Question

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?

Answer 1

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.