Chemical potential of an ion

The energy of an ion in a given medium depends not only on chemical forces but also on the electrostatic held hence the chemical potential of an ion j customarily is called its electrochemical potential and labeled fi. The electrostatic potential energy of an ion j when reckoned per mole is given by ZjF, where / is the electrostatic (inner) potential of the phase containing the ion a plus sign for cations and a minus sign for anions. Hence, the electrochemical potential can be written as the sum of two terms ... 

The chemical potential of an individual ion in solutions can never be measured because it depends on the other ions in the solution with which it interacts. We can, however, discuss p — p,/v, the mean ionic chemical potential, or the average chemical potential of an ion produced from the electrolyte. Writing p, j i, p, and p,- each in the form p = p° + RT In a gives... 

A fundamental hypothesis of the Gouy-Chapman theory is that the interaction of an ion with all the other charges can be described by a mean potential Jt(jc), where x is the distance from the surface. The chemical potential of an ion of species T with charge [Pg.383]

Availability of nutrients such as K+ and Ca2+ to plants in soil systems is related to the quantity and form of these nutrients in the solid phase. The quantity and form of the nutrients are related to their chemical potential (Beckett, 1964). However, it is not possible to directly measure the chemical potential of an ion in the solid phase, but it is possible to measure the difference in the chemical potential between two ions in the solution phase at equilibrium with the solid phase. The latter can then be related to the chemical potential difference of the two ions in the solid phase (Beckett, 1964,1972 Nye and Tinker, 1977). 

The influence of electrical potential on the chemical potential of an ion is expressed by the term ZjFE in Equation 2.4, where Zj is an integer representing the charge number of species /, F is a constant known as Faraday s constant (to be considered in Chapter 3, Section 3.1 A), and E is the electrical potential. Because water is uncharged (zw = 0), the electrical term does not contribute to its chemical potential. However, electrical potential is of central importance when discussing ions and the origin of membrane potentials both of these are examined in detail in Chapter 3 (e.g., Section 3.ID), where we explicitly consider the ZjFE term. 

Until later we drop the subscript i and note that at equilibrium the chemical potential of an ion under consideration must be the same at two different locations ri and r2. On imposing this condition on Eq. (9.5.1) we may rearrange the resultant to read... 

Electric potential is the electric work necessary to transfer the unit charge in vacuum from the infinite distance to a position, the potential of which is to be established. If this position is situated inside of a phase (metal, solution, etc.), it is called the inner electric potential and is denoted by < ). The chemical potential of an ion in the presence of an electric potential is called its electrochemical potential, jl expressed as in Eq. (1) ... 

Utilizing the familiar relationship in = juj + /ZTln a for the chemical potential of an ion in terms of its activity a,, it is seen that... 

Now iuf is the chemical potential of an ion in a (hypothetical) solution of unit molality which behaves like a solution of infinite dilution (where yt = 1, trii = 1 mol kg-1, and ftt - tuf). 

Here H(r, r ) is a steric hindrance factor (see following text) and x9 is the standard chemical potential of an ion of type i inside the pore. We use a previously obtained estimate (13)... 

We first need to investigate the relation between the chemical potential of an ion species and the electric potential of the solution phase. 

It is impossible to measure the chemical potential of an ion since ions of one charge cannot be added without adding ions of the opposite charge at the same time. The (unmeasurable) chemical potential of the cation is given by... 

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