Salt as an electrolyte

In an electrolyte solution ions are dissolved in a solvent. These solved ions are free, in contradiction with ions in highly ordered lattice structure, characteristic for crystals.

Although strong electrolytes are completely ionized, their ions are not totally free to move independently of each other. Dilute solutions are an exception, where ions move randomly due to fairly strong thermal motion. Ions are surrounded on a time average by an ‘ion atmosphere’ (caused by coulomb forces) containing a relatively higher proportion of ions carrying a charge of opposite sign to that of the central ion (Fig. 2.5a). Under the influence of an applied electronic field, movement of the ions will be slow and disrupted by thermal motions. The movement of the atmosphere occurs in a direction opposite to that of the central ion, resulting in the continuous breakdown and reformation of the atmosphere (Fig. 2.5b). Consequently the atmosphere is asymmetrically distributed, causing some attraction of the central ion in a direction opposite to that of its motion, known as relaxation. In addition, central ions experience increased viscous hinder of solved atmosphere ions moving in opposite direction, producing solvent movement in opposite direction. This phenomenon is called electrophoretic effect (Fig. 2.6). Such interactions increase with increasing concentration of the electrolyte. Two extremes exist.

On the one hand there are infinite dilutions where all interionic effects are eliminated. In these cases no restrictions are present, current passes freely and conductivity reaches a maximum value. On the other hand there exist highly concentrated solutions, with highly charged ions and high interionic attraction. Consequently discrete ion pairs (consisting of associated ions acting as ‘kinetically distinct’ species) may occur on a time-averaged scale. Bjerrum [in CRO-04] suggests that this happens when ion separation is less than a certain minimum distance. For a 1:1 electrolyte in aqueous solution at 298 K, the calculated value is 0.357 nm. When the sum of the respective ionic radii is less, then ion-pair formation will be favored.

Although the high lattice energies of crystal structures, many salts dissolve easily even with a small heating (either exotherm of endotherm). This lattice energy is the large- scale analogy of the individual dissociation energy of an ionic ‘molecule’. An explanation of this easy dissolution is the simultaneous occurrence of another process which produces sufficient energy to compensate for the energy lost in rupture of the lattice bonds, i.e. exotherm reactions of individual ions with the solvent.

+ + +

+

+

+ +

+

- - -

- - -

+ +

+ +

+

- +

- - -

- - -

+

a. b.

Fig. 2.5 An ion with a symmetrical ion atmosphere (a) versus an ion with an asymmetrically ion atmosphere (b) due to the relaxation effect during movement. [LAI-

99]

r - κ

^-1

F

_d

F

E

central ion ionic cloud

+ + + +

+ + + + +

+ + + +

+ +

+

Fig. 2.6 Electrophoretic effect [ZHA-95]

Generally, the mentioned interionic and ion-solvent interactions are so numerous and important in solutions, that no ion may be regarded as behaving independently of the others. As a result, only mean ion quantities can be measured and no individual thermodynamic properties. Dynamic properties such as ion conductance, mobility and transport number may be determined, but the values will depend on the ion environment.

To determine bulk properties the activity of an ion a_j is introduced. This parameter, which is related to the concentration (equation (2.16)), expresses the availability of the species to take part in a chemical reaction or to influence the position of an equilibrium:

,

j j s j

a =γ C (2.16)

*

j j j

a =γ x (2.17)

where γ_jis the activity coefficient and C_{s j,} the concentration. Different values for γ_j exist depending on the definition of the concentration, i.e. molarity M (mol solute/ l solution), molality m^* (mol solute/kg solvent) or mole fraction x^*_j (mol solute/ mol solution).

An important parameter in the further discussion is the chemical potential μ_j, representing the change in free energy of a system when 1 mole of uncharged species j is added. By definition in an ideal solution (with no interactions) μ_jis given by:

* ln *

j j RT xj

μ =μ + (2.18)

where μ^*_j is the standard chemical potential for the pure elements.

In a non-ideal solution (with interaction) the formula becomes:

* ln * ln * * ln * ln

j j RT aj j RT xj i j RT xj RT i

μ =μ + =μ + γ =μ + + γ (2.19)

The term RTlnγ_i is introduced to take into account effects of ion interaction. However, for solute ions with electrostatic forces between the charges, this correction is not sufficient. These charges generate an electrical potential φ_e. Consequently, the free energy of a system increases by both transfer of matter and transfer of charges, resulting in a so-called electrochemical potential μ_j, given by:

* ln * ln

j j z Fj j RT xj RT j z Fj e

μ =μ + φ μ= + + γ + φ (2.20)

Due to the Debye-Hückel (DH) theory, given below, activity coefficients become theoretically predictable quantities. To make them more meaningful, first mean ion activities (a±)^ν and mean ion activity coefficients (γ±)^ν are defined, taking into account both types of ions (positive and negative), as they are influencing each other.

The crucial step in the DH derivation is the identification of RTlnγ_j (in equation (2.20)).

The contribution for an individual ion is kTlnγ_j, which equals the work to be done to give an ion its charge z e_j , e being the electronic charge. Looking to the potential φ_e existing in the vicinity of an ion by virtue of its charge, one can distinguish two parts

, _

e central ion

φ and φ_{e atmos,} :

, _ ,

1

4 4 1

j j

e e central ion e atmos

z e z e

a a

φ φ φ κ

πε πε κ

⎛ ⎞ ⎛ ⎞ ⎛ ⎞

= + = ±⎜⎝ ⎟⎠⋅ ∓⎜⎝ ⎟ ⎜⎠⋅⎝ + ⎟⎠ (2.21)

where φe central ion_{, _} has been used to represent the contribution of the ion itself and

, e atmos

φ the contribution due to its atmosphere.

1/κ

ar

i j

Fig. 2.7 The distance of closest approach a_r for ion i and atmosphere ion j, and the Debye length 1/κ. The radius of ion atmosphere is

(

^{1/ +} κ ar

)

[CRO-94]

Based on laws of electrostatics both terms have the general form of a potential at the surface of a charged sphere, with ε_p the permittivity of the medium. The parameter a_r represents the distance of closest approach of an ion to another one (Fig. 2.7). The expression

(

^{1 +} κar

)

^/ κ or

(

^{1/ +} κ ar

)

represents an effective radius of the ion atmosphere. 1/κ is usually defined as the thickness of the ion atmosphere or Debye length.

Returning to kTlnγ_j the corresponding work may be linked to the integration of the second term of equation (2.21) with respect to e and as integration limit 0 and z e_j . The average ion activity coefficient for an electrolyte may be estimated by the resulting advanced DH limiting law modified by a linear correction term. This relationship also known as Hückel equation is given by:

log 1

e e

r e

A z z I b I B a I γ_± = − ^{⋅ + − ⋅} + ⋅

+ ⋅ ⋅ ^(2.22)

where I_e is the ionic strength of the electrolyte, i.e. 1 _, ² 2

e s j j

I =

∑

C z (mol/l). In the

case of NaCl (z₊=z₋= 1), the experimental coefficients are [JUS-97]: a_r equal to 0.4 nm, b equal to 0.055 l/mol, while the temperature dependent constants A and B are respectively 0.50925 l^1/2/mol^1/2 and 3.2864 l^1/2/mol^1/2.nm for water at 25°C.

Consequently γ_± is ranging from 0.68 to 1.00 with a minimum at a concentration of about 1 M.

No documento Transport and crystallization of dissolved salts in cracked porous building materials (páginas 44-48)