What is the molecular mass (in amu) of a gaseous element if 8.79 g occupies 4.54 L at 447.77 torr and 37.6 °C?

1 Answer
Ernest Z.
Jul 2, 2016

The molecular mass is 83.8 u.

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 #n = "mass"/"molar mass" = m/M#, we can write the Ideal Gas Law as

#color(blue)(|bar(ul(color(white)(a/a)PV = m/MRTcolor(white)(a/a)|)))" "#

We can rearrange this to get

#M = (mRT)/(PV)#

#m = "8.79 g"#
#R = "0.082 06 L·atm·K"^"-1""mol"^"-1"#
#T = "(37.6 + 273.15) K" = "310.75 K"#
#P = 447.77 color(red)(cancel(color(black)("torr"))) × "1 atm"/(760 color(red)(cancel(color(black)("torr")))) = "0.589 17 atm"#
#V = "4.54 L"#

∴ #M = ("8.79 g" × "0.082 06" color(red)(cancel(color(black)("L·atm·K"^"-1")))"mol"^"-1" × 310.75 color(red)(cancel(color(black)("K"))))/("0.589 17" color(red)(cancel(color(black)("atm"))) × 4.54 color(red)(cancel(color(black)("L")))) = "83.8 g/mol"#

∴ The molecular mass is 83.8 u.

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