Ionic strength is sometimes stated as having units of molal or molar and other times stated as being

1
The ionic strength of a solution is a measure of
the amount of ions present. As you might guess a
divalent ion (a 2 or 2- ion, like Ca2) does
more to make the solution ionic than a monovalent
ion (e.g., Na). This must be taken into account.
The other very critical thing to remember is that
the ionic strength of a solution depends on the
concentrations of all the ions in the solution,
not just the ion pair that you are calculating
the activity coefficient for. Thus, if you are
calculating the average activity coefficient of
dissolved CaCl2, but there is also dissolved NaCl
present, the ionic strength you use has
contributions from all the ions.The formula for
ionic strength is
Ionic strength is sometimes stated as having
units of molal (or molar) and other times stated
as being unitless, depending on the book you
read. The easiest way to see how to apply this
formula is to consider a few examples. First
consider 100 mM NaCl. Upon dissolving, one
obtains 100 mM Na and 100 mM Cl-. Thus
2
. First consider 100 mM NaCl. Upon dissolving,
one obtains 100 mM Na and 100 mM Cl-. Thus
Notice that for a simple salt of two monovalent
ions, the ionic strength is just the
concentration of the salt. This is not true
for a salt with one or more multivalent ions like
MgCl2. For a 100 mM solution of this
salt Note that the Mg cation is divalent
and thus it has a big effect since the charge is
squared. Also note that the chloride anion is
present at twice the concentration since there
are two chloride ions per molecule of salt.
3
What is the ionic strength of a solution of 100
mM NaCl plus 100 mM of acetic acid which has been
titrated with NaOH until the pH of the solution
is 4.75 (the pKA of acetic acid)? When the pH
equals the pKA, that means that half of the
acetic acid has been converted to the conjugate
base, sodium acetate. Acetic acid is uncharged
and does not contribute to the ionic strength.
However sodium acetate ionizes completely to form
acetate anions and sodium cations. Since half was
converted, there are 50 mM of each. Then we must
add in the 100 mM of NaCl. So there is 50 mM
acetate anion, 150 mM sodium anion, and 100 mM
chloride anion
4
ACTIVITY COEFFICIENT is in essence a "correction
factor" that accounts for the apparent decrease
of concentration because of interaction with
other ions in solution. The value of ? can be
estimated using one of the existing activity
models. Finding appropriate activity coefficients
for aqueous species especially in concentrated
multicomponent solutions is one of the most
important (but troublesome) task in calculating
equilibrium relations. If you imagine an aqueous
solution for a moment, where charged ions are
dispersed in the solvent, Coulomb's Law tells us
that the electrostatic forces acting on ions vary
inversely with the square of the distance. Hence,
the activity coefficient is expected to decrease
(i.e., "effective concentration" decrease) as the
concentrations of ions increase. The Coulombic
forces increase as the ion density increases.
This phenomenon was known for a long time, even
before we were able to formulate ways of
estimating activity coefficients.
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Calculating Activity Coefficients. Now we
actually will use the Debye-Huckel limiting law
itself. There are three very important things
about applying the Debye-Huckel theory. First, it
only applies to ions. Molecules that are not
charged have an activity coefficient of 1.0
according to this theory (in reality, that is not
true, but their activity coefficients will be
much closer to 1 than will that of an ion).
Second, the charges that appear in the equation
are only those of the salt you are calculating
the activity coefficient for. Finally, all you
can only ever calculate are average activity
coefficient of the two ions which make up the
salt you are considering. For MgCl2, you cannot
use this theory to calculate the activity
coefficient of Mg2 separately from Cl-, you can
only calculate the geometric average of the two
activities,
.
6
The Debye-Huckel limiting law is Notice
that the ionic strength is that of the whole
solution, while the charges are those of the
sodium acetate ions we are calculating the
activity coefficient for.
where A0.509 for water at 25 C. (A is an
empirical constant.) In the acetate/acetic acid
example given above, the sodium acetate ions
would have an average activity coefficient given
by