John wrote in #11:

> So, what's the general rule?

Based on this I think you are looking for:

$$ (a',b',c') \le (a,b,c) \text{ iff } c'-c = \frac{a-a'}{2} = b-b' \text{ and } c'-c \ge 0$$

I.e the amount of water we produce has to be exactly half the amount of hydrogen we consume as well as exactly the amount of oxygen we consume.

Edit: For the reversible case we can simply allow for 'negative production' by leaving off the \\( c'-c \ge 0 \\) condition.

> So, what's the general rule?

Based on this I think you are looking for:

$$ (a',b',c') \le (a,b,c) \text{ iff } c'-c = \frac{a-a'}{2} = b-b' \text{ and } c'-c \ge 0$$

I.e the amount of water we produce has to be exactly half the amount of hydrogen we consume as well as exactly the amount of oxygen we consume.

Edit: For the reversible case we can simply allow for 'negative production' by leaving off the \\( c'-c \ge 0 \\) condition.