On what factors does the true reaction Stoichiometry depend when there are multiple valid options?

Consider the following unbalanced reaction:

$$\ce{XeF4 + H2O -> Xe + XeO2 + HF + O2}$$

There are six variables to be solved, but only four equations linking them. I solved the set of equations using Gauss elimination and arbitrarily set the stoichiometric coefficient of $\ce{XeF4}$ as $3$:

$$\ce{3XeF4 + 6H2O -> (4k)Xe + (3-4k)XeO2 + 12HF + (4k)O2}$$

where $k$ is the free variable, the parameter, with $0<k<\frac 34$ (since coefficients must be positive).

Clearly, for different values of $k$, it gives radically different yet balanced equations. The very yields are different for fixed amount of $\ce{XeF4}$ and $\ce{H2O}$. This issue has been noted in a previous question.

My textbook, however, gives the balanced equation:

$$\ce{6XeF4 + 12H2O -> 4Xe + 2XeO2 + 24HF + 4O2}$$

clearly setting $k=\frac 12$. The linked question above does not offer any explanation for why a particular value of $k$ should be favoured. So, my exact question is: Why set $k=\frac 12$? Why was $\frac 12$ preferred over any other value for $k$:

• Is it determined by experimentally measuring the stoichiometry?
• Is there a theoretical explanation for it?
• Apr 23 '17 at 18:29
• chemical equations are not unlike math equations, multiplying each side by same number will give a valid equation. Similarly, addition of two (or more) equations side-wise with subsequent simplification gives a valid equation. However, if the equation depicts an actual chemical process is another matter, a well-balanced equation may be irrelevant for this reason. Apr 23 '17 at 23:41
• @Mithoron In the answer to that question, they just say that the balanced equations are different. I want to know which is correct and why? Which factors determine that? And it is not a duplicate because he mentions just 2 possibilities and I found all the solutions. Apr 24 '17 at 3:12
• I would change the title of your question to better reflect the change you made. Something along the lines of "How to determine true reaction stoichiometry among multiple valid options". Apr 24 '17 at 3:41
• There is a meta discussion on the closure of this question: Possible overreach on marked duplicate Apr 24 '17 at 16:00