$G$

Definition

$G$ is a thermodynamic quantity that represents the free energy of a system, which is the maximum amount of work that can be extracted from the system under constant temperature and pressure conditions. It is a crucial concept in understanding the spontaneity and feasibility of chemical reactions and processes.

5 Must Know Facts For Your Next Test

1. $G$ is defined as the difference between the enthalpy ($H$) and the product of absolute temperature ($T$) and entropy ($S$): $G = H - TS$.
2. The sign of $G$ determines the spontaneity of a process: if $G < 0$, the process is spontaneous; if $G > 0$, the process is non-spontaneous and requires the input of energy.
3. The change in free energy, $\Delta G$, is the key factor in determining whether a reaction or process will occur spontaneously, and the magnitude of $\Delta G$ indicates the driving force for the process.
4. Reactions with $\Delta G < 0$ are favorable and will occur spontaneously, while reactions with $\Delta G > 0$ are unfavorable and will not occur spontaneously.
5. The value of $\Delta G$ also provides information about the maximum amount of work that can be extracted from a system, as well as the direction of energy flow in the process.

Review Questions

• Explain the relationship between $G$, $H$, and $S$ and how it determines the spontaneity of a process.
  • The free energy $G$ is defined as $G = H - TS$, where $H$ is the enthalpy, $T$ is the absolute temperature, and $S$ is the entropy. The sign of $\Delta G$, the change in free energy, determines the spontaneity of a process. If $\Delta G < 0$, the process is spontaneous and will occur naturally, as the system is moving towards a lower free energy state. If $\Delta G > 0$, the process is non-spontaneous and will not occur without the input of external energy. The magnitude of $\Delta G$ also indicates the driving force for the process, with larger negative values of $\Delta G$ corresponding to a greater driving force for the reaction to occur spontaneously.
• Describe how the value of $\Delta G$ provides information about the maximum amount of work that can be extracted from a system and the direction of energy flow.
  • The change in free energy, $\Delta G$, represents the maximum amount of work that can be extracted from a system at constant temperature and pressure. If $\Delta G < 0$, the process is spontaneous and the system can perform work on its surroundings, releasing energy. The magnitude of $\Delta G$ indicates the maximum amount of work that can be extracted. Conversely, if $\Delta G > 0$, the process is non-spontaneous, and work must be done on the system by the surroundings to drive the process forward, requiring an input of energy. The sign of $\Delta G$ also indicates the direction of energy flow, with negative values corresponding to a release of energy from the system to the surroundings, and positive values indicating an input of energy from the surroundings to the system.
• Analyze how the concepts of enthalpy, entropy, and free energy can be used to predict and understand the feasibility and direction of chemical reactions and processes.
  • The relationship between enthalpy ($H$), entropy ($S$), and free energy ($G$) provides a powerful framework for predicting and understanding the feasibility and direction of chemical reactions and processes. The change in free energy, $\Delta G$, determines the spontaneity of a process, with $\Delta G < 0$ indicating a spontaneous, favorable reaction, and $\Delta G > 0$ indicating a non-spontaneous, unfavorable reaction. The magnitudes of $\Delta H$ and $\Delta S$ contribute to the value of $\Delta G$, with favorable changes in both enthalpy (negative $\Delta H$) and entropy (positive $\Delta S$) driving the system towards a lower free energy state and increased spontaneity. By analyzing the relative contributions of enthalpy and entropy, one can predict the feasibility and direction of a chemical process, as well as the maximum amount of work that can be extracted from the system.

Related terms

Enthalpy ($H$): Enthalpy is the total energy of a system, including the energy required to create the system (internal energy) and the work done to make room for it (pressure-volume work).

Entropy ($S$): Entropy is a measure of the disorder or randomness of a system, and it represents the unavailability of a system's energy for useful work.

Spontaneity: Spontaneity refers to the natural tendency of a process or reaction to occur without the input of external energy, driven by the system's desire to reach a state of lower free energy.