Overview

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:

1. Both ΔH and ΔS are positive. This condition describes an endothermic process that involves an increase in system entropy. In this case, ΔG will be negative if the magnitude of the TΔS term is greater than ΔH. If the TΔS term is less than ΔH, the free energy change will be positive. Such a process is spontaneous at high temperatures and nonspontaneous at low temperatures.
2. Both ΔH and ΔS are negative. This condition describes an exothermic process that involves a decrease in system entropy. In this case, ΔG will be negative if the magnitude of the TΔS term is less than ΔH. If the TΔS term’s magnitude is greater than ΔH, the free energy change will be positive. Such a process is spontaneous at low temperatures and nonspontaneous at high temperatures.
3. ΔH is positive and ΔS is negative. This condition describes an endothermic process that involves a decrease in system entropy. In this case, ΔG will be positive regardless of the temperature. Such a process is nonspontaneous at all temperatures.
4. ΔH is negative and ΔS is positive. This condition describes an exothermic process that involves an increase in system entropy. In this case, ΔG will be negative regardless of the temperature. Such a process is spontaneous at all temperatures.

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 ΔG_rxn 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.  

Procedure

The change in Gibbs free energy, or delta G, is the energy absorbed or released when energy-storing bonds are formed or broken, respectively.

The sign of delta G depends on the signs and the relative values of enthalpy, entropy, and temperature.

If delta H is negative and delta S is positive, delta G is negative at all temperatures. Thus, exothermic reactions where the entropy of the system increases are always spontaneous.

If both delta H and delta S are negative, delta G depends on the temperature. Reactions with negative enthalpy and entropy changes are spontaneous only at low temperatures.

Delta G is also dependent on temperature if both delta H and delta S are positive. Reactions with positive enthalpy and entropy changes are spontaneous only at higher temperatures.

When delta H is positive and delta S is negative, delta G is always positive, and the reaction is nonspontaneous at all temperatures.

For any reaction mixture composition, the delta G for the reaction is the sum of the standard free energy and RT times the natural log of the reaction quotient.

When the reactants and products are at equilibrium, the free energy change is zero, and the reaction quotient equals the equilibrium constant. So, the standard free energy change equals negative RT ln(K).

If delta G naught is less than zero, ln(K) is positive, meaning K is greater than 1. In this case, product formation is favored at equilibrium. The larger the equilibrium constant, the greater the decrease in Gibbs free energy. 

Reactions with negative delta G values involve the release of free energy to the surroundings and are called ‘exergonic’ reactions.

Conversely, if delta G naught is greater than zero, ln(K) is negative, meaning K is less than 1, and the reverse direction of the reaction is favored.

Reactions with a positive delta G absorb free energy from the surroundings and are called ‘endergonic’ reactions.