Answer:
[tex]0.045\; \rm mol[/tex].
Explanation:
Start by finding the formula of ammonium perchlorate based on its name.
"Ammonium" refers to ammonium ions [tex]\rm {NH_{4}}^{+}[/tex], each with a charge of [tex](+1)[/tex].
"Perchlorate" refers to perchlorate ions [tex]\rm {ClO_4}^{-}[/tex], each with a charge of [tex](-1)[/tex].
The charge on the two types of ions need to balance one another in the overall compound. in this example, ammonium ions [tex](+1)[/tex] need to be combined with perchlorate ions [tex](-1)[/tex] at a one-to-one ratio.
Thus, the formula of ammonium perchlorate should be [tex]\rm NH_{4}ClO_{4}[/tex].
Based on information from the question, the equation for this decomposition reaction would be:
[tex]a\, {\rm NH_{4} ClO_{4}} \to b\, {\rm N_{2}} + c\, {\rm Cl_{2}} + d\, {\rm O_{2}} + e\, {\rm H_{2}O}[/tex], where [tex]\text{$a$, $b$, $c$, $d$, and $e$}[/tex] are coefficients.
In this reaction, ammonium perchlorate is the only reactant with hydrogen atoms, whereas water is the only product with hydrogen atoms.
By the conservation of atoms, the number of hydrogen atoms among the reactants should be equal to the number of hydrogen atoms among the products.
There are four hydrogen atoms in every formula unit of ammonium perchlorate. In contrast, every molecule of water contains only two hydrogen atoms.
The question asked for [tex]0.090\; \rm mol[/tex] of water molecules. That would correspond to [tex]2 \times 0.090\; \rm mol = 0.180\; \rm mol[/tex] of hydrogen atoms. Divide by the number of hydrogen atoms in each ammonium perchlorate formula unit to find the required quantity: [tex](0.180\; \rm mol) / 4 = 0.045\; \rm mol[/tex].
Thus, it would take [tex]0.045\; \rm mol[/tex] of ammonium perchlorate to produce [tex]0.090\; \rm mol[/tex] of water through this decomposition reaction.
