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Before
discussing
chemical equilibria, it might be good to describe
the way an aquatic chemist sees the system: Dissolved ions in
solution
interact with each other (form complexes), interact with particulate
surfaces (adsorb) and possibly form solid phases (precipitate). In a
typical natural system, say a stream water, there may be 10 to 20 major
chemical components dissolved in solution. These components have the
potential to form hundreds of dissolved chemical complexes, solids
phases or adsorbed species. Some of these chemical species may be
biologically active or even toxic while others may be inert. All of
this depends on factors like the total concentration of each component,
the pH, pe, ionic strength and temperature.
This is where chemical equilibrium is really helpful. As the name
implies, chemical equilibrium assumes that all reactions have gone to
completion and are in equilibrium with one another. So time dependent
reactions -- those reactions that have kinetic restrictions -- are not
addressed in this approach. In essence, the chemical equilibrium
approach provides you with a thermodynamic snapshot of your system: the
pH, ionic strength, the distribution of dissolved chemical species, how
much solid phase formed, etc. This is the type of information that is
critical to understanding what happens chemically in water.
Metal Interactions in the
Living World
Let's look at an example. Most toxicologists
looking at the effects of heavy metals on biological systems (e.g.,
phytoplankton or fish gill) will assume that the toxic form of most
metals is the free or aquo species (Me2+).
Hydrolysis products (i.e., MeOH+, Me(OH)2,
Me(OH)3-, etc.) or
complexes with other ligands (e.g., SO42-,
PO43-, or CO32-)
are generally considered to be less harmful. If you measure the pH and
the total concentration of the different chemical components in your
system, you could use chemical equilibrium to calculate the amount of
free metal ion that is present in your system.
This is a vast improvement over just reporting the total concentration
of a metal in relation to biological response. By accounting for pH,
all side reactions and the competition between metals for ligands, you
are able to arrive at a much more insightful description of the
chemical environment -- and a much greater ability to form hypotheses
about how metals interact with organisms.
Mobility of Metals in the
Soil Environment
Here's another example. Say you are looking at a
soil system that contains a certain amount of naturally occurring lead.
The question is whether the lead is going to remain on-site or dissolve
and gradually move with the groundwater into surrounding streams and
wells. Generally this would be answered by placing monitoring wells
throughout an area and measuring the chemical concentration of lead. If
in addition to this monitoring, you were to apply the principles of
chemical equilibrium, you would be able to develop deeper insight into
the chemical mechanisms controlling the system. A monitoring program
answers what is happening in the system. Chemical equilibrium answers
why.
For instance, if in the course of your monitoring program you were to
notice that the concentration of lead was decreasing as you moved
farther down a watershed, it would be useful to know what happened to
the lead. The chemical equilibrium approach would tell you if lead
solids were forming or if an observed change in pH was due to the
addition of a new ion to solution. If most of the lead is calculated to
form a particular solid phase, if might be interesting to see how small
perturbations in the system effects the dissolution of lead. Can you
see how powerful this is? By describing the underlying mechanism you
are increasing your ability to make decisions about this system.
Analytical Insight
Here's one last example. Many laboratories
routinely analyze water samples for a whole array of ionic
constituents. It is inherent within any type of measurement that a
certain amount of uncertainty will be introduced. All that can ever be
done is to try to minimize the uncertainty -- you can never eliminate
it. Many questions come up in this type of work. For one, is the sample
well characterized (i.e., did you measure all the important anions and
cations)? Second, if you are sure that the system is well
characterized, how can you check to see that your analytical error is
within reason? Finally, are organic solutes present in your sample?
One of the first checks that researchers perform on a sample is for ion
balance. This is basically just an accounting of all the positive
(cationic) and negative (anionic) charges in the system. In the actual
system, the positive and negative charges will always balance each
other out. This is the principle of electroneutrality. But in measured
samples the introduction of analytical error will make this hard to
observe. Usually a charge discrepancy that less than 10% of the ionic
strength of the solution is considered good.
Here's the problem: You can't just calculate charge discrepancy by
adding up all the total metal concentrations and subtracting the total
ligand concentrations. Remember the system described above includes
metal complexes of all types. Each complex contributes its unique
charge to the system. So this is another example where knowledge of
chemical equilibrium would be useful. If you know the concentration of
each dissolved complex, you can calculate the charge discrepancy fairly
easily.
Not only can the charge discrepancy function as a screening criteria
for your samples, but it can help flag when to include additional ions
in a suite of analyses or to help identify the presence of organic ion
in waters.
How to Go About Performing
These Calculations
By this point you may be wondering how to perform
chemical equilibrium calculations yourself. After all, it's fine to
talk about the benefits of this technique, but if it is too complicated
to apply to your work then what good is it?
Calculating chemical equilibrium for all but the most simple waters
requires the use of a computer program. There are several around, some
of which you can get for free. Many of them base their numerical
algorithms around the MINEQL program which was developed at MIT in the
mid 1970's. I'm not going to go into a description of MINEQL here. It
suffices to say that MINEQL maintained such a robustness and elegance
that it was hard to beat. Any of the improvements that came to MINEQL
over the years never tampered with its core numerical techniques. Some
of the other models worth looking into are MINTEQA2 (developed in the
mid 1980's for the USEPA), PHREEQC (developed by the US Geological
Survey) and MINEQL+ (which I will talk more about later). In fact,
there have been hundreds of derivative programs created of the last 20
years. Many were never intended to be used by a broader audience; many
assumed that you would have a fairly advanced knowledge of computers
and programming.
Which Model is For You?
How do you go about deciding which is the best program
for you? If cost is the only consideration then it is impossible to
beat the 3 programs listed above. All of them have freeware versions that are
available on the web. But it is probably a good idea to consider how
you are going to use a program before you invest the time and energy
required to learn its proper application.
Here are some general guidelines:
1.
Do you need
this program to work in a classroom setting?
When teaching concepts in aquatic chemistry, you'll need a program that
makes it easier to focus on chemical equilibrium. You don't want to
have to teach FORTRAN as a means of teaching modeling. Chemical
equilibrium is complicated enough without introducing additional
complexity in the form of a computer. The program should clarify all
the assumptions being made in a straight forward manner. It should be
easy to visualize the results and to navigate through the various
options. The user's manual should be directed toward lessons that will
help you get the subtleties across. Ideally, it would be great if the
software maintained a perspective that was consistent with that of
standard textbooks and the overall curriculum.
2. Do you need source code so
that you can include it in a larger modeling framework? If
you're more of a nuts and bolts type of modeler, you probably don't
worry about issues such as data visualization and graphics. You're more
comfortable taking control of things from the ground up. In such a
case, you would be better off with one of the freeware programs offered
through the USEPA or USGS. The learning curve is steep, but there won't
be any surprises and you can't beat the price.
3. How much time do you have to
learn a new program? If deadlines
are more important, then you need to focus on programs that will
provide good visualization and help lead you though the problem solving
process. The documentation needs to be well organized and designed to
bring you to a specified end point.
4.
Is it important
that the program be compatible with 3rd party software like
spreadsheets, databases, or statistical software?
You need a program that will have these features built in. If you are
more inclined to making things from the ground up (see item 2), then
you can always program these features yourself. Generally, it is better
to have 3rd party compatibility built in. The reason is that
compatibility is not just a matter of reading in a specified file
format. It also requires the inclusion of certain user interface and
program compatibility issues that allow flexibility. Usually when
people program these types of special additions to software they don't
want to think about the full set of issues that are required. They
would much rather program for a specific short-term goal. Maybe this
sounds familiar?
5.
Do you need
this program to process large datasets, such as the type you would
generate in doing field research? Many
programs are designed to perform single runs and if you want to process
large datasets you would have to go through the tedious task of
submitting each set of data separately. In addition, you need to see
how the program organizes the output results. If the numbers you are
interested in are embedded within a large text report then extracting
the output data for further analyses could also be tedious (and time
consuming). Automatic processing of large datasets requires simple
methods for inputting data and extracting output.
These are a few of the things to think
about when choosing a chemical equilibrium model. Of all the items
listed above, MINEQL+ for
Windows provides excellent capabilities in all items except number 2.
MINTEQA2 and PHREEQC, while excellent models, do not place much
emphasis on how you, as the modeler, will interact with the program.
I haven't gone into any of the chemical or technical specifications of
these models for a reason: 95% of the numerical algorithms are the same
on all these programs. PHREEQC allows an expanded approach to
hydraulics as well as a reverse calculation that is unique. Otherwise,
all the programs are numerically the same. The differences come more in
the ways that human beings interact with them and the overall
assumptions that the programmers had about their audience.
For a
more in-depth comparison of these models, see:
Butler, J.N. with a Chapter by David Cogley (1998) Ionic Equilibrium.
Solubility and pH Calculations. Wiley-Interscience, New York.
A Simple
Approach to Complex Systems
Since I am the person who developed MINEQL+, perhaps I should explain
my approach. I wanted MINEQL+ to make running chemical equilibrium
problems a simple matter, so I reduced it down to three basic
questions:
1.
What chemical
components are in the water? In
MINEQL+, you use your mouse to select ions from a menu of over 145
components. Since every component available in the MINEQL+ database is
listed on-screen, nothing is hidden.
2.
How do these
components interact with one another?
MINEQL+ uses the MINTEQA2 database of thermodynamic constants as a
starting point for defining the reactions in any aqueous system. Press
a single key to load in all the complexation,
precipitation/dissolution/ adsorption, or redox reactions for your set
of chemical components.
3.
What is the
total concentration of each component?
Easily type in the molar values for each component using a Tableau
tool, or use one of the advanced Calculation Wizards.
Software that
Clarifies, not Confounds
In developing MINEQL+, it was important that everything be as visual as
possible. If you download some of the freeware models that are
available, you will find they often obscure the assumptions that go
into running the calculation. It's great if a program has a
state-of-the-art thermodynamic database, but why should you leave it to
faith that it is being applied correctly? In MINEQL+, all chemical
reaction data is visible. MINEQL+ has a Tableau
tool that allows you to add, delete, edit or just review all
reaction data prior to running a calculation. This is a very powerful
feature. It turns MINEQL+ from a model (where you
accept other people's assumptions) to a modeling system
(where you have full control of the assumptions).
The concept of visualization was also important when dealing with
output. MINEQL+ allows you to plot any chemical species (up to 10 at a
time) versus any independent variable (such as pH). So you can easily
generate logC-pH diagrams, alpha-distributions (ion fractions),
solubility plots, titration curves, or sensitivity plots. See some
example output plots
here.
I'm not going to go into all of MINEQL+'s
features. You can browse this website for more of that. The point I'd
like you to take away here is that good software should help you focus
of the subject it addresses (in our case, chemical equilibrium) and not
provide a technological impediment. All too often, we as human beings
force ourselves to adapt to technology that is poorly designed or
ill-conceived.
A great deal of work has gone into creating MINEQL+. The DOS version
was first available in 1992 and since that time I have received a lot
of user feedback. This helped me understand the broader ways that
people use chemical equilibrium calculations. The program has been
available on the web since 1995 and in that time it has been used in
over 500 colleges and universities to teach courses in aquatic
chemistry, soil chemistry, chemical cycling, and geochemistry. In 1996,
we started developing the Windows version. After 2.5 years of
improvements to the numerical engine, user interface and documentation,
MINEQL+ is not only easier to use, but more stable, robust and
numerically powerful.
If you are serious about performing chemical equilibrium calculations,
either as a teaching tool or in research, please consider purchasing
MINEQL+. It will practically make aquatic chemistry a pleasure.
Click here if you are
interested in purchasing MINEQL+ or seeing exceptions for academic
licenses.
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