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Chemical equilibrium occurs at minimum energy from "summary" of Thermodynamics and an Introduction to Thermostatistics by Herbert B. Callen

At the heart of chemical equilibrium lies the principle that a system tends to minimize its energy. When a chemical reaction reaches equilibrium, the system has found a state where the total energy is at its minimum. This means that the system has achieved a balance between the energy associated with the reactants and the energy associated with the products. In the context of chemical reactions, the energy of the system is influenced by factors such as temperature, pressure, and the concentrations of reactants and products. As the system evolves towards equilibrium, it adjusts these factors to lower its overall energy. At equilibrium, the system has settled into a state where any further change would require an increase in energy. The concept of minimum energy at chemical equilibrium can be understood through the lens of thermodynamics. Thermodynamics provides a framework for analyzing the flow and transformation of energy in physical and chemical systems. In the case of chemical equilibrium, thermodynamics tells us that the system will naturally evolve towards a state of minimum energy. At the microscopic level, the proces...
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    Thermodynamics and an Introduction to Thermostatistics

    Herbert B. Callen

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