Gibbs free energy and its applications

In the study of thermodynamics, the concept of Gibbs free energy is a fundamental concept. This topic covers the principles and applications of Gibbs free energy, which is a thermodynamic potential that can predict the direction of chemical reactions under constant temperature and pressure. More importantly, it helps us understand how energy changes in reactions affect the equilibrium and spontaneity of these reactions.

What is Gibbs free energy?

Gibbs free energy, often denoted as G, is defined as the energy associated with a chemical reaction that can be used to do work. It is a derived quantity that combines enthalpy and entropy, and is formulated as:

G = H - T * S

• G is the Gibbs free energy, measured in joules or kilojoules.
• H is the enthalpy or total heat content of the system.
• T is the temperature in Kelvin.
• S is the entropy, or the degree of disorder in the system.

Visual example

We can illustrate this relationship with a simple diagram that shows how enthalpy, entropy, and temperature work together to affect Gibbs free energy.

Applications of Gibbs free energy

Gibbs free energy is important because it predicts which reactions may occur spontaneously. The change in Gibbs free energy, represented as ΔG, can determine the spontaneity of a reaction:

• If ΔG < 0, then the process is spontaneous.
• If ΔG > 0, then the process will occur spontaneously.
• If ΔG = 0, then the process is at equilibrium.

Example 1: Combustion

Consider the combustion of glucose:

C 6 H 12 O 6 + 6O 2 → 6CO 2 + 6H 2 O

This reaction is highly exothermic, releasing energy. The enthalpy change ΔH is negative, and since entropy increases as gases are formed, ΔS is positive. Both factors contribute to a negative ΔG, indicating that the reaction is spontaneous.

Visual example

Example 2: Phase change

Consider the transformation of water from liquid to vapor:

H 2 O(l) → H 2 O(g)

This process requires energy to overcome intermolecular forces. As the temperature increases, the change in entropy ΔS multiplied by the temperature T becomes significant enough to drive the reaction forward, causing ΔG to become negative, and beyond a certain temperature the phase transition occurs spontaneously.

Calculating Gibbs free energy

The Gibbs free energy change can be calculated using standard enthalpy and entropy changes:

ΔG = ΔH - T * ΔS

Standard conditions imply:

• Temperature: 298 K (about 25°C)
• Pressure: 1 atm

Figures for ΔH and ΔS are commonly found in thermodynamic tables for the compounds involved in a reaction.

Example 3: Standard response

Calculate ΔG for the formation of ammonia:

N 2 (g) + 3H 2 (g) → 2NH 3 (g)

given:

• ΔH = -92.4 kJ/mol
• ΔS = -198.5 joules/mol·K = -0.1985 kJ/mol·K

ΔG can be calculated as:

ΔG = -92.4 kJ/mol - (298 K * -0.1985 kJ/mol K)

Thus, ΔG = -92.4 kJ/mol + 59.3 kJ/mol = -33.1 kJ/mol

Negative ΔG indicates that the reaction is spontaneous under standard conditions.

Gibbs free energy and equilibrium

The relationship between Gibbs free energy and equilibrium is fundamental. At equilibrium, ΔG = 0, which means there is no net change in the system. The energy of the system is at a minimum, and this point is defined by the equilibrium constant K

This relation is given as:

ΔG° = -RT ln(K)

• ΔG° is the standard Gibbs free energy change.
• R is the universal gas constant: 8.314 J/mol K.
• K is the equilibrium constant.

Example 4: Balance calculation

Calculate ΔG° for the reaction with K = 10 at 298 K:

ΔG° = -8.314 joules/mol·K * 298 K * ln(10)

So, ΔG° = -8.314 * 298 * 2.303 = -5718 J/mol = -5.718 kJ/mol

Negative ΔG° confirms that the forward reaction is preferred at equilibrium.

Importance of Gibbs free energy

Prediction of spontaneity

In chemical processes it is important to understand whether a reaction is spontaneous or not. Engineers and chemists use this knowledge to develop reactions and synthesize materials efficiently.

Biochemical reactions

In living organisms, biochemical reactions rely heavily on Gibbs free energy. Energy-yielding reactions such as ATP hydrolysis should have a negative ΔG under physiological conditions.

Industrial processes

Industrial chemical processes, such as the Haber process for ammonia synthesis or the production of sulfuric acid, are optimized using Gibbs free energy principles, ensuring cost-effectiveness and energy efficiency.

Conclusion

Gibbs free energy is a versatile and important concept within thermodynamics and chemistry. Understanding how it works enables us to predict reaction behavior, understand equilibrium, and apply it in both theoretical and practical scenarios across a variety of scientific disciplines.

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