Question

Question #f2a59

Answer 1

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"`