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
Ernest Z.
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.

#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#

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