_{1}

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It is shown that the state of chemical equilibrium of a closed system corresponds to the minimum density of its energy levels.

The concept of chemical affinity (A) was introduced into thermodynamics by Belgian physicist Théophile de Donder in 1922 to represent the driving force of a chemical reaction considered as the irreversible process [

The present work is an attempt to understand this important concept on the microscopic level, proceeding from the definition of entropy in quantum statistics (as proposed by Planck in 1925) and the notion of the density of energy levels of a closed system, which plays an important role in modeling the kinetics of nonequilibrium systems [

The chemical affinity is defined as the algebraic sum of chemical potentials of the initial reactants and products multiplied by the corresponding stoichiometric coefficients:

where

Here

Being an intensive variable (thermodynamic force), the chemical affinity determines an irreversible process related to a change in the composition of a system. In thermodynamics, this variable is considered jointly with the conjugated chemical variable

where

Introduction of the chemical affinity and the chemical variable into consideration allows one to reduce the number of variables

and the variation of entropy S is expressed as

Here, the sum of the first and second terms on the right-hand side represents a reversible change in the entropy

and the corresponding positive definite entropy production [

It turns out that, in the state of chemical equilibrium

First, let consider the definition of the density of energy levels of a closed system in quantum statistics [

where

Since the chemical affinity is a linear combination of chemical potentials

From Equation (9) we obtain the following expression for the chemical potential:

Using the quantum-statistical definition of entropy on the energy scale of temperature [

and taking into account expression (10), we obtain the following relation:

Not that, in deriving relation (11) at the stage of replacement of the statistical weight

Now let us proceed to calculations of the chemical affinity (A) and total entropy production (P) using the quantum-statistical expression for the chemical potential (11) and formulas (4) and (7). For the chemical affinity, this yields

Note that, in deriving relation (12) at the stage of passing from variables

Since the chemical affinity of a system upon attaining the state of equilibrium is A = 0, relation (12) with allowance for nonzero absolute temperature T shows that

It follows from formula (13) that the positive constant parameter D, as expressed by Equation (14), corresponds to zero total entropy production and (in view of its being non-negative) to the absolute minimum

M. B.Saikhanov, (2015) Chemical Affinity and the Density of Energy Levels. Journal of Modern Physics,06,1452-1455. doi: 10.4236/jmp.2015.611149