Question #963da

1 Answer
Aug 17, 2017

Answer:

The molar mass of the element is approximately 100 g/mol.

Explanation:

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 = "40 mg" = "0.040 g"#
#R = "0.082 06 L·atm·K"^"-1""mol"^"-1"#
#T = "300 K"#
#p = "1 atm"#
#V = "4.92 mL" = "0.004 92 L"#

#M = ("0.040 g" × "0.082 06" color(red)(cancel(color(black)("L·atm·K"^"-1")))"mol"^"-1" × 300 color(red)(cancel(color(black)("K"))))/(1 color(red)(cancel(color(black)("atm"))) × "0.004 92" color(red)(cancel(color(black)("L")))) = "200 g/mol"#

However, the gas is diatomic, with molecular formula #"X"_2#.

∴ The molar mass of #"X"# is 100 g/mol.