286
M. E. Sastre de Vicente· T. Vilarino
1997; De Robertis et al.1997) some of which are contributors in this volume, traditionally have been using these equations to model pK* vs. ionic strength data.
Some authors have derived equations of the following type from studies over wide
temperature and ionic strength ranges:
10gQ = f(I, T, param.)
(11.9)
which includes the dependence on both the ionic strength and temperature (Kettler
et al.I995)
With regard to these explicit equations in ionic strength, in particular Pitzer's, which
are the more general and widely used, it must be stated that these equations:
• Are able to reproduce the measured properties within the experimental error;
• Can be applied to single electrolytes and mixtures, i.e. natural waters (Millero and
Pierrot 1998), up to high concentrations;
• However, coefficients obtained from linear regression analysis of pK* vs. I data have
no clear physical meaning. Other problems are for example ill-conditioning (Fiol et al.
1994), which leads to high errors in the regression parameters.
11.4
The Mean Spherical Approximation:
Estimation of Q( y) Term by Use of the MSA Model
An alternative to modelling pK-I data is the mean spherical approximation (MSA)
(Blum 1975; Friedman 1985), the application of acid-base equilibria on the basis of the
"constant ionic medium" approach, is described below.
From a general point of view, in an electrolyte solution there must be a balance
among different types of interactions (Israelichvili 1991):
a Forces of a purely electrostatic nature that arise from Coulomb's law (e.g. interactions
between charges, permanent dipoles or quadrupoles, etc.);
b Polarization forces between dipoles induced by the action of permanent charges and
dipoles on atoms and molecules. This type of force is present in any solvent medium
(particularly in electrolyte solutions).
c Quantum mechanical forces consisting of an attractive part responsible for chemical bonding and a repulsive part of the steric type or in the form of exchange interactions that equilibrate attractive forces over very short distances.
A frequent way of describing such interactions in qualitative terms is based on
the distinction between long-range (coulomb) interactions and short-range interactions. So, schematically, the interaction between two ions in solution can be expressed
as:
Interaction between particles i, j = Coulomb Law + other kind of interactions (11.10 )
M. E. Sastre de Vicente· T. Vilarino
1997; De Robertis et al.1997) some of which are contributors in this volume, traditionally have been using these equations to model pK* vs. ionic strength data.
Some authors have derived equations of the following type from studies over wide
temperature and ionic strength ranges:
10gQ = f(I, T, param.)
(11.9)
which includes the dependence on both the ionic strength and temperature (Kettler
et al.I995)
With regard to these explicit equations in ionic strength, in particular Pitzer's, which
are the more general and widely used, it must be stated that these equations:
• Are able to reproduce the measured properties within the experimental error;
• Can be applied to single electrolytes and mixtures, i.e. natural waters (Millero and
Pierrot 1998), up to high concentrations;
• However, coefficients obtained from linear regression analysis of pK* vs. I data have
no clear physical meaning. Other problems are for example ill-conditioning (Fiol et al.
1994), which leads to high errors in the regression parameters.
11.4
The Mean Spherical Approximation:
Estimation of Q( y) Term by Use of the MSA Model
An alternative to modelling pK-I data is the mean spherical approximation (MSA)
(Blum 1975; Friedman 1985), the application of acid-base equilibria on the basis of the
"constant ionic medium" approach, is described below.
From a general point of view, in an electrolyte solution there must be a balance
among different types of interactions (Israelichvili 1991):
a Forces of a purely electrostatic nature that arise from Coulomb's law (e.g. interactions
between charges, permanent dipoles or quadrupoles, etc.);
b Polarization forces between dipoles induced by the action of permanent charges and
dipoles on atoms and molecules. This type of force is present in any solvent medium
(particularly in electrolyte solutions).
c Quantum mechanical forces consisting of an attractive part responsible for chemical bonding and a repulsive part of the steric type or in the form of exchange interactions that equilibrate attractive forces over very short distances.
A frequent way of describing such interactions in qualitative terms is based on
the distinction between long-range (coulomb) interactions and short-range interactions. So, schematically, the interaction between two ions in solution can be expressed
as:
Interaction between particles i, j = Coulomb Law + other kind of interactions (11.10 )