Gibbs Free Energy (\(\Delta G\)) quantifies the maximum amount of non-expansion work a system can perform at a constant temperature and pressure. It measures the energy available to drive a process, such as a chemical reaction. A negative \(\Delta G\) means the process is spontaneous, while a positive value indicates it requires energy to occur. Standard Free Energy (\(\Delta G^\circ\)) is the Gibbs Free Energy change calculated under a specific set of standardized conditions. These conditions are defined as 298.15 Kelvin (25 degrees Celsius), 1 atmosphere (or 1 bar) pressure, and 1 molar concentration for all dissolved species. Calculating \(\Delta G^\circ\) is the first step in predicting the thermodynamic feasibility of a chemical reaction, establishing a uniform baseline for comparison.
Calculating Standard Free Energy from Enthalpy and Entropy
The fundamental method for determining \(\Delta G^\circ\) involves combining standard enthalpy (\(\Delta H^\circ\)) and standard entropy (\(\Delta S^\circ\)). The defining equation is \(\Delta G^\circ = \Delta H^\circ – T\Delta S^\circ\). This formula shows that spontaneity is governed by a balance between the change in heat content and the change in molecular disorder.
The term \(\Delta H^\circ\) represents the standard enthalpy change, which is the heat absorbed or released by the system under standard conditions. Exothermic reactions (negative \(\Delta H^\circ\)) generally favor spontaneity. The \(\Delta S^\circ\) term is the standard entropy change, measuring the change in the dispersal of energy and matter. An increase in disorder (positive \(\Delta S^\circ\)) also favors spontaneity.
The temperature (\(T\)) is the absolute temperature in Kelvin, which weights the entropy contribution. Multiplying \(\Delta S^\circ\) by \(T\) converts the entropy change into an energy term, \(-T\Delta S^\circ\), which is directly compared to \(\Delta H^\circ\). It is important to ensure that the units for \(\Delta H^\circ\) (usually kilojoules per mole) and \(T\Delta S^\circ\) are consistent before subtraction.
When \(\Delta H^\circ\) and \(\Delta S^\circ\) have opposite signs, the reaction is always spontaneous (\(\Delta G^\circ\) is negative) at all temperatures. If both terms share the same sign, temperature becomes the deciding factor. For example, if both are positive, the reaction becomes spontaneous only at temperatures high enough for the large positive \(T\Delta S^\circ\) term to overcome the positive \(\Delta H^\circ\) term.
Calculating Standard Free Energy from Formation Values
A practical alternative to calculating \(\Delta G^\circ\) involves using tabulated standard free energies of formation (\(\Delta G_f^\circ\)). This method is often quicker because it utilizes pre-calculated values widely available in chemical reference tables. The calculation follows a simple summation rule, analogous to calculating standard enthalpy or entropy changes.
The equation used is \(\Delta G^\circ = \sum \Delta G_f^\circ (\text{products}) – \sum \Delta G_f^\circ (\text{reactants})\). This process involves summing the \(\Delta G_f^\circ\) values for all products, multiplied by their stoichiometric coefficients, and subtracting the corresponding sum for all reactants. This approach leverages the fact that Gibbs Free Energy is a state function, meaning the total change depends only on the initial and final states.
The standard free energy of formation (\(\Delta G_f^\circ\)) is defined as the change in Gibbs Free Energy when one mole of a compound is formed from its constituent elements in their most stable forms at standard conditions. By convention, the \(\Delta G_f^\circ\) for any pure element in its standard state (e.g., \(\text{O}_2\) or solid carbon) is defined as zero. This zero baseline simplifies the calculation. This formation method is particularly useful for complex reactions where directly measuring enthalpy and entropy changes might be challenging.
Connecting Standard Free Energy to the Equilibrium Constant
The standard free energy change (\(\Delta G^\circ\)) is fundamentally linked to the extent of a reaction through the equilibrium constant (\(K\)). This relationship is described by the equation \(\Delta G^\circ = -RT \ln K\). This equation connects a thermodynamic property (\(\Delta G^\circ\)) with a measure of reaction composition at equilibrium (\(K\)).
In this formula, \(R\) is the Ideal Gas Constant (8.314 J/mol·K), \(T\) is the absolute temperature in Kelvin, and \(K\) is the equilibrium constant. \(K\) describes the ratio of product concentrations to reactant concentrations when the rates of the forward and reverse reactions are equal. The \(\Delta G^\circ\) value measures the thermodynamic “driving force” for the reaction to move from standard state conditions to its equilibrium state.
The sign and magnitude of \(\Delta G^\circ\) provide direct insight into the value of \(K\) and the favored direction of the reaction.
Interpretation of \(\Delta G^\circ\) and \(K\)
Negative \(\Delta G^\circ\): The reaction favors the formation of products at equilibrium, resulting in \(K > 1\). A large negative \(\Delta G^\circ\) indicates the reaction proceeds almost entirely to completion.
Positive \(\Delta G^\circ\): The reaction favors the reactants at equilibrium, leading to \(\)K < 1[/latex].
Zero [latex]\Delta G^\circ[/latex]: [latex]K[/latex] equals 1, meaning that at equilibrium, the concentrations of products and reactants are comparable to their standard state values.