Chemical Potential in a Field

The formalism for the chemical potential presented in the previous chapter can be extended to electrochemical reactions and to systems in an external field such as a gravitational field. In the presence of a field, the energy due to a field must be included while considering changes in energy. As a result, the energy of a constituent depends on its location. 

We start with a simple system the transport of chemical species which carry electrical charge from a location where the potential is 4 j to a location where the potential is t 2. For simplicity, we shall assume that our system consists of two parts, each with a well-defined potential, but the system as a whole is closed (Fig. 10.1). It is as if the system consisted of two phases and transport of particles dNk were a chemical reaction. For the corresponding degrees of advancement we have 

Thus we see that the introduction of a potential ( ) associated with a field is equivalent to adding a term to the chemical potential. This makes it possible to extend the definition of the chemical potential to include the field. The electrochemical potential p, introduced by Guggenheim in 1929 [1], is defined 

Clearly this formalism can be extended to any field with which a potential may be associated. If vj is the potential associated with the field, the energy of interaction per mole of the component k may be written in the form For the electric field Xk = Fzk for the gravitational field x = Mk, the molar mass. The corresponding chemical potential which includes the potential is 

The affinity for the electrochemical reactions can now be defined, just as for other chemical reactions 

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Linear phenomenological laws of nonequilibrium thermodynamics lead to a general relation between mobility Tk and the diffusion coefficient Dk- This relation can be obtained as follows. The general expression for the chemical potential in a field with potential x / is given by + xjtxl/, in which is the... 

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