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.

1 Answer
May 11, 2016

Answer:

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"#