Question

Define free energy. What are its units?

Short answer

Free energy is the work a system can perform, measured in joules (J).

Step-by-step solution

Understanding Free Energy

Free energy, in a thermodynamic context, refers to the amount of work a thermodynamic system can perform. It is typically used to predict the direction of chemical reactions and to determine equilibrium conditions of a system.

Identifying Types of Free Energy

The most common types of free energy are Gibbs free energy and Helmholtz free energy. Gibbs free energy is used for processes occurring at constant pressure and temperature, while Helmholtz free energy applies to constant volume and temperature processes.

Deriving the Formula for Gibbs Free Energy

Gibbs free energy (G) is defined by the formula: \[ G = H - TS \] where \(H\) is the enthalpy, \(T\) is the temperature in Kelvin, and \(S\) is the entropy of the system.

Units of Gibbs Free Energy

Since Gibbs free energy calculations involve enthalpy (measured in joules), temperature (in Kelvin), and entropy (in joules per Kelvin), the units of Gibbs free energy as a whole are joules (J) in the SI system.

Key concepts

Thermodynamics

Thermodynamics is a branch of physics that explores how heat and energy interact within different systems. It forms the foundation for understanding free energy concepts. In thermodynamics, you deal often with terms like energy, work, and heat. These concepts are governed by the laws of thermodynamics.

**Key Aspects of Thermodynamics**:

• First Law: Also known as the law of energy conservation, states that energy cannot be created or destroyed, just transformed from one form to another.
• Second Law: Indicates that energy transformations are not entirely efficient, and some energy is always lost as heat, leading to an increase in entropy or disorder.
• Third Law: Asserts that as a system reaches absolute zero temperature, its entropy approaches a constant minimum.

Overall, by analyzing energy changes through these laws, thermodynamics allows us to predict how systems behave and under which conditions reactions proceed. This understanding is crucial when dealing with processes involving free energies like Gibbs and Helmholtz free energy.

Gibbs Free Energy

Gibbs free energy, commonly denoted as G, is a key concept in thermodynamics, particularly useful for predicting the feasibility of chemical reactions that occur at constant pressure and temperature. It combines the system's enthalpy, entropy, and temperature to forecast whether a process occurs spontaneously.

**Formula and Interpretation**:

• The formula to calculate Gibbs free energy is \[ G = H - TS \] where \( H \) is enthalpy, \( T \) is temperature, and \( S \) is entropy.
• A negative change in Gibbs free energy ( \( \Delta G < 0 \) ) indicates a spontaneous process, meaning it can proceed without additional energy input.
• A positive \( \Delta G \) indicates a non-spontaneous process that requires energy input.
• If \( \Delta G \) equals zero, the system is at equilibrium.

Therefore, Gibbs free energy becomes a powerful tool for chemists and engineers to explore reaction pathways, design systems, and understand biological processes at a molecular level.

Helmholtz Free Energy

Helmholtz free energy, represented as A, is another form of free energy in thermodynamics. It is particularly useful in situations involving constant volume and temperature, such as in closed containers or reactions in rigid vessels. This form of energy assists in determining the work that can be extracted from a system.

**Understanding Helmholtz Energy**:

• The mathematical expression for Helmholtz free energy is \( A = U - TS \), where \( U \) is the internal energy of the system, \( T \) is the temperature, and \( S \) is the entropy.
• Helmholtz free energy helps determine how much energy in a system is available for doing work, excluding that lost to entropy.
• When \( \Delta A < 0 \), the process is spontaneous at constant temperature and volume.

The concept is heavily utilized in physical chemistry and engineering, providing insights into how microscopic interactions translate into observable macroscopic behavior.