We can use the Ideal Gas Law to solve this problem:.
color(blue)(bar(ul(|color(white)(a/a)pV = nRTcolor(white)(a/a)|)))" "
Since n = m/M, we can rearrange this equation to get
pV = (m/M)RT
And we can solve this equation to get
M = (mRT)/(pV)
In your problem,
m = "283.3 g"
R = "0.082 06 L·atm·K"^"-1""mol"^"-1"
T = "(27 + 273.15) K" = "300.15 K"
p = "3.2 atm"
V = "30 L"
∴ M = ("283.3 g" × "0.082 06" color(red)(cancel(color(black)("L·atm·K"^"-1")))"mol"^"-1" × 300.15 color(red)(cancel(color(black)("K"))))/(3.2 color(red)(cancel(color(black)("atm"))) ×30 color(red)(cancel(color(black)("L")))) = "72.7 g/mol"
The molecular mass of "X"_2 is 72.7u.
The atomic mass of "X" is 36.3 u.
The atomic mass of "Cl" is 35.45 u, and the atomic mass of "Ar" is 39.95 u.
The atomic mass of "X" is closer to that of "Cl", and "Cl" also forms diatomic "Cl"_2 molecules.
Element "X" is chlorine.
