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
