation energy, which is the minimum energy barrier that must be overcome for the reaction to proceed. A reaction with a high activation energy will take place slowly, even if it is thermodynamically favorable, as the reactants require more energy to overcome the energy barrier. Conversely, a reaction with a low activation energy may proceed rapidly even if the overall ΔG is not large. In summary, a large negative ΔG value signifies a thermodynamically favorable reaction, but it is not an indicator of the reaction rate. The rate of a reaction is primarily determined by its activation energy.

Key concepts

Standard Free-Energy Change

Standard free-energy change, often symbolized as \( \Delta G^{\circ} \), is a crucial concept in thermodynamics. It represents the change in Gibbs free energy when a chemical reaction happens under standard conditions. These conditions typically include a pressure of 1 atm and a temperature of 25 °C (298 K). Essentially, \( \Delta G^{\circ} \) serves as a measure of the maximum possible work that can be extracted from a system when it moves from reactants to products under these standardized conditions.
The sign of \( \Delta G^{\circ} \) offers important insights into the reaction’s spontaneity under standard conditions:

• If \( \Delta G^{\circ} \) is negative, the reaction is spontaneous, meaning it can proceed without requiring external energy input.
• Conversely, if \( \Delta G^{\circ} \) is positive, the reaction is non-spontaneous under standard conditions, suggesting it will not proceed without energy input.

However, it's important to differentiate \( \Delta G^{\circ} \) from \( \Delta G \), which indicates the free energy change under any sets of prevailing conditions, not strictly standardized ones.

Reaction Thermodynamics

Reaction thermodynamics involves studying the energy changes that accompany chemical processes. Gibbs free energy change, symbolized as \( \Delta G \), plays a central role here.
\( \Delta G \) varies from \( \Delta G^{\circ} \), as it is applicable under specific, non-standard conditions including varying temperatures and pressures, as well as different concentrations of reactants and products.
This energy change is pivotal to determining a reaction's spontaneity:

• Negative \( \Delta G \) indicates a spontaneous reaction.
• Positive \( \Delta G \) points to a non-spontaneous reaction.
• A \( \Delta G \) of zero signifies that the reaction is at equilibrium.

Understanding these changes helps predict whether a reaction will occur naturally or require an external energy source.

Reaction Kinetics

While reaction thermodynamics deals with energy changes, reaction kinetics studies the rate at which reactions occur. Even if a reaction is thermodynamically favorable, indicated by a negative \( \Delta G \), this does not mean the reaction will proceed quickly. Instead, the rate of the reaction is influenced by the activation energy, or the minimum energy needed to initiate the reaction.
A reaction's activation energy can act as a barrier, determining the speed at which reactants transform into products:

• High activation energy means a slower reaction rate.
• Low activation energy implies a faster reaction rate.

Thus, while thermodynamic favorability can be predicted by \( \Delta G \), it is the activation energy that provides insight into how rapidly these reactions can occur.

Equilibrium in Chemical Reactions

In a chemical reaction, equilibrium refers to the state achieved when the rates of the forward and reverse reactions are equal, resulting in stable concentrations of reactants and products over time. At equilibrium, the Gibbs free energy change, \( \Delta G \), is zero, indicating no net energy change in the system.
This equilibrium position does not imply that reactants and products are equal in concentration, but that their ratio does not change as the reaction proceeds. Factors such as reaction conditions and nature of reactants/products influence this state greatly.
Understanding chemical equilibrium is fundamental to predicting the behavior of chemical systems and formulating products in various fields, including chemical engineering and biochemistry.