Vapour density is the density of a gas compared to that of hydrogen.
#color(blue)(bar(ul(|color(white)(a/a)VD = ρ_text(gas)/ρ_text(H₂)color(white)(a/a)|)))" "#
#ρ_text(gas) = "1.97 g"/"1 L" = "1.97 g/L"#
We can use the Ideal Gas Law to calculate the density of #"H"_2# at STP (0 °C and 1 bar).
#color(blue)(bar(ul(|color(white)(a/a)pV = nRTcolor(white)(a/a)|)))" "#
Since #n = m/M#, we can write
#pV = m/MRT# or # p = m/V(RT)/M#
And #ρ = m/V#, so #p = (ρRT)/M# or
#color(blue)(ρ = (pM)/(RT))#
#p = "1 bar"#
#M = "2.016 g·mol"^"-1"#
#R = "0.083 14 bar·L·K"^"-1""mol"^"-1"#
#T = "273.15 K"#
#ρ = (1 color(red)(cancel(color(black)("bar"))) × "2.016 g"·color(red)(cancel(color(black)("mol"^"-1"))))/("0.083 14" color(red)(cancel(color(black)("bar")))·"L"·color(red)(cancel(color(black)("K"^"-1""mol"^"-1"))) × 273.15 color(red)(cancel(color(black)("K")))) = "0.088 78 g/L"#
#VD = (1.97 color(red)(cancel(color(black)("g/L"))))/("0.088 78" color(red)(cancel(color(black)("g/L")))) = 22.2#
