Transcript Document

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
. 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.
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:
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 γ 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.
.
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,
The Debye-Huckel limiting law is
where A=0.509 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
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.