The study of energy and its transformations, known as thermodynamics, provides the framework for understanding why chemical reactions happen. At the heart of this field is the concept of free energy, a powerful predictive tool. Free energy is a thermodynamic property that measures the “usefulness” of the energy contained within a chemical system. This value allows chemists to predict whether a particular reaction or process is possible under a given set of conditions.
Defining Free Energy and Spontaneity
The specific measure used to predict a reaction’s feasibility is the Gibbs Free Energy, represented by the symbol \(G\). The change in Gibbs Free Energy, denoted as \(\Delta G\), represents the maximum amount of energy released from a system that is available to perform non-mechanical work. This energy could be used, for example, to power a biological process or generate electrical current in a battery.
The primary function of calculating \(\Delta G\) is to determine a reaction’s spontaneity—whether a process can occur on its own without continuous external energy input. A spontaneous reaction moves the system toward a more stable, lower-energy state. Spontaneity only indicates the direction a reaction favors, not the speed at which it occurs.
The sign of \(\Delta G\) predicts the reaction’s behavior. If \(\Delta G\) is negative (\(\Delta G < 0[/latex]), the reaction is spontaneous (exergonic) and favors the formation of products. Conversely, if [latex]\Delta G[/latex] is positive ([latex]\Delta G > 0\)), the reaction is non-spontaneous (endergonic), requiring a continuous supply of energy to proceed. When \(\Delta G\) is zero, the system is at chemical equilibrium, with no net change occurring.
The Driving Forces: Enthalpy and Entropy
The total energy available in a system is determined by the interplay of two fundamental thermodynamic components: enthalpy and entropy. These factors represent the competing tendencies of a system to achieve a lower energy state and a higher state of disorder. Gibbs Free Energy balances the influence of these two driving forces.
Enthalpy, symbolized by \(H\), is a measure of the total heat content of a system. The change in enthalpy (\(\Delta H\)) measures the heat absorbed or released during a reaction conducted at constant pressure. Systems naturally tend toward a state of lower energy, meaning reactions that release heat into the surroundings are favored.
When a reaction releases heat, it is termed exothermic, and \(\Delta H\) is negative. Examples include the combustion of fuels. Reactions that absorb heat from the surroundings are endothermic, resulting in a positive \(\Delta H\). Endothermic reactions are generally less favorable from an energy standpoint alone.
The second factor, entropy, symbolized by \(S\), is a measure of the disorder or randomness within a system. Nature tends toward increasing disorder, meaning systems favor processes that result in a more random arrangement of matter. The change in entropy (\(\Delta S\)) is positive when a reaction increases disorder, such as when a solid melts into a liquid or a molecule breaks down into smaller molecules.
A negative change in entropy (\(\Delta S < 0[/latex]) indicates an increase in order, such as when a gas condenses into a liquid. For a process to be favored by entropy, [latex]\Delta S[/latex] must be positive. The total free energy change is a negotiation between the system's desire to minimize heat (enthalpy) and maximize disorder (entropy).
Calculating Reaction Outcome: The Gibbs Equation
The relationship connecting these driving forces to free energy is defined by the Gibbs Free Energy Equation: [latex]\Delta G = \Delta H – T\Delta S\). This equation combines the change in enthalpy (\(\Delta H\)) and the change in entropy (\(\Delta S\)) to determine the overall change in \(\Delta G\). The term \(T\) represents the absolute temperature of the reaction, measured in Kelvin.
Temperature plays a moderating role by scaling the influence of the entropy term. Since temperature is always positive on the Kelvin scale, a higher temperature increases the magnitude of the \(T\Delta S\) term. This means that at higher temperatures, the entropic driving force—the tendency toward disorder—becomes more significant in determining spontaneity.
The combination of the signs of \(\Delta H\) and \(\Delta S\) leads to four possible scenarios for spontaneity. If a reaction is exothermic (\(\Delta H\) is negative) and increases disorder (\(\Delta S\) is positive), \(\Delta G\) is always negative, making the reaction spontaneous at all temperatures. Conversely, if a reaction is endothermic (\(\Delta H\) is positive) and decreases disorder (\(\Delta S\) is negative), \(\Delta G\) will always be positive, and the reaction is non-spontaneous under all conditions.
When the two driving forces oppose each other, spontaneity depends on the temperature. If a reaction is exothermic (\(\Delta H\) is negative) but decreases disorder (\(\Delta S\) is negative), it is spontaneous only at low temperatures. At high temperatures, the positive \(T\Delta S\) term dominates the negative \(\Delta H\) term, causing \(\Delta G\) to become positive.
The final scenario is an endothermic reaction (\(\Delta H\) is positive) that increases disorder (\(\Delta S\) is positive). This reaction is only spontaneous at high temperatures, where the large positive \(T\Delta S\) term overcomes the positive \(\Delta H\) term, resulting in a net negative \(\Delta G\). This temperature dependence highlights how conditions can be manipulated to control chemical feasibility.
Free Energy and Chemical Equilibrium
The concept of free energy provides a clear picture of how far a reaction is from reaching chemical equilibrium, its most stable state. At equilibrium, the rate of reactants converting into products is exactly balanced by the rate of products reverting to reactants. This dynamic balance means there is no further net change in concentrations.
When a system reaches this balanced state, the change in Gibbs Free Energy is zero (\(\Delta G = 0\)). This signifies that the system has reached the minimum free energy possible under the given conditions. With \(\Delta G=0\), there is no further energetic drive to shift in either the forward or reverse direction, meaning the reaction is neither spontaneous nor non-spontaneous.
The relationship between \(\Delta G\) and the equilibrium state is quantified by the equilibrium constant, \(K\). The standard change in free energy, \(\Delta G^\circ\), is directly related to \(K\), allowing chemists to predict the final ratio of products to reactants. A highly negative \(\Delta G\) indicates the reaction is far from equilibrium and will proceed strongly toward forming products, resulting in a large \(K\) value.