Hi. In the attached a procedure for balancing chemical equations, in a first try. It have not bugs, it have errors. But could be interesting.

ChemBal.sm (68,03 KiB) descargado 1465 vez(es).
ChemBal.pdf (147,88 KiB) descargado 910 vez(es).

Best regards.
Alvaro.

Wrote

Hi. In the attached a procedure for balancing chemical equations, in a first try. It have not bugs, it have errors. But could be interesting.

ChemBal.sm (68,03 KiB) descargado 1465 vez(es).
ChemBal.pdf (147,88 KiB) descargado 910 vez(es).

Best regards.
Alvaro.

Wooooo Esta súper genial, y muy interesante, ingresé un balance de "glucosa" para producir "etanol", al parecer funciona bien para algunas reacciones, aunque para este ejemplo, ¿cómo puedo ponerlo?

Wooooo This super cool and very interesting, I wrote a balance of "glucose" to produce "ethanol", apparently it works well for some reactions, although for this example of sucrose I can't find how to put it

Wrote

...I wrote a balance of "glucose" to produce "ethanol", apparently it works well for some reactions, although for this example of sucrose I can't find how to put it

Hi. Thanks. I guess you can't balance that. Wolfram alpha can't too:



If you add some water then you have this:



which agrees with SMath:



Best regards.
Alvaro.

Balancing chemical is difficult to near not feasible.
In Smath Community, super champion is Radovan [Martin as well].
We have few more and lots of those ... read first to get geared.

Solve Diophantine X_Y Plot.sm (21,97 KiB) descargado 1346 vez(es).
Solve Diophantine Chemical Balance.sm (47,55 KiB) descargado 1400 vez(es).
Solve Given_Find [CO2_6179 Butler].sm (163,06 KiB) descargado 1208 vez(es).
Solve Diophantine.sm (168,31 KiB) descargado 1390 vez(es).

Improved version. Now it can handle reactions with ions balancing charges and accept parenthesis into compounds. Also, the procedure for rationalize it's more robust.

ChemBal v2.pdf (350,12 KiB) descargado 1266 vez(es).
ChemBal v2.sm (143,06 KiB) descargado 1753 vez(es).

Best regards.
Alvaro.

... more chemical balance from PseudoInverse.

Matrix PseudoInverse.sm (123,11 KiB) descargado 1429 vez(es).

Wrote

... more chemical balance from PseudoInverse.
Matrix PseudoInverse.sm (123,11 KiB) descargado 1429 vez(es).

Hi Jean. The purpose of this post is to show the power of use the null space of the matrix of coefficients of a chemical reaction for get information about it, not just only balancing. For do that, because it is tedious to introduce by hand this matrix, I write a simple code for do that, with some limitations but it can handle one level of parenthesis and ions. Also isn't easy to transform a vector for the nulls space with norm one into an equivalent basis vector with integers, and there are not much literature about that, or I can't found it. I also present a robust way to get a valid answer in a lot of cases.

I don't know why you introduce fractional coefficients in your chemical reaction, but I will show them later. Here you first example balanced in a few steps, balancing your first example with integers, as usual.



Notice that all coefficients in the matrix are positive and the null space method place by itself reactants and products. For the cases with a big dimension for the null space basis that give a precious information about the reaction.

This is the math involved. The pseudinverse or the row reduced skeleton form and others methods have not the theoretical power of the null space. The routine for find the null space use the plugin dot numerics for get the singular value decomposition for the compounds matrix. So the real math involved could be very complicate, but for instance this is the procedure for solve the problem "by hand"



Here is your second example, again, with integers coefficients.



If you're not convinced yet about what I'm talking about, here are your two examples with decimals in the compositions, solved with integers coeffs for the balanced equation.




Files:

ChemBal v2 Jeean.sm (101,56 KiB) descargado 1452 vez(es).
ChemBal v2 Jeean.pdf (154,64 KiB) descargado 843 vez(es).
ChemBal v2 Jeean with decimals.sm (101,94 KiB) descargado 1419 vez(es).
ChemBal v2 Jeean with decimals.pdf (159,82 KiB) descargado 804 vez(es).

Best regards.
Alvaro.

Thanks Alvaro for your personally addressed documents.
I understand your superb approach. There was an international Standard
way to write chemical balance. I'm not update on that.
The fractional in the matrix come from the originator paper [Risteski].
It may have to do with some secret perfume recipes ?
The attached exploded version accommodates Table region.
Have a good day ... Jean

Matrix PseudoInverse Explode.sm (222,62 KiB) descargado 1352 vez(es).