Gibbs Energy, symbolised as G, plays a pivotal role in predicting the spontaneity and feasibility of chemical reactions. This set of notes delves into the application of Gibbs Energy in various chemical contexts, focusing on its calculation, the interpretation of its sign, and determining the conditions for reaction spontaneity.

**Understanding Gibbs Energy**

Gibbs Energy (G) is a thermodynamic potential that reflects the maximum reversible work that can be performed by a thermodynamic system at constant temperature and pressure. It incorporates both enthalpy (H) and entropy (S) of the system, providing a more comprehensive understanding of a reaction's spontaneity. The formula for calculating Gibbs Energy change (ΔG) in a process is:

ΔG = ΔH - TΔS

where:

- ΔG is the change in Gibbs Energy
- ΔH is the change in enthalpy
- T is the temperature in Kelvin (K)
- ΔS is the change in entropy

**Application of ΔG⦵ = ΔH⦵ − TΔS⦵ for Calculations**

In chemistry, we often deal with reactions under standard conditions, denoted by the superscript "⦵". Under standard conditions, the concentrations of all reactants and products are 1 M, the pressure is 1 bar, and the temperature is usually 298 K. The equation ΔG⦵ = ΔH⦵ − TΔS⦵ is vital for calculating the standard Gibbs Energy change for a reaction.

**Example Calculation**:- Given a hypothetical reaction with ΔH⦵ = -100 kJ/mol and ΔS⦵ = -200 J/(mol·K) at 298 K, calculate ΔG⦵.
- Convert ΔH⦵ to J/mol: -100 kJ/mol * 1000 J/kJ = -100,000 J/mol
- Plug in the values: ΔG⦵ = (-100,000 J/mol) - (298 K * -200 J/(mol·K)) = -40,000 J/mol or -40 kJ/mol

This process is crucial for determining the spontaneity and feasibility of reactions under standard conditions.

**Interpretation of ΔG**

The sign of ΔG provides insight into the spontaneity of a reaction:

**ΔG < 0**: The reaction is spontaneous and proceeds in the forward direction.**ΔG = 0**: The system is at equilibrium, and there is no net change.**ΔG > 0**: The reaction is non-spontaneous in the forward direction but spontaneous in the reverse direction.

Understanding these conditions is paramount for predicting the behaviour of chemical reactions.

**Determining the Temperature at Which a Reaction Becomes Spontaneous**

The spontaneity of a reaction can depend on the temperature. To find the temperature at which a reaction becomes spontaneous, set ΔG to 0 and solve for T:

0 = ΔH - TΔS

Using this equation allows chemists to predict under what conditions a reaction will proceed without external intervention, a crucial aspect in various fields such as industry and biochemistry.

**ΔG in Exothermic and Endothermic Reactions**

The relationship between ΔG, ΔH, and ΔS can be further analysed by considering exothermic and endothermic reactions:

**Exothermic Reactions (ΔH < 0)**: These reactions release heat. If ΔS is positive, ΔG will always be negative, and the reaction is always spontaneous. If ΔS is negative, ΔG may be negative or positive depending on the temperature.**Endothermic Reactions (ΔH > 0)**: These reactions absorb heat. If ΔS is positive, ΔG may be negative or positive depending on the temperature. If ΔS is negative, ΔG will always be positive, and the reaction is never spontaneous.

Understanding these nuances aids in the comprehensive analysis of chemical reactions.

Image courtesy of Иван Олефиренко

**ΔG and Reaction Mechanisms**

While ΔG provides information about the spontaneity of a reaction, it does not give insights into the reaction mechanism or the rate of the reaction. A reaction with a negative ΔG might be spontaneous, but it could proceed very slowly if the activation energy is high. This distinction is vital for a complete understanding of reaction dynamics.

**Importance of ΔG in Biological Systems**

In biological systems, Gibbs Energy plays a crucial role. Processes such as cellular respiration and photosynthesis are driven by changes in Gibbs Energy. Enzymes in biological systems work to lower the activation energy of reactions, ensuring that vital processes occur efficiently, even if the overall ΔG is small.

**Impact of Pressure on ΔG**

While ΔG is generally considered at constant pressure, changes in pressure can affect the value of ΔG and, consequently, the spontaneity of a reaction. For reactions involving gases, an increase in pressure can shift the equilibrium position and change the value of ΔG.

## FAQ

The sign of ΔG⦵, the standard Gibbs free energy change, has a direct influence on the value of the equilibrium constant, K, for a chemical reaction. When ΔG⦵ is negative, indicating a spontaneous reaction, K is greater than 1, meaning that the products are favoured at equilibrium. If ΔG⦵ is positive, indicating a non-spontaneous reaction, K is less than 1, meaning that the reactants are favoured. When ΔG⦵ is zero, the system is at equilibrium and K is equal to 1. The relationship between ΔG⦵ and K reflects the tendency of a reaction to proceed towards equilibrium, with a lower Gibbs free energy.

A change in pressure can affect the standard Gibbs free energy change, ΔG⦵, for a reaction involving gases due to the impact on enthalpy (ΔH⦵) and entropy (ΔS⦵) changes. For reactions that result in a change in the number of moles of gas, an increase in pressure will favour the formation of fewer moles of gas, potentially altering the values of ΔH⦵ and ΔS⦵, and consequently ΔG⦵. However, under standard conditions, the pressure is fixed at 1 bar, and ΔG⦵ is determined at this constant pressure. Therefore, ΔG⦵ values typically provided in tables are not affected by changes in pressure.

Yes, it is possible for a reaction to have a positive entropy change, ΔS⦵, and still be non-spontaneous. The spontaneity of a reaction depends on the Gibbs free energy change, ΔG⦵, not just on ΔS⦵. Even if ΔS⦵ is positive, contributing to a decrease in ΔG⦵, if the enthalpy change, ΔH⦵, is sufficiently positive or the temperature, T, is low enough, the TΔS⦵ term might not be large enough to offset ΔH⦵, resulting in a positive ΔG⦵. In such cases, the reaction would be non-spontaneous under the given conditions.

A reaction can have a negative ΔG⦵ at all temperatures if its enthalpy change, ΔH⦵, is negative (exothermic) and its entropy change, ΔS⦵, is positive, resulting in a spontaneous reaction under all conditions. In this case, both terms in the Gibbs free energy equation ΔG⦵ = ΔH⦵ - TΔS⦵ contribute to a decrease in ΔG⦵, making it negative. The negative ΔH⦵ lowers ΔG⦵, and the positive TΔS⦵ further lowers ΔG⦵. As temperature increases, the TΔS⦵ term becomes more significant, maintaining the spontaneity of the reaction.

Yes, a reaction can be spontaneous even if both ΔH⦵ (enthalpy change) and ΔS⦵ (entropy change) are negative. Spontaneity is determined by the Gibbs free energy change, ΔG⦵, and not just by enthalpy or entropy changes alone. According to the equation ΔG⦵ = ΔH⦵ - TΔS⦵, a negative ΔH⦵ contributes to a decrease in ΔG⦵, making the reaction more likely to be spontaneous. However, a negative ΔS⦵ tends to increase ΔG⦵, working against spontaneity. Therefore, whether the reaction is spontaneous depends on the magnitude of ΔH⦵ and ΔS⦵ and the temperature of the system. If the magnitude of TΔS⦵ is less than ΔH⦵ and ΔH⦵ is sufficiently negative, the reaction can still be spontaneous.

## Practice Questions

To calculate ΔG⦵, we use the equation ΔG⦵ = ΔH⦵ - TΔS⦵. First, convert ΔH⦵ to J/mol: +75 kJ/mol *1000 J/kJ = +75,000 J/mol. Then, plug in the values: ΔG⦵ = (75,000 J/mol) - (298 K *150 J/(mol·K)) = 75,000 J/mol - 44,700 J/mol = 30,300 J/mol or 30.3 kJ/mol. Since ΔG⦵ is positive, the reaction is non-spontaneous under standard conditions at 298 K.

To find the temperature at which the reaction becomes spontaneous, set ΔG⦵ to 0 and solve for T in the equation 0 = ΔH⦵ - TΔS⦵. Convert ΔH⦵ to J/mol: -50 kJ/mol * 1000 J/kJ = -50,000 J/mol. Then solve for T: 0 = (-50,000 J/mol) - T(-100 J/(mol·K)), leading to T = 500 K. Therefore, the reaction becomes spontaneous at a temperature of 500 K.