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 (69kb) downloaded 54 time(s).
ChemBal.pdf (148kb) downloaded 64 time(s).

Best regards.
Alvaro.

Edited by user 04 December 2020 04:05:47(UTC)  | Reason: Not specified

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.

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 (351kb) downloaded 54 time(s).
ChemBal v2.sm (144kb) downloaded 71 time(s).

Best regards.
Alvaro.

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 (102kb) downloaded 29 time(s).
ChemBal v2 Jeean.pdf (155kb) downloaded 19 time(s).
ChemBal v2 Jeean with decimals.sm (102kb) downloaded 35 time(s).
ChemBal v2 Jeean with decimals.pdf (160kb) downloaded 21 time(s).

Best regards.
Alvaro.