# Solve a metallurgical mass balance (system of 7 equations with 7 unknowns)?

Posted 5 years ago
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 I'm currently trying to solve a mass balance useful in metallurgical processing.There are 4 ingoing streams (streams "c", "f","h" and "o") and 3 outgoing streams ("m", "e" and "s") and 5 chemical elements: Cu, Fe, S, O, and Si. The components are written as moles/100g of the respective stream. The compositions of streams "m", "s", "o", "f" and "h" are known, but the Fe, Si and O content of stream "e" is unknown. The O content of it can be obtained by charge balance, given that the oxidation states are: Cu =+1, Fe= x (+2 Answer
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Posted 5 years ago
 You're looking for an analytic solution to something with ~30 variables? Answer
Posted 5 years ago
 What I want is to obtain a solution for just 7 unknowns, all the other "variables" are fixed, either assumed or taken from the periodic table. For the purposes of calculation in Mathematica, the ~30 "variables" should be treated as input constants:The vector A = {ACu, AFe, AS, AO, ASi } contain the fixed atomic weights from the periodic table, and all the concentrations are input data, except the following 3 ones: Oe, Sie and Fee.What I want is a a general solution so I can copy it to an EXCEL worksheet (after symplifying the resulting expressions, of course). There I could put as input the values of the element concentrations and the other parameters.Regards,Alberto Answer
Posted 5 years ago
 If you don't fill in those other 20-something 'variables' it will need to invert a large symbolic matrix, which is very very complicated (perhaps impossible?). You need those atomic weights and so on filled in. Answer