a matlab toolbox for solving acid-base chemistry problems in environmental engineering applications
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A MATLAB Toolbox forSolving Acid-Base ChemistryProblems in EnvironmentalEngineering Applications
CHETAN T. GOUDAR,1 MARK. A. NANNY2
1Process Sciences, Research and Development, Bayer HealthCare, Biological Products Division, 800 Dwight Way,
B55-N, Berkeley, California
2School of Civil Engineering and Environmental Science, Carson Engineering Center, 202 West Boyd Street,
University of Oklahoma, Norman, Oklahoma
Received 20 December 2002; accepted 8 February 2005
ABSTRACT: A MATLAB toolbox incorporating several computer programs has been
developed in an attempt to automate laborious calculations in acid-base chemistry. Such
calculations are routinely used in several environmental engineering applications including
the design of wastewater treatment systems and for predicting contaminant fate and transport
in the subsurface. The computer programs presented in this study do not replace student
thinking involved in formulating the problem solving strategy but are merely tools that simplify
the actual problem solving process. They encompass a wide variety of acid-base chemistry
topics including equilibrium constant calculations, construction of distribution diagrams for
mono and multiprotic systems, ionic strength and activity coefficient calculations, and buffer
index calculations. All programs are characterized by an intuitive graphical user interface
where the user supplies input information. Program outputs are either numerical or graphical
depending upon the nature of the problem. The application of this approach to solving actual
acid-base chemistry problems is illustrated by computing the pH and equilibrium composition
of a 0.1 M Na2CO3 system at 308C using several programs in the toolbox. As these programs
simplify lengthy computations such as ionization fraction and activity coefficient calculations,
it is hoped they will help bring more complicated problems to the environmental engineering
classroom and enhance student understanding of important concepts that are applicable to
real-world systems. The programs are available free of charge for academic use from the
authors.�2005 Wiley Periodicals, Inc. Comput Appl Eng Educ 13: 257�265, 2005; Published online in Wiley
InterScience (www.interscience.wiley.com); DOI 10.1002/cae.20051
Correspondence to C. T. Goudar (chetan.goudar.b@bayer.com).
� 2005 Wiley Periodicals Inc.
257
Keywords: acid-base chemistry; computer assisted instruction; MATLAB; wastewater
treatment
INTRODUCTION
Acid-base chemistry is an essential component of
numerous chemistry courses that are taught both at the
undergraduate and graduate level to students across
several disciplines in science and engineering. Most
Environmental Engineering programs require students
to take an environmental chemistry or an aquatic
chemistry course, which typically begins with the
discussion of acid-base chemistry. The concepts learnt
in an acid-base chemistry classroom have wide
application ranging from designing physico-chemical
methods for wastewater treatment to predicting the
fate and transport of both organic and inorganic
contaminants in the environment. Acid-base chem-
istry helps quantify the relationships between various
species of interest in the contaminated stream and is
thus an indispensable tool in the design and analysis
of waste treatment systems.
Problem solving plays an important role in
gaining a solid understanding of acid-base chemistry
concepts. While most of the simple problems are rea-
dily solved by hand, problems that require application
of concepts from multiple areas often involve lengthy
and laborious numerical calculations. This can dis-
courage the use of relatively complicated examples
that could otherwise be used in classroom discussions
or in homework assignments to illustrate application
of basic concepts for solving complex real-world
problems.
One approach of overcoming this limitation is to
automate cumbersome calculations through the use of
computers. This approach is especially attractive at
the present time given the remarkable computing
capability of the desktop computer. This has indeed
been an area of active research and several computer
programs are currently available that are aimed at
solving a variety of problems in acid-base chemistry.
They range in function from relatively simple
programs aimed at solving a specific problem [1�4]
to highly sophisticated and versatile programs [5,6]
that can solve fairly complex problems. Despite their
utility, there is a danger of using these programs as
black boxes thereby compromising the learning and
understanding components of problem solving.
In the present study, we present an approach that
utilizes the power of computers to automate lengthy
calculations in acid-base chemistry without sacrifi-
cing student learning and understanding of key
concepts. Specifically, a toolbox comprising of several
MATLAB (The Mathworks, Natick, MA) programs
has been developed with each program aimed at a
specific area of acid-base chemistry. As typical solution
of an acid-base problem requires the use of multiple
concepts and hence a combination of the above pro-
grams, the student has to individually come up with the
solution strategy and then use the programs for specific
calculations during the solution process. A schematic
of the problem solving process in this fashion is
presented in Figure 1. We believe these programs will
help bring more complex problems to the classroom
and enhance student understanding of important con-
cepts in acid-base chemistry. The programs are avail-
able free of charge for academic use from the authors.
DESCRIPTION AND ORGANIZATION OFTHE TOOLBOX
The computer programs have been written in the
student version of MATLAB 5.0 and cover several
important aspects of acid-base chemistry. A listing of
the programs along with a brief functional description
is provided in Table 1. No MATLAB programming
experience is required to use these programs. Upon
invoking any of the main programs in Table 1, an
intuitive graphical user interface is displayed where
the user enters input data required to perform the
Figure 1 A schematic of the problem solving process
using the computer programs in the acid-base
chemistry toolbox.
258 GOUDAR AND NANNY
calculations. The main programs subsequently trans-
fer this information to several sub-programs where the
necessary calculations are performed and the result is
displayed to the user in numeric or graphic format
depending on the nature of the output.
Among general utility programs, eqconst helps
compute the equilibrium constant from standard free
energy of the reaction while vanthoff can be used to
correct the equilibrium constant value for temperature
effects. Ionization fractions for mono, di, and triprotic
systems at any desired pH value can be computed
using ionfrac. Ionization fractions provide informa-
tion on the relative abundance of various species at a
particular pH, which helps make useful assumptions
during the solution of many acid-base problems. They
are fairly cumbersome to compute as seen from the
following equations that describe the ionization
fractions for a triprotic system [7]
�0 ¼½Hþ�3
½Hþ�3 þ ½Hþ�2Ka;1 þ ½Hþ�Ka;1Ka;2 þ Ka;1Ka;2Ka;3
ð1Þ
�1 ¼½Hþ�2Ka;1
½Hþ�3 þ ½Hþ�2Ka;1 þ ½Hþ�Ka;1Ka;2 þ Ka;1Ka;2Ka;3
ð2Þ
�2 ¼½Hþ�Ka;1Ka;2
½Hþ�3 þ ½Hþ�2Ka;1 þ ½Hþ�Ka;1Ka;2 þ Ka;1Ka;2Ka;3
ð3Þ
�3 ¼Ka;1Ka;2Ka;3
½Hþ�3 þ ½Hþ�2Ka;1 þ ½Hþ�Ka;1Ka;2 þ Ka;1Ka;2Ka;3
ð4Þ
where a0, a1, a2, and a3 are the ionization fractions forthe triprotic system, [Hþ] the hydrogen ion concen-
tration, and Ka,1, Ka,2, and Ka,3 the equilibrium
constants. With the use of ionfrac, values of a0, a1,a2, and a3 at any given pH value can be readily
obtained by entering the pH and equilibrium constant
information in the input dialog box. If profiles of a0,a1, a2, and a3 over a range of pH are desired, they can
be obtained though the use of distdiag, where the user
provides equilibrium constant values of the system as
the input. The resulting diagram is referred to as a
distribution diagram [7] and Figure 2 demonstrates the
use of distdiag to obtain the distribution diagram for
the phosphoric acid system whose three pKa values
are 2.1, 7.2, and 12.3.
Ionic strength and activity coefficient calculations
can be neglected in only the most dilute solutions.
However, if accurate calculations are to be performed
even at concentrations as low as 0.001 M, computa-
tion of the activity coefficients becomes necessary.
The toolbox provides two tools for computing activity
coefficients in solutions. The ionic strength of the
solution can be estimated using ionicstrength whose
input values include the concentrations and charge of
each of the ions in solution. Once the ionic strength of
a solution is known, the activity coefficients can be
computed using actcoeff, which offers a choice of the
Debye-Huckel, Extended Debye-Huckel, Guntelberg,
and Davies equations to compute ionic strength.
Care must be exercised in the use of these equations as
they are only valid over specific ranges of ionic
strength [8].
Buffers solutions are frequently used to maintain
the pH of a system at a desired value. Each buffer has
a range of pH over which it is most effective, and for
optimal performance, the buffer must be used in this
pH range. An estimate of the buffering capacity is
provided by the buffer index, which can be defined as
the amount of strong base required to increase the pH
by a small amount. Buffer index calculations are
lengthy and the program bufferind simplifies this
process. Inputs to bufferind include system pKa
information and the output can either be the buffer
Table 1 Program Listing and Function in the MATLAB Acid-Base Chemistry Toolbox
Program Function
actcoeff Computes activity coefficients for charged species using the Debye-Huckel, extended Debye-Huckel,
Guntelberg, or Davies equations. It can also compute activity coefficients for neutral species
bufferind Computes buffer index for monoprotic and diprotic systems. It can also plot the buffer index as a function of
system pH over a range of pH values
distdiag Plots distribution diagrams for monoprotic, diprotic, and triprotic systems
eqconst Computes equilibrium constants from standard free energy values
ionfrac Computes ionization fractions for monoprotic, diprotic, and triprotic systems
ionicstrength Computes the ionic strength of a solution
titcurves Plots titration curves for strong acids and bases
vanthoff Corrects equilibrium constants for temperature
MATLAB TOOLBOX FOR SOLVING ACID-BASE CHEMISTRY PROBLEMS 259
index at a specified pH value or a plot of the
buffer index over a range of pH values. This plot of
buffer index versus pH is useful in identifying the
most effective pH range for the buffer of interest as
high values of buffer index are indicators of best
buffering characteristics. Both monoprotic and dipro-
tic systems can be evaluated using bufferind.
EXAMPLE ILLUSTRATING USE OFTHE TOOLBOX FOR SOLVINGACID-BASE PROBLEMS
The carbonate system is the perhaps the most widely
studied system in aquatic chemistry. Carbonate is
present in almost all natural waters and a good
understanding of the equilibria of the carbonate
system is essential for designing wastewater treatment
systems. In this section, we will illustrate application
of the computer programs presented in this study to
characterize the equilibria of the carbonate system.
Compute the pH and EquilibriumConcentrations of All Species When0.1 M Na2CO3 is Dissolved in Pure Water
At the outset, it is important to recognize that multiple
approaches can be taken to solve this problem. We
have chosen to take the tableau approach outlined in
Reference [9] as it a very convenient method to solve
most acid-base problems. We will use the tableau
approach along with several programs in the toolbox
to arrive at the solution of this problem.
Reactions. The various reactions in this carbonate
system can be written as follows
Na2CO3 , 2Naþ þ CO2�3 ð5Þ
Hþ þ CO2�3 , HCO�
3 ð6Þ
Hþ þ HCO�3 , H2CO3 ð7Þ
H2O , Hþ þ OH� ð8Þ
Species. The various species present in the system are
as follows: Naþ, Hþ, H2CO3, OH�, HCO3
�, CO32�.
Components. The following components were
selected based on the rules suggested in Morel and
Hering [9]: Hþ, H2O, Naþ, and CO3
2�.
Tableau. Using the species and components de-
scribed above, a tableau was constructed for the
carbonate system and this is shown in Table 2.
Figure 2 Construction of the distribution diagram for phosphoric acid under standard
conditions using distdiag. Inputs include the system pKa values which are 2.1, 7.2, and
12.3, respectively.
260 GOUDAR AND NANNY
Mole Balance Equations From the Tableau. Hþ
Mole Balance
½Hþ� � ½OH�� þ 2½H2CO3� þ ½HCO�3 � ¼ 0 ð9Þ
Carbonate Mole Balance
½H2CO3� þ ½HCO�3 � þ ½CO2�
3 � ¼ ½Na2CO3�T ¼ 0:1M
ð10Þ
Naþ Mole Balance
½Naþ� ¼ 2½Na2CO3�T ¼ 0:2 M ð11Þ
System Equilibrium. The system equilibrium can be
described by the following equations
Ka1 ¼fHþgfHCO�
3 gH2CO3f g ¼ 10�6:3 ð12Þ
Ka2 ¼fHþgfCO2�
3 gfHCO�
3 g¼ 10�10:3 ð13Þ
Kw ¼ fHþgfOH�g ¼ 10�14:0 ð14Þ
Calculation of Ionic Strength. Recognizing that we
are working with a fairly high concentration of
Na2CO3, the first step is to compute the ionic strength
of the solution. The ionic strength of a solution is
given by
I ¼ 1
2
XN
i¼1
Ciz2i ð15Þ
where I is the ionic strength, and Ci and zi the
concentration and charge, respectively, of the ith
species. Using the program ionicstrength, I for the
0.1 M Na2CO3 solution was computed as 0.3 M.
Corrections for Temperature and Ionic Strength.
The values of the equilibrium constants in Equations
(12�14) are valid only at 258C and zero ionic
strength. As the system is at 308C and 0.3 M ionic
strength, the equilibrium constants have to be modi-
fied to reflect these new conditions. Temperature
corrections can be made through the use of vanthoff
which will provide estimates of the equilibrium
constants at 308C. In order to include ionic strength
corrections, activity coefficients have to be calculated
at an ionic strength of 0.3 M and this can be done
using actcoeff. Using vanthoff, the values of Ka1, Ka2,
and Kw at 308C were estimated as 10�6.278, 10�10.257,
and 10�13.838, respectively. In order to determine ionic
strength corrected values of Ka1, Ka2, and Kw, activity
coefficients at ionic strength of 0.3 M were estimated
from the Davies equation using the program actcoeff.
These values were 0.7138 and 0.2596, respectively,
for species with charges of one and two. Activity
coefficients for neutral species can also be calculated
from actcoeff and this value was 1.072.
Incorporating the temperature corrected values of
the equilibrium constants, Equations (12)�(14) can be
rewritten in terms of the species concentrations and
activity coefficients as
Ka1 ¼½Hþ�gHþ ½HCO�
3 �gHCO�3
H2CO3½ �gH2CO3
¼CKa1
gHþgHCO�3
gH2CO3
¼ 10�6:278 ð16Þ
Ka2 ¼½Hþ�gHþ ½CO2�
3 �gCO2�3
½HCO�3 �gHCO�
3
¼CKa2
gHþgCO2�3
gHCO�3
¼ 10�10:257 ð17Þ
Kw ¼ ½Hþ�gHþ ½OH��gOH� ¼CKwgHþgOH� ¼ 10�13:838
ð18Þ
where CKa1,CKa2, and
CKw are the concentration-
based equilibrium constants and g represents the
activity coefficients of the various species. Based on
the calculations from actcoeff, gHþ¼ gOH�¼gHCO�
3¼ 0.7138, gCO2�
3¼ 0.2596, and gH2CO3
¼1.072. Substituting these values in Equations
(16�18), the concentration-based equilibrium con-
stants CKa1,CKa2, and
CKw were estimated as 10�5.955,
10�9.671, and 10�13.545, respectively. These values
now incorporate both temperature and ionic strength
corrections and are representative of the system at
308C and 0.3 M ionic strength. The system equili-
brium at 308C and 0.3 M ionic strength can thus be
Table 2 Tableau for the 0.1 M Na2CO3 System
Components
Hþ CO2�3 Naþ Ka
Species
Hþ 1
OH� �1 10�14
Naþ 1
H2CO3 2 1 106.3
HCO3� 1 1 10�10.3
CO32� 1
Recipe
Na2CO3 1 2
MATLAB TOOLBOX FOR SOLVING ACID-BASE CHEMISTRY PROBLEMS 261
represented by the following equations
CKa1 ¼ 10�5:955 ¼ ½Hþ�½HCO�3 �
½H2CO3�ð19Þ
CKa2 ¼ 10�9:671 ¼ ½Hþ�½CO2�3 �
½HCO�3 �
ð20Þ
CKw ¼ 10�13:545 ¼ ½Hþ�½OH�� ð21Þ
Assumptions Based on Chemical Intuition. Once
the mole balance equation (Equations (9�11)) and
the equilibrium expressions Equations (19�21) have
been established for the system, the process of
determining the equilibrium concentrations of all the
species in the system can be initiated. It is important to
note that the combination of the mole balance and
equilibrium expressions contains all the information
necessary to estimate the equilibrium concentrations
of the species. However, the nonlinear nature of the
equilibrium expressions requires the use of nonlinear
equation solvers such as the Newton�Raphson me-
thod [10] for their solution. This approach is
incorporated into computer programs like MINEQL
and MINTEQA2 [5,6], which use a computationally
intensive approach to problem solving. However,
certain simplifying assumptions can be made based
upon our understanding of the chemistry of the system
that can lead to a set of equations that can be readily
solved using a hand-held calculator. More impor-
tantly, this process of assumption making forces the
student to think about the chemical behavior of
the system. Hence the assumption making portion of
the problem solving process can substantially con-
tribute towards student understanding of the behavior
of the chemical system under investigation.
However, past experience has shown that students
have difficulty in this step until they have a good
understanding of the chemical processes occurring in
the system under consideration. The program distdiag
can help students in the assumption making process as
it provides a visual description of the relative concen-
trations of different species as a function of system pH.
From this, it is easy to determine the dominant species
and those that are present in negligible amounts at any
given pH value. This information can often times be
directly translated into simplifying assumptions as
illustrated below for the Na2CO3 system.
When sodium carbonate is added to water, it
dissociates into sodium and carbonate ions according
to Equation (5). The resulting carbonate ions react
with water to release hydroxyl ions as follows
CO2�3 þ H2O , HCO�
3 þ OH� ð22Þ
HCO�3 þ H2O , H2CO3 þ OH� ð23Þ
As addition of sodium carbonate is accompanied by
the release of OH� ions according to Equations (22)
and (23), it is reasonable to assume that the solution
will be basic. This leads to the first assumption for the
0.1 M Na2CO3 system
½OH�� > ½Hþ� ð24Þ
Additional assumptions can be made if information on
relative concentrations of the various species in the
carbonate system is available. This information can be
readily obtained from a distribution diagram of the
carbonate system (Fig. 3). It follows from Figure 3
that at pH values of 10.5 and higher, the concentration
of the carbonate ion (represented by a2) is greater than
that of the bicarbonate ion (a1), which in turn is
significantly higher that of carbonic acid (a0). This
observation can be described as the second approx-
imation for the 0.1 M Na2CO3 system
½CO2�3 � > ½HCO�
3 � � ½H2CO3� ð25Þ
Simplifying the Hþ and Carbonate Mole Balance
Equations. Incorporating Equations (24) and (25) in
the Hþ mole balance equation (Eq. 9) results in the
following expression
½OH�� ¼ ½HCO�3 � ð26Þ
Similarly, the carbonate mole balance equation
(Eq. 10) may be simplified incorporating Equations
(24) and (25) as
½CO2�3 � ¼ 0:1 M ð27Þ
Analytical Solution of the Carbonate System. Equa-
tions (26) and (27) can be substituted in Equation (20)
to obtain
10�9:671 ¼ ½Hþ�0:1½OH�� ð28Þ
Substituting for [OH�] as CKw/[Hþ], Equation (28)
can be readily solved for [Hþ] as 7.80 � 10�12 M
which translates to a pH value of 11.11. This translates
into [OH�]¼ 3.66 � 10�3 M and as [HCO3�]¼
[OH�] from Equation (26) also provides an estimate
of [HCO3�]. Once the concentrations of [Hþ] and
[HCO3�] are known, [H2CO3] can be readily estimated
from Equation (19) as 2.57 � 10�8 M. This com-
pletes solution of the problem as system pH and
262 GOUDAR AND NANNY
concentrations of [CO32�], [HCO3
�], and [H2CO3]
have been determined.
Verifying the Validity of the Assumptions. This
first assumption was regarding the system pH and it
was stated in Equation (24) that the system was basic
as dissociation of Na2CO3 released OH� ions in
solution. Equation (24) along with the above esti-
mated concentrations of the Hþ and OH� ions can be
rewritten as
½OH�� > ½Hþ�3:66� 10�3 7:80� 10�12
ð29Þ
Similarly, the distribution diagram of the carbonate
system was used to make assumptions regarding the
relative concentrations of the various carbonate spe-
cies in Equation (25). This assumption can be compar-
ed with the actual concentration of the carbonate
species
½CO2�3 � > ½HCO�
3 � � ½H2CO3�0:1 3:66� 10�3 2:57� 10�8
ð30Þ
It is clear from Equations (29) and (30) that the
assumptions made during the problem solving process
are valid.
Summary of the Problem Solving Process. The
above example illustrates application of the acid-base
chemistry toolbox for solving a problem that involved
determining the system pH and equilibrium concen-
trations of a 0.1 M Na2CO3 system at 308C. As the
system was under nonstandard conditions of tempera-
ture and ionic strength, appropriate corrections had to
be made to the equilibrium constants that described
the chemical reactions occurring in this system. Speci-
fically, temperature corrections (Eqs. 16�18) were
made using the program vanthoff while ionic strength
corrections (Eqs. (19�21)) were made using actcoeff.
Once the approximate pH of the system was known
from Equation (24), distdiag was used to obtain a
visual description of the relative concentrations of the
various species in the 0.1 M Na2CO3 system. The
distribution diagram clearly indicated that CO32� was
the dominant species at elevated pH values and this
helped form the second assumption for the 0.1 M
Na2CO3 system (Eq. 25). Once these simplifying as-
sumptions had been made, system pH and equilibrium
concentrations of the various species were readily
determined by simple calculations as illustrated in
Equations (26)�(28). The validity of the assumptions
made during the problem solving process was verified
in Equations (29) and (30). Hence, a relatively
complex problem was solved in a fairly simple fa-
shion using the acid-base chemistry toolbox whose
programs helped simplify tedious calculations and
also provided a visual description of the chemical
system. It is also very important to note that none of
Figure 3 Construction of distribution diagram for the carbonate system at 308C and ionic
strength of 0.3 M using distdiag.
MATLAB TOOLBOX FOR SOLVING ACID-BASE CHEMISTRY PROBLEMS 263
the programs used gave a direct answer to the problem
being solved. A problem solution strategy had to be
formulated independently and the acid-base chemistry
toolbox merely helped implement this strategy in an
efficient manner.
STUDENT RESPONSE TO CLASSROOMUSE OF THE ACID-BASECHEMISTRY TOOLBOX
Based upon qualitative observations of student per-
formance and their attitude with respect to solving
acid-base chemistry calculations using the toolbox, it
is reasonable to state that allowing students to use this
computational tool is advantageous over traditional
‘‘paper and pencil’’ calculations or using more
advanced computational tools such as MINEQL and
MINTEQA2 [5,6]. The toolbox use freed students
from what they perceived as ‘‘drudgery’’ and ‘‘plugg-
ing and chugging’’ through ‘‘long and tedious calcu-
lations,’’ allowing them to ‘‘think more about the
chemistry.’’ It was observed that this toolbox provided
students with a sense of confidence in their calcula-
tions thereby making them willing to address more
challenging, complex, and real-world type problems.
Moreover, using the MATLAB toolbox, students were
willing to formulate and answer ‘‘what-if’’ questions,
for example, to model or calculate how changes to
pH or ionic strength would change the overall aqua-
tic chemistry of a specific system. This shifted
classroom discussions from ‘‘how do I do the calcu-
lations?’’ to focus more on the acid-base chemistry
being studied.
Another advantage of the MATLAB toolbox is its
simplicity; students interact with each program as a
component of an aquatic acid-base calculation. Since
each program is fairly straightforward, students
readily master its use. This is in contrast to larger,
more complex modeling programs such as MINEQL
and MINTEQA2 [5,6] which require an understand-
ing of how to enter components as well as how to
move successfully through the many levels of the
program. Moreover, as students cannot easily observe
the functions and calculations in these complex
programs, many students are willing to blindly accept
the output or feel uncomfortable in their results
because they do not know how to check if they made
an input error.
The purpose of the toolbox presented in this study
is to provide students with computational tools that
are robust enough to tackle calculations routinely
encountered in an upper-level undergraduate/graduate
level aquatic chemistry course, but not so complex
that the students require additional tutoring in their
use. This allows students to readily focus on the
fundamental concepts of the system chemistry and
have confidence and a desire to solve challenging
problems.
CONCLUSIONS
We have presented a MATLAB toolbox comprising of
several programs that automate complex and tedious
calculations involved in solving typical acid-base
chemistry problems. The toolbox is not a one-step
‘‘black-box’’ type approach towards problem solving
but instead facilitates efficient implementation of
the problem solving strategy that has to be indepen-
dently formulated by the student. By simplifying
complex calculations and providing a visual descrip-
tion of the chemical system under investigation, the
toolbox helps students focus on the chemistry instead
of being bogged down by lengthy calculations that are
usually done by hand-held calculators. The applica-
tion of the toolbox for solving acid-base chemistry
problems was illustrated for the Na2CO3 system
where it was shown that the problem solving process
could be simplified by using programs from the
toolbox. These programs could encourage the intro-
duction of more complex problems in the acid-base
chemistry classroom that illustrate application of
acid-base chemistry concepts to real-world Environ-
mental Engineering problems thereby broadening
student perspective and strengthening fundamentals
at the same time.
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264 GOUDAR AND NANNY
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BIOGRAPHIES
Chetan Goudar is a process development
scientist in the biological products division
of Bayer HealthCare in Berkeley, California,
where he is developing fermentation pro-
cesses for high-density perfusion cultivation
of mammalian cells to manufacture thera-
peutic proteins. His research interests are in
the general areas of applied mathematical
modeling, bioenvironmental engineering,
mammalian cell cultivation, and metabolic engineering. He has
authored over 25 peer-reviewed research articles and is a licensed
professional engineer in the state of California.
Mark A. Nanny is an associate professor of
environmental chemistry at the University of
Oklahoma. He received his BS (1986)
degree in chemistry from Wayne State
University, and his MS (1989) degree in
chemistry and his PhD (1994) in environ-
mental chemistry from the University of
Illinois. Dr. Nanny’s research interests
include characterizing bioavailability and
biodegradation of organic pollutants in soils, sediments, and aquatic
systems; examining the molecular-scale interactions of organic
pollutants and metabolites with natural organic matter; and
elucidating anaerobic biodegradation mechanisms in order to
predict intrinsic anaerobic biodegradation products of hydrocarbons
and biopolymers such as lignin. He is the author on over 30 peer-
reviewed research articles and book chapters and is a coauthor of the
book NMR Spectroscopy in Environmental Chemistry.
MATLAB TOOLBOX FOR SOLVING ACID-BASE CHEMISTRY PROBLEMS 265
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