Question

How would you find the molecular weight of an unknown gas?

Answer 1

I would determine the mass of a fixed volume of the gas at a known temperature and pressure and then use the Ideal Gas Law to calculate the molar mass.

Explanation:

EXAMPLE

The mass of an evacuated 255 mL flask is 143.187 g. The mass of the flask filled with an unknown gas at 25.0 °C and 265 Torr is 143.289 g.

Solution

The Ideal Gas Law is

`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 = "143.289 g - 143.187 g" = "0.102 g"`
`R = "0.082 06 L·atm·K"^"-1""mol"^"-1"`
`T = "(25.0 + 273.15) K" = "298.75 K"`
`P = 265 color(red)(cancel(color(black)("torr"))) × "1 atm"/(760 color(red)(cancel(color(black)("torr")))) = "0.3487 atm"`
`V = "0.255 L"`

∴ `M = ("0.102 g" × "0.082 06" color(red)(cancel(color(black)("L·atm·K"^"-1")))"mol"^"-1" × 298.15 color(red)(cancel(color(black)("K"))))/("0.3487" color(red)(cancel(color(black)("atm"))) × 0.255 color(red)(cancel(color(black)("L")))) = "28.1 g/mol"`

The molar mass is 28.1 g/mol.

∴ The molecular mass is 28.1 u.