Step 1. Write the balanced chemical equation.
The balanced equation is
#"2KClO"_3 → "2KCl" + "3O"_2#
Step 2. The Procedure
The problem is to convert grams of #"KClO"_3# to moles of #"O"_2# and volume of #"O"_2#.
The procedure is:
(a) Use the molar mass to convert the mass of #"KClO"_3# to moles of #"KClO"_3#.
(b) Use the molar ratio (from the balanced equation) to convert moles of #"KClO"_3# to moles of #"O"_2#.
(e) Use the Ideal Gas Law to convert moles of #"O"_2# to volume of #"O"_2#.
In equation form,
#"grams of KClO"_3 stackrelcolor(blue)("molar mass"color(white)(ml)) (→) "moles of KClO"_3 stackrelcolor(blue)("molar ratio"color(white)(ml))→ "moles of O"_2 stackrelcolor(blue)("Ideal Gas Law"color(white)(ml))(→) "volume of O"_2#
The Calculations
(a) Moles of #"KClO"_3#
#5.71 color(red)(cancel(color(black)("g KClO"_3))) × ("1 mol KClO"_3)/(122.55 color(red)(cancel(color(black)("g KClO"_3)))) = "0.046 59 mol KClO"_3 #
(b) Moles of #"O"_2#
#"0.046 59"color(red)(cancel(color(black)("mol KClO"_3))) × ("3 mol O"_2)/(2 color(red)(cancel(color(black)("mol KClO"_3)))) = "0.069 89 mol O"_2#
(c) Volume of #"O"_2#
The Ideal Gas Law is
#color(blue)(bar(ul(|color(white)(a/a)PV = nRTcolor(white)(a/a)|)))" "#
We can rearrange this to give
#V = (nRT)/P#
#n = "0.069 89 mol O"_2#
#R = "0.082 06 L·atm·K"^"-1""mol"^"-1"#
#T = "(82.1 + 273.15) K" = "355.25 K"#
#P = 711 color(red)(cancel(color(black)("mmHg"))) × "1 atm"/(760 color(red)(cancel(color(black)("mmHg")))) = "0.9355 atm"#
∴ #V = ("0.069 89" color(red)(cancel(color(black)("mol"))) × "0.082 06 L"·color(red)(cancel(color(black)("atm·K"^"-1""mol"^"-1")))
× 355.25color(red)(cancel(color(black)( "K"))))/(0.9355 color(red)(cancel(color(black)("atm")))) = "2.18 L"#
The volume of #"O"_2# produced is #"2.18 L"#.
