[curiouscat]

Normally a chemical equation  can be balanced several ways; we just typically use the one having the lowest integer coefficients.

e.g.

 2H2 + O2  2 H2O

vs.

4H2 + 2O2  4 H2O


I was wondering, is there a situation where there's two equally valid sets of "lowest integer coefficients"?

Something like:

a A + b B  Products

and

c A + d B  Products

where a <c yet d < b

That'd make it impossible to chose between either as the canonical form.

Does such a situation ever arise? Not sure if the linear algebra offers a constraint.

[Borek]

2TiO₂ + 3C + 4Cl₂ 2TiCl₄ + 2CO + CO₂

3TiO₂ + 5C + 6Cl₂ 3TiCl₄ + 4CO + CO₂

3TiO₂ + 4C + 6Cl₂ 3TiCl₄ + 2CO + 2CO₂

And so on.

Doesn't men these are correct, there is a catch 

[curiouscat]

2TiO₂ + 3C + 4Cl₂ 2TiCl₄ + 2CO + CO₂

3TiO₂ + 5C + 6Cl₂ 3TiCl₄ + 4CO + CO₂

3TiO₂ + 4C + 6Cl₂ 3TiCl₄ + 2CO + 2CO₂

And so on.

Doesn't men these are correct, there is a catch 

Very interesting! In the sense that they aren't integral multiples of each other.

OTOH strict ordering is still preserved, right? In order of minimum co-efficents: 1 < 3 < 2  Correct?

I  think the catch is normally rank(coefficents) - variables = 1 but here it is 2.

So that gave you one additional degree of freedom. So, you get two independent parameters. What that means chemically, I'm still thinking..

[Borek]

http://www.chembuddy.com/?left=balancing-stoichiometry&right=balancing-failure

Compare it to the NO/NO₂ problem (posted tonight);

[curiouscat]

http://www.chembuddy.com/?left=balancing-stoichiometry&right=balancing-failure

Compare it to the NO/NO₂ problem (posted tonight);

This is what I  got for the NO / NO2 problem. After reading your post I'm a bit unsure if it is the right answer or not.

9 Cu + 28 HNO3        9 Cu(NO3)2 + 4 NO + 6 NO2 + 14 H2O

I think one needs to be cautious only when the algebraic method throws up an additional degree of freedom. Here it doesn't. Hence I'd hope there are no embedded independent reactions.

[Borek]

NO/NO₂ ratio given in the other thread takes care of the additional degree of freedom adding another equation, but I don't like this approach (nor the question). These are two separate reactions and they should be treated separately, ratio information can be used in the stoichiometric calculations at another stage.

While both approaches can be equivalent when it comes to the final result, there are at least pedagogical reasons to not use the "balanced" equation. Students think that's the correct approach, and they immediately forget they were given an additional constraint, then later they try the same approach to other problems (without constraints) and they are surprised it doesn't work.

[curiouscat]

While both approaches can be equivalent when it comes to the final result, there are at least pedagogical reasons to not use the "balanced" equation. Students think that's the correct approach, and they immediately forget they were given an additional constraint, then later they try the same approach to other problems (without constraints) and they are surprised it doesn't work.

When you say "both approaches" what's the other?  Treating them as two equations? I agree.

OTOH, the pedagogical hole I see is that when presented with a "balanced eq." students are never taught to question if or not it can be split into independent parts. That could bite at times?

PS.

Does Chembuddy / EBAS have the ability to split an equation like "KClO3 + HCl -> KCl + H2O + Cl2 + ClO2" automatically into its component equations? I was wondering.

That would be interesting to implement. Would it be some sort of eigenvector analysis?