Question #f2a59

1 Answer
Ernest Z.
May 6, 2017

The density of nitrogen at NTP is 1.16 g/L.

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 = m/M#, we can substitute this to get

#pV = (m/M)RT#

We can rearrange this to

#pM = m/VRT#

But #"density"= "mass"/"volume"# or #color(brown)(bar(ul(|color(white)(a/a)ρ = m/Vcolor(white)(a/a)|)))" "#

∴ #pM = ρRT#

and

#color(brown)(bar(ul(|color(white)(a/a)ρ = (pM)/(RT)color(white)(a/a)|)))" "#

NTP — Normal Temperature and Pressure — is defined as 20 °C and 1 atm.

In your problem,

#p = "1 atm"#
#M = "28.01 g/mol"#
#R = "0.082 06 L·atm·K"^"-1""mol"^"-1"#
#T = "20 °C" = "293.15 K"#

∴ #ρ = (1color(red)(cancel(color(black)("atm"))) × 28.01color(white)(l) "g"·color(red)(cancel(color(black)("mol"^"-1"))))/("0.082 06" "L"·color(red)(cancel(color(black)("atm·K"^"-1""mol"^"-1"))) × 293.15color(red)(cancel(color(black)("K")))) = "1.16 g/L"#

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