The Gibbs Free Energy (\(G\)) is a thermodynamic potential used to predict the maximum amount of non-expansion work a closed system can perform at constant temperature and pressure. Calculating the change in Gibbs Free Energy (\(\Delta G\)) for a process determines whether that process is feasible. It combines the two major driving forces in nature—the tendency toward lower energy and the tendency toward greater disorder—into a single, quantifiable value. Calculating this value is fundamental to understanding the direction and limits of chemical reactions.
The Fundamental Equation and Components
The core calculation for the change in Gibbs Free Energy is \(\Delta G = \Delta H – T\Delta S\). This formula unites three distinct thermodynamic properties to assess the overall energy available for useful work. The calculated value is typically given in units of Joules (J) or Kilojoules (kJ) per mole of reaction.
The term \(\Delta H\) represents the change in enthalpy, which is the heat energy absorbed or released by the system at constant pressure. \(\Delta H\) accounts for the energy stored in chemical bonds; a negative value means the reaction releases heat.
The variable \(T\) is the absolute temperature of the system, measured in Kelvin. \(\Delta S\) is the change in entropy, which is a measure of the system’s disorder or randomness. When a reaction increases disorder, \(\Delta S\) is positive, and this increase in randomness contributes favorably to the overall spontaneity of the process.
The equation shows that the total energy change (\(\Delta G\)) is a balance between the heat exchanged (\(\Delta H\)) and the energy associated with increasing disorder (\(T\Delta S\)). Multiplying the entropy change (\(\Delta S\)) by the absolute temperature (\(T\)) ensures the disorder component is expressed in consistent energy units.
Determining Standard Gibbs Free Energy
To calculate the Gibbs Free Energy for specific conditions (\(\Delta G\)), one must first determine the Standard Gibbs Free Energy (\(\Delta G^\circ\)). The degree symbol indicates standard state conditions: 1 atmosphere (or 1 bar) pressure, 1 M concentration for all solutes, and a specified temperature, usually \(298.15 \text{ K}\) (\(25^\circ \text{C}\)).
One method for finding \(\Delta G^\circ\) uses the fundamental equation with standard state values: \(\Delta G^\circ = \Delta H^\circ – T\Delta S^\circ\). This requires looking up the standard enthalpy change (\(\Delta H^\circ\)) and the standard entropy change (\(\Delta S^\circ\)) for the reaction, using \(T = 298.15 \text{ K}\).
Alternatively, \(\Delta G^\circ\) can be calculated using tabulated Standard Free Energies of Formation (\(\Delta G_f^\circ\)). The change in standard free energy for a reaction is found by subtracting the sum of the standard free energies of formation of the reactants from the sum of the products. The formula is: \(\Delta G^\circ = \sum n\Delta G_f^\circ (\text{products}) – \sum m\Delta G_f^\circ (\text{reactants})\), where \(n\) and \(m\) are the stoichiometric coefficients. This method is often simpler because \(\Delta G_f^\circ\) values for elements in their standard state are defined as zero.
Relating Gibbs Free Energy to Equilibrium and Non-Standard Conditions
Calculating \(\Delta G\) for reactions not at standard conditions or at equilibrium requires specific equations. At equilibrium, the system experiences no net change, meaning the driving force is zero (\(\Delta G = 0\)). This allows for a direct relationship between the standard free energy change (\(\Delta G^\circ\)) and the equilibrium constant (\(K\)).
This relationship is defined by \(\Delta G^\circ = -RT\ln K\), where \(R\) is the ideal gas constant (\(8.314 \text{ J} \cdot \text{mol}^{-1} \cdot \text{K}^{-1}\)) and \(\ln K\) is the natural logarithm of the equilibrium constant. This formula allows \(K\) to be calculated from thermodynamic data, or vice versa. A large negative \(\Delta G^\circ\) corresponds to a large \(K\), indicating the reaction strongly favors product formation at equilibrium.
For non-standard conditions (concentrations or pressures not at \(1 \text{ M}\) or \(1 \text{ atm}\)), the actual Gibbs Free Energy change (\(\Delta G\)) is calculated using \(\Delta G = \Delta G^\circ + RT\ln Q\). Here, \(\Delta G^\circ\) is the standard free energy change, and \(Q\) is the reaction quotient. \(Q\) is calculated using the current non-standard concentrations or pressures and measures the reaction’s current position relative to equilibrium.
The term \(RT\ln Q\) acts as a correction factor. If \(Q\) is less than \(K\), the term is negative, causing \(\Delta G\) to be negative, which drives the reaction forward toward equilibrium. If \(Q\) is greater than \(K\), the term is positive, making \(\Delta G\) positive and driving the reaction backward.
Interpreting the Value: Predicting Reaction Spontaneity
Once \(\Delta G\) is calculated for a reaction under specific conditions, its sign determines the reaction’s spontaneity. The \(\Delta G\) value predicts whether a process will occur without the continuous input of external energy. This interpretation applies universally to processes occurring at constant temperature and pressure.
If \(\Delta G\) is negative (\(\Delta G < 0[/latex]), the reaction is spontaneous in the forward direction. This favorable process will proceed on its own to form products. Such a reaction is described as exergonic, meaning it releases energy that can be used to do work. A positive value ([latex]\Delta G > 0\)) signifies that the reaction is non-spontaneous in the forward direction. This unfavorable process will not proceed unless energy is constantly supplied to the system. If the forward reaction is non-spontaneous, the reverse reaction will be spontaneous (having a negative \(\Delta G\)).
If the calculation results in zero (\(\Delta G = 0\)), the reaction is at equilibrium. At this point, the rates of the forward and reverse reactions are equal, and there is no net tendency for the system to change.