5 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 sh

5
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 IO3- Ksp = 1.3 x 10-18 = [Hg22+][ IO3-]2
concentration
table before 0 0
after x 2x
If we solve for the solubility we get Ksp = x(2x)2 = 4x3
_____
[Hg22+] = 3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.
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).
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 B3-
Ksp = 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.
XXXXXX
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).
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.
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 non-ideal
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.

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