Chemistry of Freshwaters - Principles of Environmental Chemistry - page 85

where [i] is the concentration of solute ion, i; z i is the integral charge
associated with solute ion, i.
Ionic strength, expressed in terms of mol L 1 , is most accurately
determined by carrying out a total water analysis, i.e. quantification of
the concentrations of all ionic species in solution and calculation of I
using Equation (3.2). It may, however, be estimated from measurements
of either the TDS in solution or, preferably, the specific conductance
(SpC) of the solution, e.g. I ¼ 2.5 10 5 TDS (mg L 1 )orI ¼ 1.7
10 5 SpC (mScm 1 ). 12
The simplest theoretical relationship between I and g i is expressed in the
Debye-Hu¨ ckel (DH) Equation (3.3). z The DH model assumes that ions
can be represented as point charges, i.e. of infinitely small radius, and that
long-range coulombic forces between ions of opposite charge are respon-
sible for the differences between the observed chemical behaviour,
i.e. activity, and the predicted behaviour on the basis of solute concent-
ration.

p

log g i ¼ 0 : 5 z i I DH equation ð 3 : 3 Þ

p p Extended DH equation ð 3 : 4 Þ

log g i ¼ 0 : 5 z i

= 1 þ 0 : 33 a i

I I

p = 1 þ p

G ¨untelberg approximation

log g i ¼ 0 : 5 z i

ð 3 : 5 Þ

An infinitely dilute solution is defined as having an ionic strength o 10 5
mol L 1 and activity coecients calculated by any of the above
equations would have a value of unity. For freshwaters where I is in
the range 10 5 -10 2.3 mol L 1 , activity coecients can be calculated
using the DH Equation (3.3). Where I is in the range 10 2.3 -10 1 mol
L 1 , however, the values calculated using Equation (3.3) differ from
experimental data and this stems from the assumption that the solute
ions are point charges. The extended DH expression (3.4) includes a
parameter, a i , which is related to ion size. Example 3.2 illustrates the use
of both DH and extended DH expressions to calculate single-ion activity
coecients.

z The general forms of the DH and extended DH equations are log g i ¼ Az i 2 O I and log g i ¼
Az i 2 ( O I/(1 þ Ba i O I)), respectively, where A and B are temperature dependent constants. A ¼
1.824928 10 6 r 0 0.5 (eT) 1.5 0.5 and B ¼ 50.3 (eT) 0.5

0.33 at 298 K, where r 0 is the density

B B

and e is the dielectric constant of water at 298 K.