الفهرس 
acknowledgmentOnly 14 pages are availabe for public view
 |  | from | 16 |  |  |
| | | from | 16 | | |
Abstract
Random thermal motion of ions in solutions of strong electrolytes constantly brings anions and cations
into proximity. Electrostatic attraction then alters the ionic motions so as to bring the ions closer together,
occasionally to contact or near contact distances. Such pairs remain together until sufficiently large thermal
fluctuations again send the ions apart. The tendency of the ions to associate in this way depends upon the
balance between the interionic coulomb forces and thermal energy – thus upon the ion valancies, the
dielectric constant and the temperature. It depends also on the solvation energy of the ions. Since the heat of
solutions is small, dissolution of soluble salt as free ions requires sufficient solvation energy almost
completely offset the lattice energy. Dissolution as ion-pairs requires solvation energy only approximately
equivalent to the sublimation energy. Thus poor solvation promotes ion association.
1.1.1. Solvent effect on ion association:
The effect of a solvent on the equilibrium constant of ionic association (KA) is of major interest for
the theory of electrolytic solutions.1 many investigations have established a relation between KA and the
micro- and macroproperties of the electrolytic system, starting from the Bronsted equation 2 to the most
general Izmallov equation.3 The crystallographic or effective ionic radii, ion-ion and ion-dipole interaction
energies belong to the former, the latter are crystalline lattice energy and solvent permittivity (ε).
For symmetrical electrolytes, where cospheres of a pair of ions Mn+ and Xn- overlop, the net charge is
equal to zero and thus taken no part in charge transport. On the other hand, in case of asymmetrical
electrolytes the formed ion-pair has a charge and contribute in conducting process but less than that of the
free ion.
The term ion association is frequently employed and was firstly introduced by Bjerrum 4 that defined,
for dilute solutions, the probability of finding an ion of charge (z-eo) in dr thickness spherical shell of
radius r around a reference ion of charge (z+eo) by the equation:
Pr = (4π ni
o) eλ/r r2 dr ........................................................................................ (1-1)
Where
λ=z+z-eo
2/DkT ………………………………………………………………. (1-2)
where λ equal to emperical value .
Bjerrum 4 plotted, for dilute solutions, the probability of finding an oppositely charged ion at a given
distance from a central ion. This distribution curve, Figure (1), shows that pr goes through a minimum for a
particular value of r, which was named the critical distance and Bjerrum put it equals to the distance q. this
minimum occurs at
q = λ/2 = (zizjeo
2/2DkT) = 3.57 Ao for (1:1) electrolyte at 25° C in water.
Fig. 1: The probability Pr of finding an ion of one type of charge as a function of distance.
Accordingly, q represents the distance at which the electrostatic potential energy of the two ions
assumes the value of (zizj) eo
2/Dq is equal to 2kT.
Bjerrum 4 concluded that ion-pair formation occurs when an ion of one type of charge, e.g., a
negative ion, enters a sphere of radius, a, drawn around a reference ion of the opposite charge, but it is the
ion size parameter which defines the closest approach distance (ao) of a pair of ions. The Bjerrum
hypothesis can, therefore, be stated as follows: if ao > q, then ion-pair cannot occur, if ao < q, the ion