Summer 2000 CONFCHEM
Internet
Conference on Chemistry
| Welcome to Summer 2000 CONFCHEM Internet Conference on Chemistry |
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A system may be set up according to some theories. For example, van der Waals equation can be used for real gases to illustrate how real gases differ from the ideal gas. These equations are implemented in a Java applet to simulate a system for a user to explore the difference. From this simulation, a user is asked to find out conditions in which the ideal gas law gives results within a set error limit.
A Java applet is written to simulate properties of gases. A user can choose one of several gases to investigate at a time. The temperature and volume are two independent variables that can be altered, and the pressures calculated by the two models are presented. This is a deterministic simulation, but the calculated pressures may be misleading. One of the suggested application is to ask students to formulate a general statement regarding the conditions, under which the model is valid. Gases such as He, H2, N2, H2O, CO2, etc are included the Java applet.
Differential equations are excellent for defining a system. Instead of solving these differential equations for explicit form, numerical methods may be applied. Numerical methods are often used for computer simulations.
Monte Carlo Simulation is another popular method used to explore systems involving large ranges of parameters. Instead of covering the entire range, results at some random points are calculated to represent the results over the entire range. Some examples of Monte Carlo simulations will be presented.
Some years ago, one of us taught a course Application of Computers in Chemical Problem Solving. Programs have been written to illustrate animations and simulations, and we will outline some of these projects.
Scientific investigations model nature under some limited conditions.
Nature is complicated, ant it has many rules and parameters.
Few people agree if we consider Nature as a complicated simulator,
but there are many similar aspects between a simulation and Nature.
Despite the many laws discovered and validated in the past, there are still
more to be explored or discovered. Of course, building a simulator of Nature
is impossible, because we still do not have all the rules or laws.
However, by putting in as many rules as possible, many computer simulations
have been built to predict the results under a set of conditions.
A simulation incorporates one or more rules to define a model.
These rules apply within some limited conditions. Thus, a simulation
is a good model for exploration or learning. Unfortunately, most
educators create simulations as a hobby, we lack the expertise or
time to construct sophisticated models.
In this paper, we present some simulations that have been used
in general chemistry. We recognize their limitations, but we have had
the pleasure in their creation, and they have delighted some students.
A few Java applets are included to illustrate their potential.
These applets are preliminary, because we have not had much
experience in using Java to write simulations.
The first step to create a simulation is to define an appropriate
system and collect the theories governing the changes in it.
The foundation of the system is built on well-tested theories.
A simulation for teaching general chemistry is usually based on
a few theories in the domain of this level. Perhaps the major
attraction in these simulations is a lively visual effect to
teach these theories. When creating a computer simulation,
we plan to present the theory more attractively than those using words,
equations, tables, and graphs. To achieve this goal, however,
depends on many factors.
Changes in nature are usually continuous, but quantities in computers
are discrete. The digital representation of quantities often causes
problem for the simulation of physical and chemical changes.
Special conditions have to be imposed in the program for meaningful
results.
There are many books regarding computer simulations, and we list three
(1, 2 & 3) for general guidance. We follow some
typical steps for our creation of simulations:
Among these types, we choose to model the conversion from A to
C via an intermediate B as indicated below.
where ka and kb are rate
constants for the indicated steps. These models apply to
the kinetics of consecutive radioactive decays, and also
to an isomeric conversion with an intermediate. In the case
of decomposition to produce two products, C represents
the amount of one of the products.
For simplicity, we consider both steps follow a first order mechanism, and
the differential equations for the chemical kinetics are:
These are the rules that govern the changes of the system.
Rate constants ka and kb
are independent variables. Furthermore, we assume the system starts with
an initial amount of A, and for simplicity, the initial
conditions are restricted. A more sophisticated system allows
the user to set up an initial amount of A and B.
Quantities A, B and C are evaluated by
numerical methods
(4, 5 & 6)
in the Java program. The italicized letters denote
the amounts of the various species. A more complicated simulation can
include the order of the reactions to be different from the first order.
In this simple simulation, the user may choose any combination of values for
ka and kb.
When the values are chosen, the amounts of A, B, and C vary as
functions of time. A bar graph shows the variations of the amounts
as the functions are plotted.
There are many different ways to present the results for each simulation,
but a choice has to be made. The present choice is somewhat academic,
because the plots require additional interpretation.
If a definite set of instructions is given, students will simply follow
the instructions. Thus, we suggest some questions for the students to
answer as they explore the simulation. It will be interesting to ask
students to write a report to discuss how they have used the simulation
if the class is small.
We have used this simulation to demonstrate how the intermediate B
varies as the ratio of the two rate constants change, but there are other
applications. We will be interested in knowing how you might use it.
We have also written a simulation to show the variation of reactants
and products using random rate constants and order of reactions.
The object of this simulation is for the user to figure out the
order and the rate constants. Some aids were built in. For example,
by pressing certain keys, the user can plot diagrams to figure out
the order of the reactions. Evaluation of the rate constant is easy.
For real gases, the van der Waals equation provides a slight improvement
in predicting the gas properties compared to the ideal gas law.
However, both the ideal gas law and the van der Waals equation work well
only for some ranges of temperatures and pressures. Few students at this
level paid much attention to the limitations. An interesting exercise
is to ask them to find out the limitations of a simulation for the
modelling of real gases. In this simulation, some conditions will
result in negative pressures, meaningless quantities.
In this simulation, the properties of helium are given as the default.
Please change the gas from helium to a different gas to begin, because
for some unknown reason, the simulation from the default at the start
does not give the desirable results. On the other hand, once a different
gas has been chosen, the simulation works fine. This error may be caused
by a bug in Java or the Netscape 4.6 browser.
The user can investigate a gas by changing the amount in moles,
the volume in L and the temperature in K. The simulation gives the
pressures calculated according to Model A and Model B.
We will develop a more sophisticated simulation, but in the
time frame we have, this preliminary version is included here.
The wavefunctions of molecular orbitals of H2 can be a
linear combination of atomic orbitals (LCAO) of the two hydrogen
atoms in the molecule. Utilizing appropriate normalizing factors,
the bonding orbital is the sum of two 1s atomic orbitals,
whereas the antibonding orbital is the difference of the atomic orbitals.
The electron density is proportional to the square of the wavefunctions.
To calculate the electron density throughout the entire space is
time consuming, and impractical even if a very coarse grid is
chosen. However, we can randomly (the Monte Carlo method) choose
points in the space of interest to us and evaluate the square of the
wavefunction. The program actually places a dot at that point in
the 2-dimensional space if a random value is greater than the
probability. Thus, the density of the dots is proportional to
the electron density of the orbitals.
Since the points are randomly chosen, it takes very little time to plot
many dots to fill the entire plane. Since the dots fall randomly on
the plane, the actual plotting is very interesting to watch. It is
particularly impressive to plot the dots in a dark room with light
blue dots. A plot resembles a clear night sky.
In this simulation, symmetry of the wave functions is assumed in plotting
the dots, but electron density does not have to follow the symmetry.
The presentation is a matter of choice.
The effect of this type of simulation depends on the computer speed.
When we first execute a version of this simulation, we adjust the speed
of plotting to make watching the plot rather interesting.
When the same version is executed later in fast computers, the dots are
plotted too fast to be interesting.
In this Java applet, we limit the number of dots plotted. Otherwise,
the dots will cover the entire window in little time.
Since downloading a file is much more trouble than browsing it on the screen,
only a few programs that require no additional data files are included for
those who are interested.
when one of the reagent is in excess. For a seasoned chemist, this
animation is trivial, but atomic science is stressed in this simulation.
with a forward and a backward reaction rate constants,
kf and kb. In this version,
any value is accepted for these rate constants, including negative
ones. The strategy for this type of simulations has been discussed
in Chemical Reaction Simulations earlier.
Few students while taking general chemistry have said much about
the simulations or animations. However, a few senior students plus some
graduates have commented that they appreciate having seen the simulations.
As they mature, they appreciate the amount of work in making the
simulations. Today, students are familiar with computers,
and they probably are not excited by simple simulations.
Computer simulations are used for education, problem solving, and prediction
of natural phenomena. These simulations involve many theories and parameters,
and their calculations are very complicated. For example,
H. M. Bell at Virginia Tech has written PC software for NMR,
radioactive decay, and IR simulations.
A Compilation of Educational NMR Software collected by P. Lundberg
gives many sites that have NMR simulations.
Overview of interactive programming methods for the World Wide
Web by B. M. Tissue includes simulations using JavaScript and
Java applets. A search on the Internet usually results in many
links related to simulation.
There are many different ways to make up simulations and animations.
D.E. Mencer's
Internet site gives simulations made up using forms on the web page
and scripts on the server. He has discussed this aspect in his paper:
Developing and Implementing Web-based Computer Simulations
for In-Class, Individual, and Small Group Work (Summer 2000 CONFCHEM,
Paper A-1). Students' usage can be monitored with
scripts in the server for this type of implementation.
Animations and simulations have been made up using
Macromedia Director
by B. Pankuch, who has presented some of these in his paper:
Why use animations and simulations? (Paper A-3)
The extensible markup language XML is on the horizon for simulations.
Some examples of its application can be found in the
MoDL tutorial. We have attempted these options, but we have yet to
implement any animation or simulation using these technologies.
Java applets are suitable for course Internet sites. We have
An Internet Site for General Chemistry for many years, and
we are planning to add Java applets to some of the pages.
Java applets are now widely accepted by most browsers. However, the
computer technology changes rapidly, and we work hard at catching up.
The dependence of simulation on technology is a discouragement
for us, because by the time we have caught up, the situation is
again different.
However, change is the invariance of life, and we have accepted it.
E-mail: cchieh@uwaterloo.ca
Introduction
Simulation means different things to different people.
In the broad sense, science is a simulation of nature.
Newton used simple formulas to simulate the motion of objects, and
the ideal gas law simulates the properties of most gases.
However, these simulations have been around for such a long time that
we accept them as fact, because so many people have validated
these models or simulations.
Creating Models
Because energy and mass are not created, they cannot be destroyed.
On the other hand, artwork, computer programs, buildings, machines
and social systems are created, and they can be destroyed.
A simulation is also a creation, and as such, it has a limited life
and its application depends on the technology and time.
These steps are easy to follow, but artistic design, test, getting feedback,
and revise take time and patience. The design of interface between
the user and the computer is very important. How a user changes the
parameters and how the results are presented require careful
consideration. Often, a number of design changes have been made.
Chemical Reaction Simulations
Chemical reactions form the backbone of chemistry, and on this topic, we
usually concentrate on the rate laws because we want students to learn
the skills needed to calculate the variations of reactants or products
in the system.
There are many types of chemical reactions, and their modelling depends
on the reactants, the products, and the rate constants. Every reaction
is a unique model, and they may be divided into many types.
A ---ka®
B ---kb® C
dA
- -----
dt
= ka A
dB
- -----
dt
= kb B dC
= -----
dt
Properties of Gases
Properties of gases are integrated in general chemistry.
Avogadro's law, Boyle's law, Charles's law, and Dalton's law (the
ABCD laws of gases) and the ideal gas law have always
been important parts of general chemistry. Thus, a simulation on the
properties of gases is interesting.
Suggestions for Using the Simulation
The following questions or points are suggested, but use your imagination
and feel free to use the simulation in any way you see fit.
Again, your suggestions are more than welcome.
This example simulation that presents numerical values rather
than graphics. Students may be asked to plot the data in a graph to
represent a law of gases from the data of the simulation. For this purpose,
a simulation with a cylinder and a barometer is more attractive.
Electron Densities of the Hydrogen Molecule
The Monte Carlo Method can be applied to plot the electron densities of
atomic orbitals and molecular orbitals. This method applies to any
number of dimensions, but we choose a 2-dimensional approach to simulate
the electron densities of bonding and antibonding orbitals of the
hydrogen molecule on the plane bisecting and containing the nuclei
of the two atoms.
Other Examples
The following simulations were written in Quick Basics 4.5, and they
cannot be executed within your browser. If you are interested, you can
download one or more programs into your computer and then execute them.
All programs require the file BRUN45.EXE to run. Please download this
file and place it into a temporary directory in your computer.
kf
A ¨ B
kb
Chemical Simulations on the Internet
No doubt, more chemical simulations will appear for this
CONFCHEM session.
In the mean time, we have noted some other chemical simulations
on the Internet as well. Some examples are given below:
Discussion
A BASIC program showing similar plots as the Chemical Reaction Simulation
was shown to many science faculty members in the 1980s when the personal
computers appeared on the market. The biologists and earth scientists were
enthusiastic, because they thought this type of simulation could be employed
to show phase transitions, growth and decay of populations in colonies,
and transformation of mineral types. Using simultaneous differential
equations to state the rules is an excellent approach to simulation.
Since then, we have employed simulations for students to use on their
own and shown them during lectures.
References
CONFCHEM Discussion