a matlab toolbox for solving acid-base chemistry problems in environmental engineering applications

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 ([email protected]).

� 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


ð2Þ

�2 ¼½Hþ�Ka;1Ka;2


ð3Þ

�3 ¼Ka;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.


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


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


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.


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.

REFERENCES

[1] W. J. Lambert, BUFCALC: A program for the

calculation of buffers of specified pH, ionic strength,

and buffer capacity, J Chem Educ 67 (1990), 150�153.

[2] R. W. Clark, G. D. White, J. M. Bonicamp, and E. D.

Watts, From titration data to buffer capacities: A

computer experiment for the chemistry lab or lecture, J

Chem Educ 72 (1995), 746�750.

[3] R. W. Ramette, Buffers Plus, J Chem Educ 75 (1998),

1504.

[4] R. de Levie, A general simulator for acid-base

titrations, J Chem Educ 76 (1999), 987�991.

[5] J. C. Westall, J. L. Zachary, and F. M. M. Morel,

MINEQL. A computer program for the calculation of

chemical equilibrium of aqueous systems, Department

of Civil Enineering, Massachusetts Institute of

Technology, Cambridge, MA, Technical Note 18,

1976.


[6] J. D. Allison, D. S. Brown, and K. J. Novo-Gradac,

MINTEQA2/PRODEFA2. A Geochemical Assesment

Model for Environmental Systems, Version 3.0 User’s

Manual, EPA/600/3-91/021. 1991.

[7] V. L. Snoeyink and D. Jenkins, Water chemistry, Wiley,

New York, 1980.

[8] W. Stumm and J. J. Morgan, Aquatic chemistry, 4th

ed., Wiley, New York, 1996.

[9] F. M. M. Morel and J. G. Hering, Principles and

applications of aquatic chemistry, Wiley, New York,

1993.

[10] W. H. Press, S. A. Teukolsky, W. T. Vettering, and B. B.

Flannery, Numerical recipies in FORTRAN: The art of

scientific computing, Cambridge University Press,

New York, 1992.

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.


a matlab toolbox for solving acid-base chemistry problems in environmental engineering applications

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