In this section, we will uncover the nuanced relationship between the equilibrium constant and the Gibbs energy change, exploring the critical role they play in pinpointing the exact position of a chemical reaction.

**Relationship Between the Equilibrium Constant and Gibbs Energy Change**

**Gibbs energy change (ΔG)** is a vital thermodynamic quantity that indicates the spontaneity of a chemical reaction. A fundamental grasp of this relationship can offer essential clues about the position of equilibrium.

**Fundamentals of Gibbs Energy Change:**- When ΔG is negative, it signifies that the reaction proceeds spontaneously in the forward direction. Conversely, when ΔG is positive, the reaction is non-spontaneous.
- At the equilibrium point, the Gibbs energy change ΔG is zero. This is because there's no net change in the concentrations of reactants or products.
- The
**standard Gibbs energy change (ΔG⦵)**connects with the equilibrium constant (K) through the equation: ΔG⦵ = -RT ln KWhere:- ΔG⦵ is the standard Gibbs energy change (in joules or kilojoules).
- R represents the universal gas constant (8.314 J mol⁻¹ K⁻¹).
- T is the absolute temperature in kelvin.
- K stands for the equilibrium constant.

**Insights from the Equation:**- When
**K > 1**, ΔG⦵ becomes negative. This situation means the forward reaction is predominant. - On the other hand, if
**K < 1**, ΔG⦵ turns positive, favouring the reverse reaction.

- When

Gibbs energy as a function of the extent of the reaction for describing ΔG° (negative, positive, or zero).

Image courtesy of Hai Nguyen Tran

**Calculations Involving ΔG⦵ and K**

Understanding the mathematical relationship between ΔG⦵ and K is vital. It's the bridge that connects thermodynamic and kinetic observations.

**Calculating ΔG⦵ from K:**Once you know the value of K, it's straightforward to determine ΔG⦵.- Example: Given a reaction with K = 50 at 298K: ΔG⦵ = -8.314 x 298 x ln(50)This yields a significant negative value, confirming the forward reaction's spontaneity.
**Calculating K from ΔG⦵:**By rearranging our key formula, we find: K = e^{(-ΔG⦵/RT)}- Example: Given ΔG⦵ = -5000 J for a reaction at 298K: K = e
^{(5000/ (8.314 x 298))}This calculation will give us a value significantly greater than 1, reinforcing our understanding that the forward reaction is favoured. - A reminder for students: Always ensure consistent units when using formulas. The choice between joules or kilojoules requires using the appropriate R value.

Image courtesy of Chad Shaw

**Gibbs Energy's Role in Determining Reaction Favourability**

The Gibbs energy of a system is essentially a snapshot of its potential to do work. By understanding this energy, we can predict how a reaction will behave and its equilibrium position.

**Driving Force of Reactions:**- Gibbs energy offers insights into the spontaneity of reactions. A reaction will proceed in the direction where Gibbs energy is minimised. So, for spontaneity, the system's Gibbs energy should show a net decrease, corresponding to a negative ΔG.

**Position of Equilibrium:****Before Equilibrium:**When a reaction has not yet reached equilibrium, ΔG provides valuable insights. If ΔG is negative, it will move in the forward direction, while a positive value pushes it in the reverse direction.**At Equilibrium:**Here, ΔG is zero, marking a state where there's no net change and the rates of forward and reverse reactions are identical.**Far from Equilibrium:**The magnitude of ΔG, whether extremely positive or negative, signals that the reaction is considerably distant from equilibrium, possessing ample potential to proceed.

Image courtesy of The Chemistry Notes

**Interplay with Le Châtelier’s Principle:**While Le Châtelier’s principle provides a macroscopic perspective, focusing on shifts due to external changes, it's fundamentally connected to Gibbs energy. External disruptions (e.g., changes in concentration, temperature, or pressure) compel the system to counteract, driven by the innate desire to minimise Gibbs energy. This intrinsic connection between the principle and Gibbs energy is a testament to the comprehensive nature of thermodynamics in understanding chemical reactions.

As we delve deeper into the fascinating world of chemical reactions, it's evident that concepts like equilibrium and Gibbs energy are not isolated topics but deeply interconnected. This synthesis offers a holistic view of the thermodynamics and kinetics of reactions, allowing for precise predictions and deep understanding. Students should endeavour to internalise these relationships, as they form the bedrock of many advanced topics in chemistry.

## FAQ

No, a large negative ΔG⦵ indicates spontaneity and the favourability of a reaction in the forward direction, but it doesn't comment on the rate of the reaction. A reaction can be thermodynamically favourable but still proceed very slowly if it has a high energy barrier or activation energy. Reaction kinetics, which deals with reaction rates, and thermodynamics, which addresses the energy changes and direction of reactions, are two different branches. A reaction may be spontaneous due to a negative ΔG⦵ but could be slow due to kinetic constraints.

The value of ΔG⦵ is temperature-dependent. As temperature changes, ΔG⦵ can also change, leading to a shift in the equilibrium position. The relationship between ΔG⦵ and temperature is embedded within the Van't Hoff equation. An increase in temperature can make ΔG⦵ more positive or more negative, depending on the endothermic or exothermic nature of the reaction. As ΔG⦵ and K are related by the equation ΔG⦵ = -RT ln K, a change in ΔG⦵ due to temperature will also lead to a change in K, potentially shifting the position of equilibrium.

Yes, ΔG⦵ can change without altering the concentrations or pressures of reactants and products. While concentrations and pressures play a crucial role in determining the reaction's Gibbs energy under non-standard conditions (ΔG'), ΔG⦵, being the standard Gibbs energy change, is defined for standard conditions. Factors like temperature, as mentioned earlier, can influence ΔG⦵. Changes in the surroundings, including solvents or other conditions that affect the inherent energy states of reactants and products, can also impact ΔG⦵ without altering their concentrations or pressures.

The value of ΔG under non-standard conditions, often represented as ΔG', takes into account the actual concentrations or pressures of reactants and products at any given moment, not just at equilibrium. The relationship is given by ΔG' = ΔG⦵ + RT ln Q, where Q is the reaction quotient. Depending on whether Q is greater or lesser than K, ΔG' can be positive or negative, respectively. If ΔG' is negative, the system will shift towards products, and if positive, it will shift towards reactants. Hence, non-standard conditions can shift the equilibrium position by influencing the value of ΔG'.

At equilibrium, there is no net change in the concentrations of reactants or products. The rates of the forward and reverse reactions are equal, which means there's no driving force pushing the reaction in one direction or the other. When there's no tendency for the reaction to favour the products or reactants, the potential for the system to do work is nullified. As ΔG represents the maximum work the system can do, a ΔG value of zero at equilibrium indicates the system cannot perform any more work in terms of driving the reaction in either direction.

## Practice Questions

The given value of ΔG⦵ is -2400 J/mol and we also know R, the universal gas constant, is 8.314 J mol⁻¹ K⁻¹. The relationship between ΔG⦵ and the equilibrium constant, K, is given by the formula ΔG⦵ = -RT ln K. Rearranging this formula, we get K = e^{(-ΔG⦵/RT)}. Plugging in the given values: K = e^{(2400/ (8.314 x 298))}. When you perform this calculation, the value of K will be greater than 1, indicating that the forward reaction is favoured.

A negative ΔG⦵ indicates that a reaction is spontaneous in the forward direction and that the products are favoured at equilibrium. This means the reaction will proceed until a significant amount of products is formed, leading to an equilibrium position where products dominate. Conversely, a positive ΔG⦵ suggests that the reaction is non-spontaneous in the forward direction, and reactants are favoured at equilibrium. Therefore, if the reaction were to proceed, it would primarily do so in the reverse direction, resulting in an equilibrium position with predominantly reactants. The value of ΔG⦵ provides essential insights into the direction and extent to which a reaction will occur before reaching equilibrium.