Step 1. Use the Ideal Gas Law to calculate the moles of hydrogen.
The Ideal Gas Law is
#color(blue)(|bar(ul(PV = nRT)|)#,
where
- #P# is the pressure
- #V# is the volume
- #n# is the number of moles
- #R# is the gas constant
- #T# is the temperature
We can rearrange the Ideal Gas Law to get
#n = (PV)/(RT)#
#P = 750 color(red)(cancel(color(black)("mmHg"))) × "1 atm"/(760 color(red)(cancel(color(black)("mmHg")))) = "0.9868 atm"#
#V = "31.0L"#
#R = "0.082 06 L·atm·K"^"-1""mol"^"-1"#
#T = "(23 + 273.15) K" = "296.15 K"#
#n = (PV)/(RT) = (0.9868 color(red)(cancel(color(black)("atm"))) × 31.0 color(red)(cancel(color(black)("L"))))/( "0.082 06" color(red)(cancel(color(black)("L·atm·K"^"-1"))) "mol"^"-1" × 296.15 color(red)(cancel(color(black)("K")))) = "1.259 mol"#
Step 2. Calculate the moles of #"Fe"#.
The balanced equation is:
#"Fe" + "2HCl" → "FeCl"_2 + "H"_2"#
#"Moles of Fe" = 1.259 cancel("mol H"_2) × ("1 mol Fe")/(1 cancel("mol H"_2)) = "1.259 mol Fe"#
Step 3. Calculate the mass of #"Fe"#
#"Mass of Fe" = 1.259 color(red)(cancel(color(black)("mol Fe"))) × ("55.84 g Fe")/(1 color(red)(cancel(color(black)("mol Fe")))) = "70.3 g Fe"#
