Question

What is the density of `NO_2` in a 3.50 L tank at 780.0 torr and 37°C?

Answer 1

The density of `"NO"_2` under these conditions is is 1.85 g/L.

Explanation:

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

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

Since `"moles" = "mass"/"molar mass"` or `n = m/M`, we can write

`PV = m/MRT`

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(blue)(|bar(ul(color(white)(a/a)ρ = (PM)/(RT)color(white)(a/a)|)))" "`

`P = 780.0 color(red)(cancel(color(black)("torr"))) × "1 atm"/(760 color(red)(cancel(color(black)("torr")))) = "1.026 atm"`
`M = "46.01 g/mol"`
`R = "0.082 06 L·atm·K"^"-1""mol"^"-1"`
`T = "(37 + 273.15) K" = "310.15 K"`

∴ `ρ = (1.026 color(red)(cancel(color(black)("atm"))) × "46.01 g"·color(red)(cancel(color(black)("mol"^"-1"))))/("0.082 06" color(red)(cancel(color(black)("atm")))·"L"·color(red)(cancel(color(black)("K"^"-1""mol"^"-1"))) × 310.15 color(red)(cancel(color(black)("K")))) = "1.85 g/L"`