There are four steps involved in this stoichiometry problem:
Step 1. Write the balanced chemical equation.
#M_r:color(white)(mmmmmmm) 36.46#
#color(white)(mmm)"H"_2 + "Cl"_2 → "2HCl"#
2. Convert grams of #"HCl"# to moles of #"HCl"#
#"Moles of HCl" = 292 color(red)(cancel(color(black)("g HCl"))) × ("1 mol HCl")/(36.46 color(red)(cancel(color(black)("g HCl")))) = "8.009 mol HCl"#
Step 3. Convert moles of #"HCl"# to moles of #"Cl"_2#
#"Moles of Cl"_2 = 8.009color(red)(cancel(color(black)("mol HCl"))) × ("1 mol Cl"_2)/(2 color(red)(cancel(color(black)("mol HCl")))) = "4.004 mol Cl"_2#
4. Calculate the volume of #"Cl"_2#
At STP (1 bar and 0 °C), the molar volume of a gas is 22.71 L.
∴ #V = 4.004 color(red)(cancel(color(black)("mol"))) × "22.71 L"/(1 color(red)(cancel(color(black)("mol")))) = "90.9 L"#
The volume of #"Cl"_2# used is 90.9 L.
Here's a useful video on mass-volume conversions.
