Background

I written a chemical equation balancing program.

elem=Alternatives@@Reverse@SortBy[StringLength]@Array[ElementData[#,"Symbol"]&,112]; chem=StringCases[#,e:elem~~n:DigitCharacter...:>{e,n}]/.""->"1"&; group=List@@@Normal[GroupBy[#,First->Last,Total@ToExpression[#]&]]&; name2mat=group/@chem[ToString/@#]&;  ChemicalSolver[input_List]:=Block[{all,elemts,null},   all=name2mat[input];   elemts=Union[First@Transpose[Flatten[all,1]]];   null=NullSpace@Transpose[(elemts/.Rule@@@#&/@all)/._String->0];   Thread[input->Transpose@null] ]; 

Give a chemical equation:

$ $ C_2H_5OH+O_2==H_2O+CO_2$ $

The first part name2mat change the chemicals to lists, then ChemicalSolver calculate the nullspace and find the solution.

So one of the solutions is :

$ $ C_2H_5OH+3O_2==3H_2O+2CO_2$ $

Problems

But there are some flaws, firstly it can’t recognize the brackets, like Al2(CO3)3.

Secondly can’t recognize the non-existent element, (These symbols not in ElementData), a symbol like Abcd also can be a kind of element. Some times they’ll use abbreviations in organic chemistry.

※ Thirdly can’t recognize the ion reactions like "(CO3)2-", this maybe hard, it’s {{"C", 1}, {"O", 3}, {"e", -2}}, this is not necessary. ChemicalSolver still works on this case I think.

※ Small problem, ChemicalSolver can’t recognize reactant. Output of NullSpace‘s positive and negative looks random.

Goal

A function expr2mat overcome these shortcomings.

Input:

input="C2H5OH+O2=H2O+CO2" expr2mat[input] 

Output:

{{{"C",2},{"H",6},{"O",1}},{{"H",2},{"O",1}},{{"O",2}},{{"C",1},{"O",2}}}