Topic: bjerrum diagram

hallo world

i am trying to plot a diagram type named bjerrum diagram, (a pH/mol graph)
example: http://net.biolyt.dk/docs/M2/kemi/Bjerr … Alanin.png
but i need it on a non logarimisk plot,

the graph funktion is:
f(x)=a+log((1-x)/x)

is it possible

2 (edited by pin 2011-03-31 17:21:44)

Re: bjerrum diagram

The example graph looks as a plot of your function but reversed: x=a+log((1-y)/y). Hence: f(x)=1/(1+10^(x-a));
But I have no idea what the Bjerrum diagram is. sad

3 (edited by superzip 2011-03-31 17:31:36)

Re: bjerrum diagram

of course stupid me. thank you very very very much

a bjerrum diagram (it might be called something other on your languish) is often used in chemistry, to determent the strength of a acid.
i will use it to determent the rate of chance in my groups experiments on the university

4 (edited by superzip 2011-03-31 18:23:03)

Re: bjerrum diagram

ok i tryed to make a general funktion (custom funktion)
1+(-$b/(1+$d^(x-$c)))
but then graf come with a error and will not draw a graf

then i tryed 3 other funktions
1+(-$b/(1+10^(x-$c))) (the blue line)
1+(-$b/(1+8^(x-$c)))   (red line)
1+(-$b/(1+1.5^(x-$c))) (purple line)

and i get what you see on the picture, the funktion with 1.5^ is far better then the other 2, but dosent fit perfectly.

now i ask is there a way to make graph draw a line to make it fit the graph (change the potens)

Post's attachments

bj test.png, 7.43 kb, 780 x 481
bj test.png 7.43 kb, 158 downloads since 2011-03-31 

Re: bjerrum diagram

I suppose you inserted your general function as a User defined model into "Insert trendline" dialog. By default, initial values for your constants are $b=1, $c=1, $d=1, very much different from resulting figures. The program runs 100 iterations to find reasonable results, and will stop with an error if initial values are too far from those expected. Try again the general model and use constants from the 3rd line as initial values. You'll get it!

Post's attachments

Attachment icon bjerrum.grf 961 b, 164 downloads since 2011-04-01 

Re: bjerrum diagram

"I suppose you inserted your general function as a User defined model into "Insert trendline" dialog. By default, initial values for your constants are $b=1, $c=1, $d=1, very much different from resulting figures."
you are correct, i did do that.

from our raw data I can easily find the $b value

but here is the problem
i need to find the $c value from the best possible graph aka. R^2=1 (or very close)
and i find the best graph by finding the best $d value. with is a little different from every experiment we made
and even with only 2 variables it still come with an error

i can inset random numbers until i get close but it will take to long.
you say "The program runs 100 iterations to find reasonable results", can i force the program to make more?

Re: bjerrum diagram

You cannot expect exact results from statistical methods. Any individual constant in your expression cannot have better value then the others. For your set of experimental results there should exist just one optimal combination of all the constants which gives the least sum of deviations from the function expression.

You have to ask Ivan, father of this nice application, if number of iterations could be increased. Help says 100.

Re: bjerrum diagram

If 100 iterations are not enough, 10000 iterations will probably not help. Instead you have to change the default guess. After entering your model, here 1+(-$b/(1+$d^(x-$c))), you need to use the Add model button. Now you can give the model a name, e.g. Bjerrum and change the default guess. Graph will suggest 1 as the default guess, but that will not work here. Instead you can try with $b=1, $d=1.5, $c=50.

Re: bjerrum diagram

thank you, it is working now.
i don't hope i get problems with the other data i have.

Re: bjerrum diagram

nice copy paste you got there habib
and the problem have been sorted