Understanding Chemical Thermodynamics and Free Energy

Gibbs free energy (G) is a thermodynamic potential that measures the maximum reversible work obtainable from a thermodynamic system at constant temperature and pressure. The equation G = H - TS describes this relationship, where H represents enthalpy, T is the absolute temperature, and S is entropy. This equation indicates that the free energy decreases as the entropy of the system increases, which is crucial for determining the spontaneity of processes: a negative change in Gibbs free energy signifies a spontaneous reaction.

A positive ΔG indicates that the Gibbs free energy of the products is greater than that of the reactants, suggesting that the reaction requires an input of energy to proceed. This means that under standard conditions, the reaction does not occur spontaneously and is considered nonspontaneous. In contrast, a negative ΔG would indicate a spontaneous reaction, while a ΔG of zero would suggest that the system is at equilibrium.

ΔG = 0 indicates that there is no net change in the concentrations of reactants and products over time, meaning the forward and reverse reactions occur at the same rate. At this point, the system is in a state of balance, and while the reactions continue to occur, there is no overall change in free energy. This signifies that the system has reached equilibrium, where the concentrations of reactants and products remain constant.

Standard free energy change is denoted as ΔG° to indicate the change in free energy under standard conditions, typically at 1 M concentration for solutes, 1 atm pressure for gases, and a specified temperature, usually 25°C. This notation helps distinguish it from the free energy change (ΔG), which can vary with conditions. ΔG° provides a reference point for predicting the spontaneity of a reaction, with negative values indicating spontaneous processes under standard conditions.

According to the third law of thermodynamics, as the temperature of a perfectly crystalline substance approaches absolute zero (0 K), its entropy approaches a minimum value. For a perfect crystal, this minimum value is defined as zero because there is only one possible microstate—the ordered arrangement of its particles. At 0 K, the system is in its ground state, and there is no disorder, leading to zero entropy. This principle underscores the relationship between temperature, order, and entropy in thermodynamic systems.

In thermodynamics, the relationship between enthalpy (H) and entropy (S) for a spontaneous process at constant temperature is described by the Gibbs free energy equation, ΔG = ΔH - TΔS. Here, ΔG represents the change in free energy, which indicates the spontaneity of a process. A negative ΔG signifies that a process can occur spontaneously. The equation shows that the change in free energy is influenced by both the heat content (enthalpy) and the degree of disorder (entropy) in the system, with temperature acting as a scaling factor for entropy.

When ΔH is negative, it indicates that the reaction releases heat (exothermic), while a positive ΔS signifies an increase in entropy, or disorder. According to the Gibbs free energy equation (ΔG = ΔH - TΔS), a negative ΔH and positive ΔS will always yield a negative ΔG, making the reaction thermodynamically favorable and spontaneous at any temperature. Thus, regardless of temperature changes, the combination of these two factors ensures that the reaction proceeds spontaneously.

Standard entropies are measured under specific conditions to ensure consistency and comparability. The standard state is defined as 1 bar (approximately 1 atm) of pressure and a specified temperature, typically 25 °C (298.15 K). This temperature is chosen as it is close to room temperature, making it a practical reference point for most chemical reactions and processes. Using these conditions allows for the standardization of thermodynamic data, facilitating calculations and comparisons across different substances.

Increasing temperature generally leads to greater molecular motion and disorder within a substance. As temperature rises, particles gain kinetic energy, resulting in more possible microstates and configurations. This increase in randomness and disorder contributes to a higher entropy value, reflecting the system's increased uncertainty and energy dispersal. Therefore, as temperature increases, the entropy of a substance also increases.

To determine the sign of ΔG, we use the Gibbs free energy equation: ΔG = ΔH - TΔS. Here, ΔH is negative (-18.0 kJ), indicating an exothermic reaction, while ΔS is also negative (-139.7 J/K), suggesting a decrease in entropy. At 25 °C (298 K), TΔS becomes a positive value, which is larger than ΔH in magnitude. Thus, ΔG becomes positive, indicating that the reaction is non-spontaneous under these conditions.