Difference Between Free Energy and Enthalpy

Key Difference – Free Energy vs Enthalpy
 

Free energy and enthalpy are two thermodynamic terms used to explain the relationship between heat energy and chemical reactions that occur in a thermodynamic system. Free energy or thermodynamic free energy is the amount of work that a thermodynamic system can perform. In other words, free energy is the amount of energy that is available in that thermodynamic system to perform thermodynamic work. Enthalpy, on the other hand, is a thermodynamic quantity that represents the total energy content in a thermodynamic system. The key difference between free energy and enthalpy is that free energy gives the total energy available to perform thermodynamic work whereas enthalpy gives the total energy of a thermodynamic system that can be converted to heat.

CONTENTS

1. Overview and Key Difference
2. What is Free Energy
3. What is Enthalpy
4. Relationship Between Free Energy and Enthalpy
5. Side by Side Comparison – Free Energy vs Enthalpy in Tabular Form
6. Summary

What is Free Energy?

Free energy is the amount of energy available for a thermodynamic system to perform thermodynamic work. Free energy has the dimensions of energy. The value of the free energy of a thermodynamic system is determined by the present state of the system; not by its history. There are two main types of free energy often discussed in thermodynamics; Helmholtz free energy and Gibbs free energy.

Helmholtz Free Energy

The Helmholtz free energy is the energy that is available in a closed, thermodynamic system to perform thermodynamic work at constant temperature and volume. Hence, the negative value of Helmholtz energy indicates the maximum work that a thermodynamic system can perform by holding its volume constant. In order to keep the volume constant, some of the total thermodynamic work is done as boundary work (to keep the boundary of the system as it is). The equation of Helmholtz energy is given below.

A   =   U   –   TS

Where A is the Helmholtz free energy, U is the internal energy, T is a temperature, which is a constant and S is the entropy of the system. Entropy is a thermodynamic quantity representing the unavailability of a system’s thermal energy for conversion into mechanical work.

Gibbs Free Energy:

The Gibbs free energy the energy that is available in a closed, thermodynamic system to perform thermodynamic work at constant temperature and pressure. The volume of the system can vary. Free energy is denoted by G. The equation of Gibbs free energy is given below.

G    =   H   –   TS

In the above equation, G is Gibbs free energy, H is the enthalpy of the system, Y is the temperature, which is a constant and S is the entropy of the system.

What is Enthalpy?

Enthalpy of a system is a thermodynamic quantity equivalent to the total heat content of a system. It is equal to the internal energy of the system plus the product of pressure and volume. Therefore, it is a thermodynamic property of a system. The equation of enthalpy is given below.

H    =   U   +   PV

Accordingly, H is the enthalpy of the system, U is the internal energy of the system, P is the pressure and V is the volume. The enthalpy of a system is the indication of that system’s capacity to release heat (to do non-mechanical work). The enthalpy is denoted by the symbol H.

Determining the enthalpy of a system allows us to indicate if a chemical reaction is exothermic or endothermic. The change in enthalpy of a system can be used to determine the heat of reactions and also to predict if a chemical reaction is spontaneous or non-spontaneous.

What is the Relationship Between Free Energy and Enthalpy?

The Gibbs free energy and enthalpy are related through the following equation.

G    =   H   –   TS

In the above equation, G is Gibbs free energy, H is the enthalpy of the system, Y is the temperature, which is a constant and S is the entropy of the system. Both G and H has the same units of measurement.

What is the Difference Between Free Energy and Enthalpy?

Free Energy vs Enthalpy
Free energy is the amount of energy available for a thermodynamic system to perform thermodynamic work.	Enthalpy of a system is a thermodynamic quantity equivalent to the total heat content of a system.
Concept
Free energy gives the total energy available to perform thermodynamic work.	Enthalpy gives the total energy of a system that can be converted to heat.
Conversion
Free energy gives the energy that can be converted to mechanical work of the system.	Enthalpy gives the energy that can be converted to non-mechanical work of the system.

Summary – Free Energy vs Enthalpy

Free energy and enthalpy of a thermodynamic system represent energy that is available in a system. The key difference between free energy and enthalpy is that free energy gives the total energy available to perform thermodynamic work whereas enthalpy gives the total energy of a system that can be converted to heat.

Reference:

1.The Editors of Encyclopædia Britannica. “Free energy.” Encyclopædia Britannica, Encyclopædia Britannica, inc., 5 Jan. 2012. Available here
2.Helmenstine, Anne Marie, D. “What Is Enthalpy in Chemistry and Physics?” ThoughtCo, Jan. 25, 2018. Available here
3.“Helmholtz free energy.” Wikipedia, Wikimedia Foundation, 17 Feb. 2018. Available here
4.“Gibbs (Free) Energy.” Chemistry LibreTexts, Libretexts, 12 Jan. 2018. Available here

Image Courtesy:

1.’Hermann von Helmholtz’ (Public Domain) via Commons Wikimedia