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The Boltzmann distribution

Peter Atkins, Julio de Paula, David Barton Smith

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Abstract

This chapter highlights the Boltzmann distribution, which is used to predict the populations of states in systems at thermal equilibrium. It considers the Boltzmann distribution as one of the most important equations in chemistry as it summarizes the populations of states and provides insight into the nature of temperature. It also reviews how thermodynamic properties, the temperature dependence of equilibrium constants, and the rates of chemical reactions can be interpreted in their terms. The chapter recognizes temperature as the most probable distribution of molecules over the available energy levels subject to certain restraints. It looks at the concept of the Boltzmann distribution that underlie all the descriptions of the relation between the individual properties of molecules and the properties of bulk matter.

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What this paper is about

This chapter highlights the Boltzmann distribution, which is used to predict the populations of states in systems at thermal equilibrium. It considers the Boltzmann distribution as one of the most important equations in chemistry as it summarizes the populations of states and provides insight into the nature of temperature. It also reviews how thermodynamic properties, the temperature dependence of equilibrium constants, and the rates of chemical reactions can be interpreted in their terms. The chapter recognizes temperature as the most probable distribution of molecules over the available energy levels subject to certain restraints. It looks at the concept of the Boltzmann distribution that underlie all the descriptions of the relation between the individual properties of molecules and the properties of bulk matter.

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Available abstract

This chapter highlights the Boltzmann distribution, which is used to predict the populations of states in systems at thermal equilibrium. It considers the Boltzmann distribution as one of the most important equations in chemistry as it summarizes the populations of states and provides insight into the nature of temperature. It also reviews how thermodynamic properties, the temperature dependence of equilibrium constants, and the rates of chemical reactions can be interpreted in their terms. The chapter recognizes temperature as the most probable distribution of molecules over the available energy levels subject to certain restraints. It looks at the concept of the Boltzmann distribution that underlie all the descriptions of the relation between the individual properties of molecules and the properties of bulk matter.

Key concepts: Boltzmann constant, Boltzmann distribution, Statistical physics, Distribution (mathematics), Boltzmann equation, Thermodynamics, Maxwell–Boltzmann distribution, Thermal equilibrium

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