[Big-Daddy]

Fair enough. What's the method using simultaneous equations? I like to apply algebra to these things.

I haven't tried but my idea was something like:

a *(C + 0.5 O2 -CO ) +b *( CO + 0.5 O2 -CO2) + .= 4 CO + 8H2 -3 CH4 -CO2 -2 H2O

now on left side collect terms containing CO, O2, H2 etc.

Eventually the expression for CO equates to 4, for H2 8 and so on.

For O2 etc. equate to zero since they are absent in the target. You should get 7 equations in 7 unknowns (if my calculations are right!)

That ought to give you all potential solutions.

Again, I haven't tried it but since you seem so interested try it out and let me know. I hope your enthusiasm can motivate you to do the number crunching?

The presence of multiple solutions tells us there is more than one way of fitting all of the equations we could write. The method will work to generate the equations quite nicely though (e.g. -a*Rxn(1)+b*Rxn(2)=4 according to the method and indeed any solution we come up with has to fit this).

Sorry, it was infinitely easier to do it by guesswork :p, and I can't see how a single solution will be produced anyway so I won't try and solve it myself.

When you use your 2000-equation handbook you need not actually work out the reaction manipulation surely - just use enthalpies of formation (products minus reactants) or combustion (reactants minus products) for each reactant/product?

[curiouscat]

The presence of multiple solutions tells us there is more than one way of fitting all of the equations we could write.

In this question yes. Because Raderford showed us two solutions. In the general case how do you know?

There could be a unique solution. There could be multiple solutions. There could even be no solutions.

Sorry, I don't see how you can be so sure about the "presence of multiple solutions".

Sorry, it was infinitely easier to do it by guesswork :p, and I can't see how a single solution will be produced anyway so I won't try and solve it myself.

You asked Mister I-like-to-apply-algebra-to-these-things..  I will concede though that Chemistry is much more comfortable as a spectator sport; sadly I'm guilty of that often myself. 

I've been burnt often enough though to realize that unless I work through it or see it worked in detail even the most reasonable and obvious sounding analysis and strategies are often wrong in hindsight. Devil's in the details. Ergo, I'm still not sure if or not my suggested strategy will work here. Perhaps. Perhaps not.

This is a common pattern though: The easiest strategy to solve small cases by hand is never the same as the best way to solve a large system and using a computer. Often reducing your problem to linear algebra helps becauase the toolkit there is so rich and efficient.

When you use your 2000-equation handbook you need not actually work out the reaction manipulation surely - just use enthalpies of formation (products minus reactants) or combustion (reactants minus products) for each reactant/product?

Nope. Real life isn't that clean unfortunately.

[Big-Daddy]

In this question yes. Because Raderford showed us two solutions. In the general case how do you know?

There could be a unique solution. There could be multiple solutions. There could even be no solutions.

Sorry, I don't see how you can be so sure about the "presence of multiple solutions".

I was talking about this particular case - and explaining why I won't solve it by hand! Raderford came up with 2 solutions and I came up with a different one, and I'm sure there are more than 3 ... so either your simultaneous equations must somehow boil out to a cubic or higher degree polynomial (they won't as they're all linear) or they will only form a list of conditions that must be fulfilled, not guarantee a solution.

You asked Mister I-like-to-apply-algebra-to-these-things..  I will concede though that Chemistry is much more comfortable as a spectator sport; sadly I'm guilty of that often myself. 

I've been burnt often enough though to realize that unless I work through it or see it worked in detail even the most reasonable and obvious sounding analysis and strategies are often wrong in hindsight. Devil's in the details. Ergo, I'm still not sure if or not my suggested strategy will work here. Perhaps. Perhaps not.

This is a common pattern though: The easiest strategy to solve small cases by hand is never the same as the best way to solve a large system and using a computer. Often reducing your problem to linear algebra helps becauase the toolkit there is so rich and efficient.

No I love solving the problems. But I have yet to come across one (except one particular example which had 10 equations ...) which I can't do by guessing. I do like algebra, but this method takes too long for most examples. I will keep it in mind in case I come across any "insane" questions with reaction manipulation I can't solve by guesswork. A bit like simultaneous equations - if it looks easy, just guess!

Nope. Real life isn't that clean unfortunately.

Huh ... so you must be working with chemicals that don't have well-known enthalpies of formation/combustion?

[curiouscat]

Huh ... so you must be working with chemicals that don't have well-known enthalpies of formation/combustion?

Sure. Fairly often.

Other times the known values are for the wrong allotrope. Or known at a temperature different from that of interest.

You'd say, fine, use specific heats. Those may not be known. Lot's of problems. Industrial problems are messy and forget the technical complications. Most often lack of data is the biggest hurdle.