VBA Macros for Solving Problems
in Water Chemistry
Chad Jafvert
Purdue University
The Educational Objectives of the Tools: Students will:
Design and create VBA Macros (i.e., programs) that solve analytical
and numerical problems in aquatic chemistry and related fields.
(Levels 5 (Synthesis) & 3 (Application) in Bloom’s Taxonomy of
Educational Objectives)
This computer-based learning tool consists of the instructions and
example programs that students can apply and mimic in designing their
own solution algorithms.
The Ingredients: Excel (Microsoft Office) loaded on any PC
Development Time: ?
Development Time (for students): 1 to 2 50-min lectures to convey
the tools to the students, 5 min to 40 hrs for students to write a
successful VBA macro.
Educational Outcomes: The computer skills, program language
backgrounds, and programming phobias of students entering
graduate environmental engineering and science programs are wideranging, yet these students always have in common the ability to
perform mathematical operations in spreadsheets like Excel. With
very little additional instruction, they are using VBA in Excel as a
programming language and solving rather complex mathematical
problems with software they are comfortable with, that is ubiquitous in
nature (including on their own PCs), and that has immediate
graphical output.
Web Address where Instructions and Examples can be
Downloaded: http://bridge.ecn.purdue.edu/~jafvert/Macros.html
Downloads (demos):
Instructions: An Acrobat file contains the instructions for writing VBA
macros in Excel and further explanations on each of the sample
spreadsheets below. (15 pages)
Introduction to VBA.xls: An Excel spreadsheet that contains an example
VBA macro that shows how to: (i) dimension variables and arrays, (ii) write
'For . . . Next‘ loops, (iii) read and write to the spreadsheet, (iv) format
common mathematical expressions, (v) etc.
Functions.xls: A simple spreadsheet than contains some user-defined
functions (volume of a cylinder, roots to the quadratic equation, and the sin
of an angle measured in degrees).
pKa.xls: A spreadsheet that calculates buffer composition
and draws the pC-pH diagram of a simple acid.
Downloads (cont.)
Case 3 p60 in Morel & Hering.xls: A spreadsheet that solves a
system of three equations and three unknowns by Newton-Raphson
iterations. The 'recipe' for the problem is the same as 'Case 3' on page
60-63 in the text "Principles and Applications of Aquatic Chemistry" by
Morel and Hering.
Stratified Lake.xls: A spreadsheet that solves a system of 2
simultaneous ODE's with Euler's method. The example case is the
transport of TCE in a stratified lake - presented on pages 551-574 in
"Environmental Organic Chemistry" by Schwarzenbach, et al. The 2
ODE's are eqs 15-30a and 15-30b (p. 569) in the text.
1D Diffusion.xls: The central difference solution to the 1-D diffusion
equation with an impulse input at the center of the media. The
numerical solution is calculated with a VBA macro and is compared to
the analytical solution calculated directly on the spreadsheet. A second
macro calculates the mass under the concentration profile with
Simpson's Method.
A Very Simple Example VBA program that reads and writes:
In Excel, Type ‘3’ in cell B4, then click on ‘Tools’, ‘Macro’, ‘Macros’.
Provide a name for your macro, click on ‘create’
Type the following lines and click on ‘Run’, ‘Run Sub’:
Now you are ready to solve 3 simultaneous equations:
f1 (H

, CO32 , A )
f2 (H

[H  ][CO32 ]
Kw'
 0 

 2  [CO32 ]  [A  ]  [H  ]  2  CT,Ca 2

'
[H ]
Ka,2
, CO32 , A  )
f3 (H

 0 
, CO32 , A  )
[H  ] 2 [CO32 ]
Ka' ,1
 0 
 K a' ,2

[H  ][CO32 ]
[H  ][A  ]
K a'
Ka' ,2
 [CO32 ]  CT ,CO 2 
3
 [A  ]  CT ,A
By finding the roots with the Newton-Raphson method:
 x1 
 
 
x2 
 
 
x 
 3  i1

 x1 
 
 
x2 
 
 
x 
 3 i

 f1

 x1
 f2

 x1
 f
 3
 x1
f1
x2
f2
x2
f3
x2
1
f1 
 f1 

x3 
 
 
f2 
  f2 
x3 
 
 
f3 
f 

3
x3  i   i
First, solve for the
functions and the partial
derivatives with initial
guesses, invert the matrix,
and do the math to solve
for the new guesses, all on
the spreadsheet.
Next, replace the old guesses with the new guesses with a
simple ‘read and write’ VBA program. Repeat (iterate) until
the problem converges.