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Lecture 4
Chemical Activity
10-09-02
Today I am going to talk about the concept of chemical activity. This is covered in the
very short chapter 8 in the book and we bring it up now because the geochemistry portion
of the program is going to be using chemical activity in the very near future.
The explanation of Activity in Harris is one of the best I have seen. This whole topic
comes up because experimentally equilibrium constants are found not be constant even at
constant T. In particular the equilibrium constants vary with changes in the nature and
concentration of ions in the solution.
The example from the book is the solubility of mercury(I) iodate or mercurous iodate
Hg2(IO3)2(s) < == > Hg22+ + 2 IO3concentration
table before
0
0
after
x
2x
Ksp = 1.3 x 10-18 = [Hg22+][ IO3-]2
If we solve for the solubility we get Ksp = x(2x)2 = 4x3
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2+
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[Hg2 ] = Ksp/4 = 6.9 x 10-7 M
Indeed this is the concentration that is found in a saturated solution of mercurous iodate
in distilled water. However, if the solution already contains 0.050 M KNO3 (or we can
add KNO3 to a saturated mercurous iodate solution), the presence of the K+ and NO3- ions
increases the solubility to 1.0 x 10-6 M.
This means the Ksp has changed to (1.0 x 10-6) (2.0 x 10-6)2 = 4.0 x 10-18 and the
concentration of mercurous ion has increased by about 50%.
This increase in solubility of a sparsely soluble substance with the addition of an "inert"
salt is a general observation.
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This graphs shows that solubility increases for other substances in the presence of
increasing amounts of “inert” potassium nitrate. We see the solubility of barium sulfate
goes up over a factor of 2 as the KNO3 concentration increases.
We can also see that if we keep solutions dilute we don’t have a problem.
The explanation for this phenomenon requires thinking about the nature of ions in
solution. When an ionic compound dissolves in water, the cation and anion becomes
surrounded by a solvent cage that separates, shields and isolates the ions from one
another.
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We think about precipitation as a point where there are so many ions in solution that the
cations and anions "see" each other and are attracted, form neutral ion pairs and come out
of solution.
It takes energy to disrupt the solvent cage, and so the ions must be close enough so that
their charge attraction overcomes the stability of the solvent cage.
A saturated solution is one where the process of seeing each other and dissolving are at
equilibrium, i.e. the rates of the reactions are equal.
Now consider what happens if there are other ions in solution. A particular cation is now
going to be surrounded not only by water, but other cations and anions in solution.
Even though the solution is homogeneous, for the average cation, there will be more
anions than cations near it, because anions are attracted to cations, but cations are
repelled. These interactions create a region of net negative charge around any particular
cation.
This region is called the ionic atmosphere and ions continually diffuse in and out of this
volume. The net charge of the cation in this atmosphere is less than the charge on the
cation because of the excess of negative charges in the region.
So in the presence of other ions in solution the charge on the cation is lowered compared
to that present in distilled water.
Thus, Hg22+ and IO3- ions are surrounded by charged ionic atmospheres that partially
screen the ions from each other. The formation of Hg2(IO3)2(s) requires the disruption of
these ionic atmospheres surrounding the ions.
Increasing the concentrations of ions in solution, by adding KNO3, increases the size of
these ionic atmospheres. Since more energy is now required to disrupt the ionic
atmospheres, there is a decrease in the formation of Hg2(IO3)2(s), and an apparent
increase in the equilibrium constant.
Systematic studies have shown that the effect of added electrolyte on equilibria is
independent of the chemical nature of the electrolyte but depends upon a property of the
solution called the ionic strength. This quantity is defined as
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ionic strength =  = ½ ([A]ZA2 + [B]ZB2 + [C]ZC2 + ……..
(mu)
where [A], [B], [C], represent the species molar concentrations of ions A,B, C, . . and ZA,
ZB, ZC, are their charges.
Suppose we have a 0.10 M Na2SO4 solution. The concentration of [SO42-] = 0.10 M and
[Na+] = 0.20 M (be sure you know why sodium is twice that of sulfate).
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The ionic strength of this solution is then
 = ½ ([0.10]22 + [0.20]12) = 0.30 M note ionic strength has units of molarity.
In order to describe quantitatively the effective concentration of participants in an
equilibrium at any given ionic strength, chemists use a term called activity, a. Our book
uses a fancy script A, but most texts use a lower a (usually italicized). Your Geochem
book by Hem uses a lower case a.
The true thermodynamic equilibrium constant is a function of activity rather than
concentration.
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The activity of a species, aA, is defined as the product of its molar concentration, [A], and
a solution-dependent activity coefficient, γA (gamma) which is dimensionless.
aA = γA [A]
The activity coefficient vary with ionic strength such that substitution of aA for [A] in any
equilibrium-constant expression frees the numerical value of the constant from
dependence on the ionic strength.
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To illustrate, if A3B2 is a slightly soluble solid, the thermodynamic solubility product
expression is defined by the equation
A3B2(s) <= => 3 A2+ + 2 B3Ksp = aA3 . aB2 = A3 B2 [A]3[B]2 = A3 B2 K'sp
Here K'sp is the concentration solubility product constant and Ksp is the thermodynamic
equilibrium constant. The activity coefficients x and y vary with ionic strength in such a
way as to keep Ksp numerically constant and independent of ionic strength (in contrast to
the concentration constant K'sp).
The Ksp values in tables are almost always the thermodynamic equilibrium constants.
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Properties of activity coefficients:
1. The activity coefficient of a species is a measure of the effectiveness with which that
species influences an equilibrium in which it is a participant.
2. In very dilute solutions, where the ionic strength is minimal, this effectiveness
becomes constant, and the activity coefficient is unity.
Under such circumstances, the activity and the molar concentration of the species are
identical (as are thermodynamic and concentration equilibrium constants).
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This is a major reason why models of solutions assume ideal solutions where all solutes
behave as if they were infinitely dilute. This is also why a first course in chemistry
simplifies equilibrium by assuming ideal conditions where all activity coefficients are
unity.
3. As the ionic strength increases an ion loses some of its effectiveness and its activity
coefficient decreases. I.e. they become shielded by their “ionic atmosphere”.
4. In solutions that are not too concentrated, the activity coefficient for a given species is
independent of the nature of the electrolyte and dependent only upon the ionic strength.
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5. For a given ionic strength, the activity coefficient of an ion departs farther from unity
as the charge carried by the species increases. The activity coefficient of an uncharged
molecule is approximately unity, regardless of ionic strength.
6. At any given ionic strength, the activity coefficients of ions of the same charge are
approximately equal. The small variations that do exist can be correlated with the
effective diameter of the hydrated ions.
The activity coefficient of a given ion describes its effective behavior in all equilibria in
which it participates, i.e. not just solubility, but complex ion formation, dissociation, etc.
Harris gives the extended Debye-Huckel equation for calculating activity coefficients on
page 153.
log  =
.
-0.51 z2 √μ
.
1 + (α √μ/305)
In the equation, the log of the activity coefficient is a function of solution ionic strength μ
in mol/L, ion charge z and ion size in picometers, pm.
A separate way to determine activity coefficients is to use Table 8-1 on page 154.
In a few minutes we will calculate activity coefficients using both methods.
Buried in the text on page 153 is the statement that the extended Debye-Huckel equation
works fairly well for solutions with ion strengths less than or equal to about 0.1 M.
Unfortunately there are these places with names like Soap Lake, Alkali Lake, Great Salt
Lake that waters with high ionic strengths. You can image with mu must be for a brine
solution.
Geochemists have worked out other equations for use with should situations. I am sure
Jim will be glad to share these equations with you.
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Okay, so what does all this mean? In general chemistry you were taught the ideal gas law
and you used it for all kinds of gas calculations. However you were also told that gases
are rarely ideal and that there are conditions under which you need to correct for this nonideal behavior.
The same is true for ions in solution. The ideal solution is one that is infinitely dilute.
Most real solutions deviate widely from ideality.
The book will usually neglect activity coefficients and simply use molar concentrations in
applications of equilibrium. This recourse simplifies the calculations and greatly
decreases the amount of data needed. But, at times, Harris will ask you to take activity
into consideration.
For most purposes, the error introduced by the assumption of unity for the activity
coefficient is not large enough to lead to false conclusions. However the disregard of
activity coefficients may introduce significant numerical error in calculations.
Thus you should be alert to the conditions under which the substitution of concentration
for activity is likely to lead to the largest error.
1. Significant discrepancies occur when the ionic strength of the solution is large (>0.01)
2. when the ions involved have multiple charges.
For analytical chemistry this means we try to use dilute solutions when concentrations
become important to our calculations.
The book will signal when activities are important to a topics or analytical method. You
will see activities in acid/base and complex-ion equilibria and in redox equilibria so pay
attention to types of calculations you are making and the kinds of systems you are using.
On the other hand, chemical activities are nearly always employed for geochemical
calculations. There may be a few times when Dr. Stroh says you can use concentrations,
but most of the time you will use activities.
Homework: Turn in what you were able to finish.
Turn in the rest when you are done.
There is likely to be time on the field trip for some chemistry help sessions.
Today at 1 I will be in the Chem Cave for anyone who wants tuoring about
chemistry.
Is there anyone in here who feels they understand the chemistry well enough to help
others? Just 3 or 4 hours a week would be a great help. The pay is $8.50 an hour, plus
the gratitude of many of the students in the program.