Question

Calculate the mass density of a pure sample of oxygen gas at a pressure of 1.0 atm, a volume of 7.8 L at 197.2C?

Calculate the mass density of a pure sample of oxygen gas at a pressure
of 1.0 atm, a volume of 7.8 L at 197.2C.

Answer 1

The density of `"O"_2` under these conditions is is 0.83 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 = "1.0 atm"; M = "32.00 g/mol"; R = "0.082 06 L·atm·K"^"-1""mol"^"-1"; T = "197.2 °C" = "470.35 K"`

∴ `ρ = (1.0 color(red)(cancel(color(black)("atm"))) × "32.00 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"))) × 470.35 color(red)(cancel(color(black)("K")))) = "0.83 g/L"`