δg = δh - tδs

Definition

The equation $$ ext{δg} = ext{δh} - t ext{δs}$$ represents the relationship between the change in Gibbs free energy (δg), the change in enthalpy (δh), and the change in entropy (δs) at a constant temperature (t). This equation is crucial for understanding how energy changes in a system and predicting the spontaneity of reactions, as it links thermodynamic quantities that describe both heat and disorder.

5 Must Know Facts For Your Next Test

1. The sign of δg determines whether a process is spontaneous: if δg < 0, the reaction occurs spontaneously; if δg > 0, it is non-spontaneous.
2. At equilibrium, the Gibbs free energy change (δg) is zero, indicating that the system is in a state of maximum stability.
3. The equation can be rearranged to show how changes in enthalpy and entropy affect the Gibbs free energy, highlighting their competing roles in determining spontaneity.
4. Temperature plays a crucial role in this equation; as temperature increases, the significance of entropy change (tδs) can lead to different spontaneity outcomes.
5. Understanding this equation is essential for predicting phase changes, chemical reactions, and other processes where energy transformations occur.

Review Questions

• How does the Gibbs free energy change (δg) relate to spontaneity in chemical reactions?
  • The Gibbs free energy change (δg) is directly linked to the spontaneity of chemical reactions. If δg is negative, it indicates that the reaction can proceed spontaneously without additional input of energy. Conversely, if δg is positive, it means that the reaction is non-spontaneous and would require external energy to occur. This relationship helps chemists predict whether a given reaction will occur under specified conditions.
• In what ways can temperature influence the Gibbs free energy equation, especially concerning enthalpy and entropy changes?
  • Temperature has a significant impact on the Gibbs free energy equation because it directly affects the entropy term (tδs). As temperature rises, even a small increase in entropy can make a larger contribution to δg, potentially turning a non-spontaneous process into a spontaneous one. Additionally, higher temperatures can also alter the contributions of enthalpy changes (δh), influencing whether a reaction is favorable overall. Thus, understanding how temperature interacts with these terms is critical for predicting reaction behavior.
• Evaluate how this equation can be applied to predict phase transitions in substances.
  • This equation can be applied to predict phase transitions by analyzing changes in enthalpy and entropy during these processes. For example, during melting or boiling, the enthalpy change reflects the energy required to overcome intermolecular forces, while the entropy change indicates an increase in disorder as a solid becomes a liquid or liquid becomes gas. By applying $$ ext{δg} = ext{δh} - t ext{δs}$$, one can determine at which temperatures phase transitions become spontaneous. When δg equals zero at specific temperatures, it signifies equilibrium between phases, marking critical points like melting and boiling points.

Related terms

Gibbs Free Energy: A thermodynamic potential that measures the maximum reversible work obtainable from a system at constant temperature and pressure.

Enthalpy: A measure of the total energy of a thermodynamic system, including internal energy and the energy required to make room for it by displacing its environment.

Entropy: A measure of the disorder or randomness in a system, indicating the amount of energy unavailable to do work.