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In an ideal solution, the chemical potential of species i (μ i) is dependent on temperature and pressure. μ i0 (T, P) is defined as the chemical potential of pure species i. Given this definition, the chemical potential of species i in an ideal solution is
is the number of gas particles; is the Boltzmann constant (1.381 × 10 −23 J·K −1). The probability distribution of particles by velocity or energy is given by the Maxwell speed distribution. The ideal gas model depends on the following assumptions:
where T = temperature, S = entropy, p = pressure, V = volume. N i is the number of particles of type i in the system and μ i is the chemical potential for an i-type particle.The set of all N i are also included as natural variables but may be ignored when no chemical reactions are occurring which cause them to change.
The relative activity of a species i, denoted a i, is defined [4] [5] as: = where μ i is the (molar) chemical potential of the species i under the conditions of interest, μ o i is the (molar) chemical potential of that species under some defined set of standard conditions, R is the gas constant, T is the thermodynamic temperature and e is the exponential constant.
A constituent particle is one that cannot be broken into smaller pieces at the scale of energy k·T involved in the process (where k is the Boltzmann constant and T is the temperature). For example, in a thermodynamic system consisting of a piston containing water vapour, the particle number is the number of water molecules in the system. The ...
The number of particles is, like volume and entropy, the displacement variable in a conjugate pair. The generalized force component of this pair is the chemical potential. The chemical potential may be thought of as a force which, when imbalanced, pushes an exchange of particles, either with the surroundings, or between phases inside the system.
The molar gas constant (also known as the gas constant, universal gas constant, or ideal gas constant) is denoted by the symbol R or R. It is the molar equivalent to the Boltzmann constant , expressed in units of energy per temperature increment per amount of substance , rather than energy per temperature increment per particle .
The total energy of the system at any value of x is given by the internal energy of the gas plus the potential energy of the weight: = + + where T is temperature, S is entropy, P is pressure, μ is the chemical potential, N is the number of particles in the gas, and the volume has been written as V=Ax.