CHAPTER 11 . Acid-Base Equilibria in Saline Media: Application of the MSA
11.7
Data We Need for Working With the
Mean Spherical Approximation
1. Electrical charges, Zj, are defined by the corresponding equilibrium model.
289
2. Numerical densities, Pj' Taking into account that a constant ionic medium requires
that the supporting electrolyte be present at a much higher concentration than the
substance whose ionization equilibria is being studied, the sole numerical densities
that will appreciably contribute to the different parameters to be determined can be
assumed to be those for the electrolyte ions.
3. Ionic diameters (O"j)
Using the MSA model to calculate activity coefficients requires the prior knowledge of the diameters of all species present in the system:
a Background electrolyte. The diameters of the ions that make up the most
usual electrolytes can be replaced with Pauling diameters as shown by Marcus
(1988), who found ionic radii of dissolved species to be largely consistent
with Pauling's crystal radii. Also, taking into account the well-known fact
that cation sizes increase to a greater extent with increasing concentration than
do anion sizes, the former are often assumed to vary with the concentration,
while the latter remain constant and equal to Pauling values (Triolo et al. 1976,
1977. 1978).
O"+(c) = 0"0(1 + Lanc n )
(11.14)
where an are coefficients to be determined from experimental data.
b Species involved in the equilibria. Owing to the few reported diameters (Kielland
1937) for the different ionic species that result from the ionization of organic compounds, we often estimate such diameters from Van der Waals volumes calculated
from group contributions (Bondi 1964).
4. Dielectric constant
Although the MSA model can use the dielectric constant for the medium at zero
electrolyte concentration, the use of a dielectric constant dependent on the concentration of the particular electrolyte improves the results as it accounts for the
fact that dielectric shielding must be smaller in the more concentrated solutions,
where ions, on average, are closer to one another and hence less strongly shielded
by the solvent.
The expression for the dielectric constant of an electrolyte solution is usually a
simple polynomial, whether linear or slightly more complex (Barthel et al. 1998;
Fawcett and Tikanen 1996; Whitfield and Turner 1981), which relates £ to the molar
concentration, hence considering the decrease in the constant with the increase in
concentration.
£(c) = £0(1 + Lf3nC n )
(11.15)
where f3n are coefficients to be determined from experimental data.
11.7
Data We Need for Working With the
Mean Spherical Approximation
1. Electrical charges, Zj, are defined by the corresponding equilibrium model.
289
2. Numerical densities, Pj' Taking into account that a constant ionic medium requires
that the supporting electrolyte be present at a much higher concentration than the
substance whose ionization equilibria is being studied, the sole numerical densities
that will appreciably contribute to the different parameters to be determined can be
assumed to be those for the electrolyte ions.
3. Ionic diameters (O"j)
Using the MSA model to calculate activity coefficients requires the prior knowledge of the diameters of all species present in the system:
a Background electrolyte. The diameters of the ions that make up the most
usual electrolytes can be replaced with Pauling diameters as shown by Marcus
(1988), who found ionic radii of dissolved species to be largely consistent
with Pauling's crystal radii. Also, taking into account the well-known fact
that cation sizes increase to a greater extent with increasing concentration than
do anion sizes, the former are often assumed to vary with the concentration,
while the latter remain constant and equal to Pauling values (Triolo et al. 1976,
1977. 1978).
O"+(c) = 0"0(1 + Lanc n )
(11.14)
where an are coefficients to be determined from experimental data.
b Species involved in the equilibria. Owing to the few reported diameters (Kielland
1937) for the different ionic species that result from the ionization of organic compounds, we often estimate such diameters from Van der Waals volumes calculated
from group contributions (Bondi 1964).
4. Dielectric constant
Although the MSA model can use the dielectric constant for the medium at zero
electrolyte concentration, the use of a dielectric constant dependent on the concentration of the particular electrolyte improves the results as it accounts for the
fact that dielectric shielding must be smaller in the more concentrated solutions,
where ions, on average, are closer to one another and hence less strongly shielded
by the solvent.
The expression for the dielectric constant of an electrolyte solution is usually a
simple polynomial, whether linear or slightly more complex (Barthel et al. 1998;
Fawcett and Tikanen 1996; Whitfield and Turner 1981), which relates £ to the molar
concentration, hence considering the decrease in the constant with the increase in
concentration.
£(c) = £0(1 + Lf3nC n )
(11.15)
where f3n are coefficients to be determined from experimental data.