The spontaneity of a process depends upon the temperature of the system. Phase transitions, for example, will proceed spontaneously in one direction or the other depending upon the temperature of the substance in question. Likewise, some chemical reactions can also exhibit temperature-dependent spontaneities. To illustrate this concept, the equation relating free energy change to the enthalpy and entropy changes for the process is considered:
The spontaneity of a process, as reflected in the arithmetic sign of its free energy change, is then determined by the signs of the enthalpy and entropy changes and, in some cases, the absolute temperature. Since T is the absolute (kelvin) temperature, it can only have positive values. Four possibilities therefore exist with regard to the signs of the enthalpy and entropy changes:
The free energy change for a process may be viewed as a measure of its driving force. A negative value for ΔG represents a driving force for the process in the forward direction, while a positive value represents a driving force for the process in the reverse direction. When ΔGrxn is zero, the forward and reverse driving forces are equal, and the process occurs in both directions at the same rate (the system is at equilibrium).
Recall that Q is the numerical value of the mass action expression for the system, and its value may be used to identify the direction in which a reaction will proceed in order to achieve equilibrium. When Q is less than the equilibrium constant, K, the reaction will proceed in the forward direction until equilibrium is reached and Q = K. Conversely, if Q > K, the process will proceed in the reverse direction until equilibrium is achieved.
The free energy change for a process taking place with reactants and products present under nonstandard conditions (pressures other than 100 kPa; concentrations other than 1 M) is related to the standard free energy change according to this equation:
R is the gas constant (8.314 J/K mol), T is the kelvin or absolute temperature, and Q is the reaction quotient. For a system at equilibrium, Q = K and ΔG = 0, and the previous equation may be written as
This form of the equation provides a useful link between these two essential thermodynamic properties, and it can be used to derive equilibrium constants from standard free energy changes and vice versa. The relations between standard free energy changes and equilibrium constants are summarized below.
If K > 1, ΔG° < 0 and the products are more abundant in the reaction mixture.
If K < 1, ΔG° > 0 and the reactants are more abundant in the reaction mixture.
If K = 1, ΔG° = 0 and the reactants and products are comparably abundant in the reaction mixture.
This text is adapted from Openstax, Chemistry 2e, Section 16.4: Free Energy.
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