Free Energy
Understanding Free Energy
Free energy is a thermodynamic quantity that measures the amount of work that can be extracted from a system at constant temperature and pressure. It is a useful concept because it helps predict the direction of chemical reactions and the equilibrium position of the reactions. There are two main types of free energy: Gibbs free energy (G) and Helmholtz free energy (A).
Gibbs Free Energy (G)
Gibbs free energy, named after Josiah Willard Gibbs, is the most commonly used measure of free energy. It is defined for a system at constant pressure and temperature. The change in Gibbs free energy, denoted as $\Delta G$, can be calculated using the following formula:
$$ \Delta G = \Delta H - T\Delta S $$
where:
- $\Delta G$ is the change in Gibbs free energy
- $\Delta H$ is the change in enthalpy (heat content)
- $T$ is the absolute temperature (in Kelvin)
- $\Delta S$ is the change in entropy
Spontaneity and Equilibrium
The sign of $\Delta G$ determines the spontaneity of a process:
- If $\Delta G < 0$, the process is spontaneous (it can occur without external input).
- If $\Delta G > 0$, the process is non-spontaneous (it requires external energy to occur).
- If $\Delta G = 0$, the system is at equilibrium.
Standard Gibbs Free Energy Change ($\Delta G^\circ$)
The standard Gibbs free energy change is the change in free energy that occurs when reactants in their standard states are converted to products in their standard states. The standard state is defined as the most stable form of a substance at 1 bar pressure and a specified temperature, usually 298 K.
Helmholtz Free Energy (A)
Helmholtz free energy is defined for a system at constant volume and temperature. The change in Helmholtz free energy, denoted as $\Delta A$, is given by:
$$ \Delta A = \Delta U - T\Delta S $$
where:
- $\Delta A$ is the change in Helmholtz free energy
- $\Delta U$ is the change in internal energy
- $T$ is the absolute temperature (in Kelvin)
- $\Delta S$ is the change in entropy
Helmholtz free energy is particularly useful in the study of systems where volume does not change, such as in the case of solid-state reactions.
Differences and Important Points
| Property | Gibbs Free Energy (G) | Helmholtz Free Energy (A) |
|---|---|---|
| Definition | Energy available to do work at constant pressure and temperature | Energy available to do work at constant volume and temperature |
| Formula | $\Delta G = \Delta H - T\Delta S$ | $\Delta A = \Delta U - T\Delta S$ |
| Conditions | Constant pressure (P) and temperature (T) | Constant volume (V) and temperature (T) |
| Spontaneity | $\Delta G < 0$ for spontaneous processes | $\Delta A < 0$ for spontaneous processes |
| Equilibrium | $\Delta G = 0$ | $\Delta A = 0$ |
| Standard State | 1 bar pressure and 298 K | Not commonly used |
Examples
Example 1: Spontaneous Reaction
Consider the reaction of hydrogen gas with oxygen gas to form water at standard conditions:
$$ 2H_2(g) + O_2(g) \rightarrow 2H_2O(l) $$
The standard Gibbs free energy change for this reaction is negative, indicating that the reaction is spontaneous at standard conditions.
Example 2: Non-Spontaneous Reaction
The decomposition of water into hydrogen and oxygen gases is non-spontaneous under standard conditions:
$$ 2H_2O(l) \rightarrow 2H_2(g) + O_2(g) $$
The standard Gibbs free energy change for this reaction is positive, meaning that it requires an input of energy (such as electricity in electrolysis) to proceed.
Example 3: Equilibrium
At equilibrium, the free energy of the system is at a minimum, and there is no net change in the composition of the system. For example, in a closed container with liquid water and its vapor, the system reaches equilibrium when the rates of evaporation and condensation are equal. At this point, $\Delta G = 0$.
Conclusion
Free energy is a fundamental concept in thermodynamics that helps predict the direction and extent of chemical reactions. Gibbs free energy is most commonly used in chemistry, especially for reactions at constant pressure and temperature. Understanding free energy is crucial for fields such as physical chemistry, biochemistry, and engineering, as it provides insights into the feasibility and efficiency of chemical processes and reactions.