δg = δh - tδs

Definition

The equation $$ ext{δg} = ext{δh} - t ext{δs}$$ represents the Gibbs free energy change of a system, linking enthalpy (δh), temperature (t), and entropy (δs). This relationship is crucial for understanding the spontaneity of chemical reactions, where a negative Gibbs free energy indicates that a process can occur spontaneously. It highlights how both heat content and disorder influence the overall energy available to do work in chemical reactions.

5 Must Know Facts For Your Next Test

1. The Gibbs free energy change (δg) determines whether a reaction is spontaneous at constant temperature and pressure.
2. A negative δg indicates that the reaction can occur spontaneously, while a positive δg means the reaction is non-spontaneous under those conditions.
3. At equilibrium, the Gibbs free energy change (δg) equals zero, indicating no net change in the system.
4. The equation reveals that increasing temperature (t) can affect spontaneity by amplifying the influence of entropy changes (δs).
5. Reactions that are endothermic (positive δh) can still be spontaneous if they lead to a significant increase in entropy (positive δs).

Review Questions

• How does the Gibbs free energy equation help predict the spontaneity of chemical reactions?
  • The Gibbs free energy equation $$ ext{δg} = ext{δh} - t ext{δs}$$ allows us to predict the spontaneity of chemical reactions by analyzing the contributions from enthalpy and entropy. If δg is negative, it signifies that the reaction can proceed spontaneously without any external input. Conversely, if δg is positive, it indicates that the reaction is not spontaneous under the given conditions. Thus, this equation helps chemists understand how energy changes influence reaction behavior.
• Discuss the significance of temperature in relation to entropy and Gibbs free energy as described by the equation.
  • Temperature plays a critical role in the Gibbs free energy equation because it directly impacts the contribution of entropy changes to overall free energy. As temperature increases, the term $$-t ext{δs}$$ becomes more significant. This means that if a reaction has a large positive change in entropy, it can become spontaneous at higher temperatures even if it is endothermic. Therefore, understanding this relationship helps predict how varying temperatures can shift reaction favorability.
• Evaluate how this equation can explain the behavior of both exothermic and endothermic reactions in terms of spontaneity.
  • The equation $$ ext{δg} = ext{δh} - t ext{δs}$$ illustrates how both exothermic and endothermic reactions can exhibit spontaneous behavior depending on their enthalpy and entropy changes. Exothermic reactions (negative δh) generally favor spontaneity due to releasing heat; however, endothermic reactions can also be spontaneous if they result in a significant increase in entropy (positive δs). By evaluating these factors together with temperature, we can predict various scenarios where reactions may proceed spontaneously despite seeming unfavorable based solely on heat absorption or release.

Related terms

Enthalpy (H): A measure of the total heat content of a system, often associated with the energy required to break bonds during chemical reactions.

Entropy (S): A measure of the disorder or randomness in a system, reflecting the number of ways a system can be arranged.

Spontaneity: The tendency of a process to occur without outside intervention, typically indicated by a negative Gibbs free energy change.