Question

How do you find the gas?

17.3 grams of an unknown gas is placed in a 5.00 L container under a pressure of 546.8 torr at 60°C. Identify the gas.

Answer 1

The gas could be any molecule with a molar mass of 131 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`

Also, we can solve this equation to get

`M = (mRT)/(pV)`

In your problem,

`m = "17.3 g"`
`R = "0.082 06 L·atm·K"^"-1""mol"^"-1"`
`T = "60 °C = 333.15 K"`
`p = 546.8 color(red)(cancel(color(black)("torr"))) × "1 atm"/(760 color(red)(cancel(color(black)("torr")))) = "0.7195 atm"`
`V = "5.00 L"`

∴ `M = ("17.3 g" × "0.082 06" color(red)(cancel(color(black)("L·atm·K"^"-1")))"mol"^"-1" × 333.15 color(red)(cancel(color(black)("K"))))/(0.7195 color(red)(cancel(color(black)("atm"))) × 5.00 color(red)(cancel(color(black)("L"))))= "131 g/mol"`