[LON-CAPA-users] Titration problem--extracting limited data from an array

[Robley Light]

I'm hoping someone can suggest a better way to handle this, either by coding
or by a mathmatical manipulation.
Is this something that maxima could do?

I found the code for plotting titration curves at Tom O'Havers' web site:
monoprotic acid: http://www.wam.umd.edu/~toh/models/TitrationDemo.html
triprotic acid: http://www.wam.umd.edu/~toh/models/Titration.html

So this is easy to code for gnuplot.  For example, in the problem
res/fsu/GeneralChemLib/Lab/Titration/StandardizeBase.problem

I generate the arrays to be plotted as follows:

<script type="loncapa/perl">
$VolA=&random(10,80,10);
$ConcA=&random(0.01,0.08,0.0001);
$mmolA=$VolA*$ConcA;
$mmolB=$mmolA;
$VolBeq=&random(22.4,27.6,0.1);
$ConcB=$mmolB/$VolBeq;
$pKa=-1;
$pKw=14;
$Ka=10**-$pKa;
$Kw=10**-$pKw;

for ($pH=0; $pH<=12.99; $pH+=0.33){
    push @pH, $pH;
  $Hconc = 10**-$pH;
    push @Hconc, $Hconc;
  $VolB =
-$VolA*(($Hconc**3+$Ka*$Hconc**2-($Kw+$Ka*$ConcA)*$Hconc-$Kw*$Ka)/($Hconc**3
+($Ka+$ConcB)*$Hconc**2+($Ka*$ConcB-$Kw)*$Hconc-$Ka*$Kw));
    push @VolB, $VolB;
}</script>

As O'Haver points out, this is an "inverse" solution, where [H+] is the
independent variable and the volume of base is the dependent variable, even
though one is plotting the other way.

This array gives a set of values in @pH and @VolB that vary in regular
increments of $pH (of 0.33 units), which is okay for plotting purposes. (I
could make the increments as small as I like).

What I would like to do for a different prelab problem is to generate array
data that is in regular increments of $VolB (say 0.05 mL), or roughly if not
exactly regular increments,--which is more like data one is likely to
generate in a lab titration. I want to present these array values in a table
rather than in a plot.

Short of solving the equation specifically for [H+] as a function of VolB
(probably possible in this case, very complicated in the di- and tri-protic
acid cases), is there a way to extract such data from the arrays generated
by the above code?  My Perl knowledge is relatively limited.

Robley


*************************************************************
Robley J. Light                  Professor Emeritus of Chemistry and
Biochemistry
Department of Chemistry          Phone:   (850) 644-3844
   and Biochemistry              Email:  rlight@chem.fsu.edu  
Florida State University         Fax:      (850) 644-8281
Tallahassee, FL 32306-4390    Home Page:
http://www.chem.fsu.edu/editors/rlight   
                    



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