# The density of a gas at s.t.p is 1.750 g dm^(-3)3. How do you calculate the relative molecular mass of the gas?

Sep 9, 2016

The relative molecular mass of the gas is 39.74.

#### Explanation:

We can use the Ideal Gas Law to solve this problem.

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

Since $n = \text{mass"/"molar mass} = \frac{m}{M}$,

we can write the Ideal Gas Law as

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

We can rearrange this to get

$M = \left(\frac{m}{V}\right) \frac{R T}{P}$

or

color(blue)(bar(ul(|color(white)(a/a)M = (ρRT)/Pcolor(white)(a/a)|)))" "

STP is defined as 1 bar and 0 °C.

ρ = "1.750 g/dm"^3
$R = \text{0.083 14 bar·dm"^3"·K"^"-1""mol"^"-1}$
$T = \text{273.15 K}$
$P = \text{1 bar}$

M = ("1.750 g"·color(red)(cancel(color(black)("dm"^"-3"))) × "0.083 14" color(red)(cancel(color(black)("bar·dm"^3"·K"^"-1")))"mol"^"-1" × 273.15 color(red)(cancel(color(black)("K"))))/(1 color(red)(cancel(color(black)("bar")))) = "39.74 g/mol"

${M}_{r} = 39.74$