Animated Solution for Chemistry - s and p-Block Elements: The reaction of Xe and ${\text{O}}_2{\text{F}}_2$ gives a Xe compound P. The number of moles of HF produced by the complete hydrolysis of 1 mol of P is _______.

When we look at the reaction between Xenon ($Xe$) and dioxygen difluoride ($O_2{F}_2$), we are dealing with an incredibly potent fluorinating agent. The beauty—and the trick—of this specific JEE Advanced problem lies in what is not said. The question does not specify the stoichiometric ratio of the reactants.

Because the ratio is missing, the Xenon compound P could theoretically be any of the three stable Xenon fluorides: $Xe{F}_2$, $Xe{F}_4$, or $Xe{F}_6$. To find the number of moles of $HF$ produced, we must explore the complete hydrolysis of all three possibilities.

Hydrolysis of $Xe{F}_2$

Let's imagine that the reaction produced Xenon difluoride ($Xe{F}_2$). When $Xe{F}_2$ reacts with water, it undergoes a straightforward redox reaction where Xenon is reduced back to its elemental gaseous state, and water is oxidized to oxygen gas.

The balanced chemical equation is:

From this equation, it is crystal clear that $2$ moles of $Xe{F}_2$ yield $4$ moles of $HF$. Therefore, exactly $1$ mole of $Xe{F}_2$ produces $2$ moles of $HF$.

Hydrolysis of $Xe{F}_4$

Now, what if the compound P is Xenon tetrafluoride ($Xe{F}_4$)? The hydrolysis of $Xe{F}_4$ is notoriously complex because it involves a disproportionation reaction. Xenon in the $+4$ oxidation state disproportionates into Xenon gas ($0$ oxidation state) and Xenon trioxide ($+6$ oxidation state).

The balanced chemical equation is:

Looking at the stoichiometry, $3$ moles of $Xe{F}_4$ generate a massive $12$ moles of $HF$. Simplifying this ratio, we find that $1$ mole of $Xe{F}_4$ produces $4$ moles of $HF$.

Hydrolysis of $Xe{F}_6$

Finally, let's consider Xenon hexafluoride ($Xe{F}_6$). Unlike $Xe{F}_4$, the complete hydrolysis of $Xe{F}_6$ is not a redox reaction. It is a simple substitution where all six fluorine atoms are replaced by three oxygen atoms from water, forming the highly explosive Xenon trioxide ($Xe{O}_3$).

The balanced chemical equation is:

Here, the math is direct: $1$ mole of $Xe{F}_6$ yields exactly $6$ moles of $HF$.

Because the initial compound P was ambiguous, the number of moles of $HF$ produced from $1$ mole of P could legitimately be $2$, $4$, or $6$. In the official JEE Advanced evaluation, all three of these integer values were accepted as correct answers! This problem is a fantastic reminder to always trust your balanced equations and consider all chemical possibilities when constraints are lifted.