Re: [math-fun] Balancing chemical equations by hand
There must be more to it than just determinants & linear algebra, because you aren't guaranteed to get integers. Or do you simply multiply by the (integer-valued) determinant to clear the fractions? Is there any chance that you might end up doing "integer linear programming", which is considerably harder than linear programming (because it subsumes hard problems like the knapsack problem) ? At 08:04 PM 4/24/2011, mcintosh@unam.mx wrote:
Can anyone come up with a nice way to balance chemical equations manually?
All the web seems to offer is either vague "fiddle around until it works" or the nuclear option "translate into a simultaneous linear system and solve".
As an undergraduate, I discovered how to balance chemical reactions using determinants. Teacher response: This is MY course and we will do it MY way! Actually I had added conservation of charge to conservation of mass because redox equations were otherwise ambiguous.
I wonder of thete is really any alternatice to conservation equations and linear algebra, even if most textbook equations can be solved by inspection. Of course the algebra part is rely mentioned in a chemistry course.
-hvm
Henry, see my comment 'above' about finding the least common multiple to clear the fractions. On Sun, Apr 24, 2011 at 11:21 PM, Henry Baker <hbaker1@pipeline.com> wrote:
There must be more to it than just determinants & linear algebra, because you aren't guaranteed to get integers. Or do you simply multiply by the (integer-valued) determinant to clear the fractions?
Is there any chance that you might end up doing "integer linear programming", which is considerably harder than linear programming (because it subsumes hard problems like the knapsack problem) ?
At 08:04 PM 4/24/2011, mcintosh@unam.mx wrote:
Can anyone come up with a nice way to balance chemical equations manually?
All the web seems to offer is either vague "fiddle around until it works" or the nuclear option "translate into a simultaneous linear system and solve".
As an undergraduate, I discovered how to balance chemical reactions using determinants. Teacher response: This is MY course and we will do it MY way! Actually I had added conservation of charge to conservation of mass because redox equations were otherwise ambiguous.
I wonder of thete is really any alternatice to conservation equations and linear algebra, even if most textbook equations can be solved by inspection. Of course the algebra part is rely mentioned in a chemistry course.
-hvm
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There must be more to it than just determinants & linear algebra, because you aren't guaranteed to get integers. Or do you simply multiply by the (integer-valued) determinant to clear the fractions?
Is there any chance that you might end up doing "integer linear programming", which is considerably harder than linear programming (because it subsumes hard problems like the knapsack problem) ?
Well, I didn't pursue it that far. But since the solution would be rational, presumably a multiple would suffice. In truth, there is a problem of reaction kinetics involved, an there is an implicit assumption of stable compounds; otherwise the reaction could just as well be reversible. (hence your second question) But this is all simple introductory chemistry. And I was mostly delighted that I had found a rational scheme for understanding those reaction equations. -hvm
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