$G$ 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.
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$G$ is defined as the difference between the enthalpy ($H$) and the product of absolute temperature ($T$) and entropy ($S$): $G = H - TS$.
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.
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.
Reactions with $\Delta G < 0$ are favorable and will occur spontaneously, while reactions with $\Delta G > 0$ are unfavorable and will not occur spontaneously.
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 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.