Gibbs free energy is a fundamental concept in chemistry and physics, providing insight into the spontaneity of a process. This thermodynamic quantity helps predict whether a reaction or physical change will occur on its own under constant temperature and pressure. It is broadly applicable, influencing fields such as biology (metabolic reactions) and materials science, and quantifies the maximum work extractable from a system.
The Core Components
To understand Gibbs free energy, it is important to grasp its foundational components. Enthalpy, symbolized as ΔH, represents the heat content within a system at constant pressure. A negative ΔH indicates an exothermic process (heat released), while a positive ΔH signifies an endothermic process (heat absorbed).
Entropy, denoted as ΔS, measures the distribution of energy within a system, often described as its disorder. A positive ΔS indicates an increase in disorder, such as a solid melting into a liquid, which favors spontaneity. Conversely, a negative ΔS suggests a decrease in disorder.
The third component, temperature (T), acts as a weighting factor for entropy’s contribution and must always be expressed in Kelvin (K) for calculations. To convert Celsius to Kelvin, add 273.15.
The Defining Equation
The interplay of enthalpy, entropy, and temperature is encapsulated in the Gibbs free energy equation: ΔG = ΔH – TΔS. ΔG represents the change in Gibbs free energy, indicating spontaneity. ΔH signifies the change in enthalpy, reflecting heat exchanged. The term TΔS accounts for the change in entropy (disorder) weighted by absolute temperature.
This equation combines two primary thermodynamic driving forces: a system’s tendency to achieve a lower energy state (enthalpy) and its tendency towards greater disorder (entropy). The subtraction of the TΔS term from ΔH shows that entropy’s effect on spontaneity becomes more pronounced at higher temperatures. At elevated temperatures, the TΔS term can outweigh ΔH, making a reaction spontaneous even if it is endothermic.
Calculating Gibbs Free Energy
Calculating Gibbs free energy involves a straightforward application of the defining equation, requiring careful attention to units. The first step is to identify the given values for enthalpy (ΔH), entropy (ΔS), and temperature (T).
Next, ensure unit consistency, especially between ΔH and ΔS. Enthalpy values are commonly given in kilojoules per mole (kJ/mol), while entropy values are often in joules per mole-Kelvin (J/mol·K). The entropy value must be converted to kilojoules per mole-Kelvin by dividing by 1000. Temperature must always be in Kelvin; if given in Celsius, convert by adding 273.15.
Once all units are consistent, the values can be directly substituted into the equation ΔG = ΔH – TΔS. For example, if ΔH is -10 kJ/mol, ΔS is 50 J/mol·K, and the temperature is 25°C: convert ΔS to 0.050 kJ/mol·K and temperature to 298.15 K. Then, ΔG = -10 kJ/mol – (298.15 K 0.050 kJ/mol·K), resulting in ΔG ≈ -24.91 kJ/mol.
Interpreting Calculation Results
The numerical value for ΔG provides information about a process’s spontaneity under specified conditions. A negative ΔG (ΔG < 0) indicates the process is spontaneous, meaning it is favored and can proceed without continuous external energy input. Conversely, if ΔG is positive (ΔG > 0), the process is non-spontaneous. The reverse process would be spontaneous, or external energy would be required to drive the reaction forward.
When ΔG equals zero (ΔG = 0), the system is at equilibrium, meaning no net change occurs; forward and reverse process rates are equal.
It is important to note that “spontaneous” in thermodynamics does not imply a reaction will occur quickly, only that it is energetically favorable. Reaction speed is determined by kinetics, not spontaneity.