What is the implication of not being able to balance the complete combustion reaction equation of methanol?

This question has been intriguing me since 10th or 11th grade. The teacher just told us about it but didn't get into the details of the why. Recently I asked a biochemist but couldn't get an answer. So I bring it here.

$$\ce{CH3OH + O2 -> CO2 + H2O}$$

is the complete combustion equation of methanol. But the problem is it can't be balanced. What is the practical implication, and significance of this fact?

Side question:

What is the mathematical reasoning behind the inability to balance the equation?

• Wait, what do you mean it cannot be balanced? – LordStryker Jan 29 '14 at 21:58
• Maybe it was some other equation. Just can't recall it, I'll update the question. – Bleeding Fingers Jan 29 '14 at 22:02
• Please do. I'm very curious now. – LordStryker Jan 29 '14 at 22:03
• I'm pretty sure every single valid chemical equation balances, as long of course as you know all the products. You could conceivably use a reaction as an analog computer (a very cumbersome one!) to solve a linear system of equations. If nature does it, then math must do it. – Nicolau Saker Neto Jan 29 '14 at 22:41
• This question has awoken the fire of linear algebra in me! I believe it is possible to prove that any system of equations resulting from a valid reaction has $n$ variables and $n-1$ equations, i.e. the system is always underdetermined by one equation and therefore has infinite solutions, all of which lie in a line in $\mathbb{R}^n$ sand are multiples of eachother by some arbitrary real number. Let me try formalizing the argument. Unfortunately I'm kind of tired, so I can't guarantee I'll be able to wade through the notation properly. – Nicolau Saker Neto Jan 29 '14 at 23:09

Here is the balanced eqn...

$$\ce{2 CH3OH + 3 O2 → 2 CO2 + 4 H2O}$$

• While i was typing the the mathjaxed equation, you were faster submitting. So I beautify yours :-D – Klaus-Dieter Warzecha Jan 29 '14 at 22:02
• @KlausWarzecha Can you beautify me next?? – LordStryker Jan 29 '14 at 22:06
• @LordStryker I might be good, but not THAT good :-P – Klaus-Dieter Warzecha Jan 29 '14 at 22:10
• beatify or beautify? – ron Jan 29 '14 at 22:23
• @ron Blessed are the cheesemakers. – Klaus-Dieter Warzecha Jan 29 '14 at 22:53

Mass is conserved, charge is conserved, ignore spectator ions until the end. If it is a redox reaction, begin by listing each active atom's reduction or oxidation, e.g.,

Mn(+7) + 5e to Mn(+2)

Cr(+3) - 3e to Cr(+6)

and find the least common denominator (here, 15). That gives you the primary stoichiometry, here 5Cr(+3) (going to chromate) with 3Mn(+7) (coming from permanganate). Add the other atoms, slop in H2O, OH-, or H+, add back the spectator ions. Confirm the same number of each kind of atom on both sides. Try it out,

CuSCN + KIO3 + HCl to CuSO4 + KCl + HCN + ICl + H2O

[Cr(N2H4CO)6]4[Cr(CN)6]3 + KMnO4 + H2SO4 to K2Cr2O7 + MnSO4 +CO2 + KNO3 + K2SO4+ H2O