Question

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?

Answer 1

The relative molecular mass of the gas is 39.74.

Explanation:

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

`color(blue)(bar(ul(|color(white)(a/a)PV = nRTcolor(white)(a/a)|)))" "`

Since `n = "mass"/"molar mass" = m/M`,

we can write the Ideal Gas Law as

`color(blue)(bar(ul(|color(white)(a/a) PV = m/MRTcolor(white)(a/a)|)))" "`

We can rearrange this to get

`M = (m/V)(RT)/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 = "0.083 14 bar·dm"^3"·K"^"-1""mol"^"-1"`
`T = "273.15 K"`
`P = "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`