# 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?

##### 1 Answer

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

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.

∴

∴