Question

Question #963da

Answer 1

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.