Start with the only known quantity in this question
#m("KClO"_3) = 30 color(white)(l) g#
#n("KClO"_3) = 30 color(white)(l) g * (1 color(white)(l) "mol")/(138.55 color(white)(l) "g")=0.217 color(white)(l) "mol"#
The balanced equation of the decomposition of potassium perchlorate
#color(navy)(2) color(white)(l) "KClO"_3 (s) stackrel(Delta)(to) 2 color(white)(l) "KCl" (s) + color(purple)(3) color(white)(l) "O"_2 (g)#
suggests the stoichiometric relationship
- #color(navy)(2) color(white)(l) "mol" color(white)(l) "KClO"_3# decomposes to produce #color(purple)(3) color(white)(l) "mol" color(white)(l) "O"_2 (g)#
Hence the amount of oxygen required for the complete combustion of the unknown amount of #"H"_2 (g)# produced would be
#n("O"_2) = 0.217 color(white)(l) "mol" color(white)(l) "KClO"_3 * (color(purple)(3) color(white)(l) "mol" color(white)(l) "O"_2 )/(color(navy)(2) color(white)(l) "mol" color(white)(l) "KClO"_3)=0.326 color(white)(l) "mol" color(white)(l) "O"_2 #
Oxygen reacts with hydrogen by the equation
# color(purple)(1) color(white)(l) "O"_2 (g) + color(navy)(2) color(white)(l) "H"_2 (g)stackrel("*")(to) 2 color(white)(l) "H"_2"O" (g)#
at a #color(purple)(1): color(navy)(2)# ratio, meaning that the combustion would consume
#n("H"_2) = 0.326 color(white)(l) "mol" color(white)(l) "O"_2 * (color(navy)(2) color(white)(l) "H"_2 )/(color(purple)(1) color(white)(l) "O"_2)=0.651 color(white)(l) "mol" color(white)(l) "H"_2#
of hydrogen. All these #"H"_2# came from the reaction between #"Zn"# and dilute sulfuric acid #"H"_2 "SO"_4# as seen in the following equation
#color(navy)(1) color(white)(l) "Zn"(s) + "H"_2"SO"_4 (aq) to color(navy)(1) color(white)(l) "H"_2 (g) + "ZnSO"_4 (aq)#
where for each mole of #"H"_2 (g)# produced, #color(navy)(1) color(white)(l) "mol"# of #"Zn"# is consumed. That is:
#n("Zn") = n("H"_2) = 0.651 color(white)(l) "mol"#
Hence the mass of #"Zn"#
#m("Zn") = n("Zn") * M("Zn") = 42.56 color(white)(l) g#
