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?

The of ##"O"_2## under these conditions is is 0.83 g/L.

We can use the 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"##