PERSONAL COMPUTERS IN TEACHING PHYSICAL CHEMISTRY

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I. TEACHING PHYSICAL CHEMISTRY

Special group of students with profound studying of  mathematics and physical chemistry exists at  Moscow  State  university  for many years. Fundamental course of physical chemistry  for  these students  contains  classical  and  statistical  thermodynamics, kinetics and catalysis.

We use PC at teaching physical chemistry  to  students  of  this group with main proposes:

A. During practical work:

1.  To  treat  experimental  data  obtained  during   laboratory sessions  with  the  help  of  various   programs:   statistical calculations (mainly  linear  least  squares)  by  our  original program REPRO;  spreadsheets  provided  calculations  and  chart drawing, etc;

2. To carry out  problems  modelling  the  behavior  of  complex systems, for  example:  investigation  of  oscillating  chemical reactions using our original program Lotka-Volterra. This  model is defined with the following kinetic scheme:

              k1
       A + X ---> 2X
              k2
       X + Y ---> 2Y
              k3
       Y + B ---> E

With the help of computer program student may  investigate  this chemical process in time. One  can  change  parameters  of  this system (k1, k2, k3 and the initial concentration of A,  B,  X, Y substances) and see the conforming graph with the kinetic curves for X and Y substances. Teacher may also set the values for rate constants and put a test graph to student, who in this case must estimate  these  values   from   graph   using   the   following
relationships:

time of oscillations period is equal to:

      t = 2*pi/SQRT(k1*k3*[A]*[B])  and

      k2*(X1-X2)-k3*[B]*ln(X1/X2) = k1*[A]*ln(Y1/Y2)-k2*(Y1-Y2),

where Xi, Yi are the current values of intermediates  X,  Y  and letters  in  brackets  denote  concentration  for  corresponding substances (which are constant for this model). Fig. 1 is the snapshot of the PC screen with such test graph.

3. To calculate chemical equilibrium for studied  reaction  from thermodynamic data of its components using our original  program CHET.

B. During class work:

1. Solving complicated equations, for example: determination of rate constant values for  two  step  consequent reaction

        k1    k2
      A --> B --> C.

In this case  the  location  of  maximum  for  intermediate  (B) concentration is determined by two equations:

      t([B]max) = ln(m)/(k2-k1)  and

      [B]max = [A]o*m^(m/(1-m)),

where m=k2/k1. Usually this equations are solved graphically  or by repeated trials. The numerical calculation is very simple  if we use solving program like Borland's EUREKA (fig. 2).

2. Using PC teacher can ascertain some  correlations  which  are not so evident  for  students  if  they  see  only  mathematical formulas. For example. When  we  analyze  kinetics  of  chemical reaction

         k
      nA --> Products

at    heating    with    constant    rise     of     temperature (dT/dt=Theta=const), the rate of reaction is:

             n     dC                             n
      w = k*C  = - -- * Theta = ko*exp(-E/(R*T))*C ,     (*)
                   dT

where C is concentration of substance A and n  is  the  reaction order. Location of function dC/dT vs T maximum is determined  by the equation:

   ko          E            n-1
- ----- * ----------- = n* C   *exp(-E/(R*Tmax)).
  Theta   R*Tmax*Tmax

The analytical integration  of  differential  equation  for  the reaction rate (*) is impossible. So in this case we solved  this problems by means of numerical integration and  drew  dependence of C and dC/dT vs T (figs. 3 and 4). And  what  is  interesting. Difference between concentration of substance A in reactions  of various order is negligible below  the  temperature  of  maximum value of  dC/dT  (fig.  3).  Therefore  you  want  to  determine reliably order of this reaction, values  of  ko  and  E,  it  is necessary to use experimental data above  this  temperature.  It also turns out that locations of maximum of dC/dT as function  T for different n (1-3) at constant ko and Theta lies in 5 degrees interval (fig. 4).

3. Analysis of functions' behavior.
a. For example, very often students are thinking that there  are only two types of heat capacity: Cp and  Cv.  But  these  values correspond only to processes at constant pressure (p) or  volume (v). Heat capacity in general case are defined by equation:

      C = (n*Cv-Cp)/(n-1),

where n is exponent in polytrope equation: p*v^n=const. Analysis of this equation  shows  that  C=0  for  adiabatic  process  and indefinite for  isothermal process (fig. 5).

b. Next example is analysis of dividing of chemical reactor with ideal mixing into sections. The efficiency of such  reactor  may be enhanced by dividing into sections. The question is how  many sections is significant to rise degree of conversion (y) and  to decrease the total volume of reactor as much  as  possible.  The ratio of  total  volume  of  m  sections  (m*Vi)  to  volume  of unsectioned reactor (V1) is equal to:

  m*Vi/V1  =  m[1-(1-y)^(1/m)](1-y)^((m-1)/m)/y,

where m is the quantity of sections. We solved this problem with the help of spreadsheet (MicroSoft Excel) and drew  the  diagram (fig. 6) from which it is  seen,  that  at  small  values  of  y dividing the reactor has little influence to its efficiency. But at high y it is significant and 3-4 sections is enough.

c. To find the answer to various problems of physical  chemistry we must solve systems of differential equations. Obvious example is  the  analysis  of  chemical  kinetics  of  complex  chemical reaction. For this purpose  we  use  KINET  program  written  by associate professor of our faculty A.V.Abramenkov.  Along  using this program student write chemical  equation  for  each  simple reaction and value of rate  constant  of  this  reaction.  After solving the system of differential equations it is  possible  to receive graph for time dependence of the concentrations  for  up to 15 substances involved in maximum 10 reactions and  table  of current concentrations. This program also allows us to determine the values of rate constants using experimental data of  current concentrations.

d. One more example is to draw phase diagram  of  binary  system after Schreder equation for ideal systems:

ln(Ni ) = -(DeltaHi/R)*(Tm-T)/(Tm*T),
     T
where Ni  - molar part of i-th component of  binary  system,  Tm
        T
and  DeltaHi  -  its  melting  point   and   heat   of   melting respectively, T - melting point for system with definite Ni. Students  do  laboratory  work  with   diphenylamine-naphthalene system and later in computer room may  calculate  dependence  of melting point as function of composition for it  (see  fig.  7). They may see that for this system  cited  equation  satisfactory describes system behavior.

4. Viewing graphs.
a. Every student draws phase diagram of water very  easily.  But is is difficult to draw this chart in S,  T  coordinates.  After seeing  it  on  display  students  understand  that  two   phase equilibria  may  be  depicted  not  only  as  a  line  in  p,  T coordinates but as fields in S, T diagram (fig. 8).

b. Computer also allows us to draw full  scale  detailed  chart. For instance the phase diagram of water in most of textbooks  is drawn schematically. It is  very  useful  to  see  real  picture (fig.9,10).

c. For many students it is difficult to  imagine  the  shape  of potential energy surface when studying  theory  of  transitional state in chemical kinetics. Using the program like SURFER it  is possible to draw such picture and  our  experience  showed  that after analysis of this picture all  students  can  draw  general view  of  this  surface  and  any   of   its   section   without embarrassment (fig. 11).

5. Obtaining reference information.
During classes and laboratory  work  we  often  need  to  obtain equilibrium constants of chemical reactions  or  composition  of mixture in the equilibrium state. In this case we  use  our  own program  CHET.  This  program  uses  built  in  data   bank   of thermodynamic  properties  of   individual   substances,   which contains 2000 records. It can represent temperature dependencies of  thermodynamic   functions   in   tabular   form,   calculate equilibrium constant of a given chemical reaction or equilibrium composition of complex mixture of  chemical  compounds  for  the
specified pressure and temperature.


II. SOFTWARE PROBLEMS.

A. Two reasons for using computers.
There exist at least two reasons why computers are readily  used by students and teachers.  The  first  is  that  computer  is  a universal teaching tool. It provides fast access to  information (data  bases,  hypertext);  enables  modelling  of  experiments; adapts education speed to individual  student.  This  stimulates the development of specific  educational  software.  Most  often this results in a large  number  of  relatively  small  programs which don't resemble each other in there interface.

The second reason is less discussed, but is  always  taken  into account. All students are aware  that  computers  will  be  very helpful in there post graduate life. In other words computerized education teaches not only the subject of education (chemistry), but also how chemists use computers. That's why we use  much  of standard software  (text  processors,  electronic  spreadsheets, solvers and so on) in education.

B. Expenses.
Besides well known advantages education with computers has  some expenses. And our aim is to make them as small as possible.  Our experience  evidences  that  main  difficulty  in  using  PC  is mastering various programs by students. It takes much  time  and diverts them from problems in physical chemistry.

C. Using interface standards.
The  first  step  towards  the  minimum  in  computer  interface expenses is to use Graphics User Interface (GUI)  which  has  in fact become an industrial standard. If a student learns  how  to work with several basic packages under Windows then  he  or  she often feels comfortable when mastering another  Windows  program or even when using Mac or X-Windows software. 

In order to transfer education to the Windows media we should do the following:
* Provide appropriate hardware. You can hardly  run  Windows  if you have only 1MB of memory in your computer.
* Reform freshman computer course.
* Create Windows user interface for the educational software  we use.

D. Windows are not a panacea.
Though Windows has  powerful  facilities  which  allows  placing textual material, complex formula,  and  graphics  together,  it doesn't solve all interface problems. Imagine the situation when during the lesson a student must start  3-4  different  programs and load several data files in them. How much time will  he  (or she) spend in selecting appropriate names from relatively  large lists? It would be much better if all  these  files  had  direct
association with some definite sense context. 

Another  problem  with  Windows  comes  from  its   multitasking capabilities. It's great that  we  can  start  several  programs simultaneously, exchange their data, compare their results  just on one screen. But it takes time to place multiple windows in  a most convenient manner.

E. HyperBook.
Thus we had come to an idea of creating  a  special  educational hypertext system under GUI, which we will call here "Hyperbook". Let us see its functions on one example (figure 12). The warp of the hyperbook fabric is a set of pages with educational text. We use here a broad  meaning  of  "text"  which  includes  formula, schemes, graphics and other illustrations. You can include  some small program in this text as well. In  this  case  we  call  it moving  or  interactive  illustration.  Such  a  program  starts automatically when the page  is  opened  (thus  having  definite sense context) and its window is always in a definite  place  on the page (compare with the previous paragraph).

As you may have noted, there are portions of highlighted text on the page on figure 12. This is another feature  of  hypertext  - active contexts. When you activate them with, say, mouse  click, the hyperbook performs some job  appropriate  to  the  sense  of context. This can be showing the definition of  a  term,  moving to another page of hyperbook or launching some application. 

Our nearest intent is to create  with  the  help  of  this  tool computer aided physical chemistry course.

QUESTIONS FOR READERS.

We tried to  use  several  solvers  available  in  DOS:  Eureka, Mercury,   MathCAD,   but   all   of   them   have   significant disadvantages. Which solvers do you use if any and which is  the best?

When you want to use a lot of small computer programs during the lesson  do  you  think  it  is  worth  including  them  into  an integrated environment  like  hyperbook?  Or  is  it  better  to encourage their use through the commands of operating system? 

Are there any other ways to lessen expenses of  using  computers in teaching chemistry?


FIGURES.

All figures are 640x480 16-color .GIF files.

1. Test picture for Lotka-Volterra reaction. Students  ought  to estimate the values of k1, k2, k3.

2. The calculation of values of k1 and k2 for  reaction  A->B->C from values of t max and C max of B substance.

3. The dependence of degree of conversion (alpha) of A substance on temperature for reaction nA -> Products during constant  rise of temperature (theta). n - order of reaction.

4. The dependence of d(alpha)/dT vs T for reaction nA->Products.

5. The change of heat  capacity  value  upon  increasing  of  n, exponent in polytrope equation (p*V^n=const). Ideal gas.

6. The influence of  dividing  the  ideal  mixing  reactor  into sections on degree of conversion (y). m - quantity of  sections, Vi - volume of  single  section,  V1  -  volume  of  unsectioned reactor.

7. The phase diagram of naphthalene-diphenylamine  system  drawn after Schreder  equation  calculation.  T  -  melting  point  of system, N - molar ratio of naphthalene.

8. Phase diagram of water at S, T coordinates. I - solid,  II  - liquid, III - vapor IV - solid-liquid, V  -  solid-vapor,  VI  - liquid-vapor transitions

9. Phase diagram of water drawn accordingly experimental data.

10. The same as  at  fig.9.  but  for  the  narrow  interval  of temperature.

11.  View  of  potential  energy   (a.u.)   surface   for   F+H2 interaction.  J.S.Wright,J.Williams  Chem.Phys.Lett.  184,   159 (1991).

12. Figure 12 presents contents of the window with  one  of  the first pages of the  hyperbook  on  chemical  kinetics.  Text  in russian gives definitions  of  basic  concepts  of  kinetics.  A picture  with  two  buttons  and  a  graph  is  an   interactive illustration. When the user pushes 'Start' button it  begins  to change in time  acoording  to  kinetic  equations,  thus  giving students the sense of kinetic curves and the comparison of first and second order reactions. Just above the main window there  is a  popup  window  with  additional  information.  This   windows appeared when the user clicked blue active context.