# Question de30c

Jun 27, 2017

The vapour density of the gas is 22.2.

#### Explanation:

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 ${\text{H}}_{2}$ at STP (0 °C and 1 bar).

$\textcolor{b l u e}{\overline{\underline{| \textcolor{w h i t e}{\frac{a}{a}} p V = n R T \textcolor{w h i t e}{\frac{a}{a}} |}}} \text{ }$

Since $n = \frac{m}{M}$, we can write

$p V = \frac{m}{M} R T$ or $p = \frac{m}{V} \frac{R T}{M}$

And ρ = m/V, so p = (ρRT)/M or

color(blue)(ρ = (pM)/(RT))

$p = \text{1 bar}$
$M = \text{2.016 g·mol"^"-1}$
$R = \text{0.083 14 bar·L·K"^"-1""mol"^"-1}$
$T = \text{273.15 K}$

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"#

$V D = \left(1.97 \textcolor{red}{\cancel{\textcolor{b l a c k}{\text{g/L"))))/("0.088 78" color(red)(cancel(color(black)("g/L}}}}\right) = 22.2$