Question

What is the density at STP of the gas sulfur hexafluoride, `SF_6`?

Answer 1

The density of `"SF"_6` at STP is 6.43 g/L.

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 `"moles" = "mass"/"molar mass"` or `n = m/M`, we can write

`PV = m/MRT`

We can rearrange this to

`PM = m/VRT`

But `"density"= "mass"/"volume"` or `color(brown)(|bar(ul(color(white)(a/a)ρ = m/Vcolor(white)(a/a)|)))" "`

∴ `PM = ρRT` and

`color(blue)(|bar(ul(color(white)(a/a)ρ = (PM)/(RT)color(white)(a/a)|)))" "`

STP = 1 bar and 0 °C, and the molar mass of `"SF"_6` is 146.06 g/mol.

∴ `ρ = (1 color(red)(cancel(color(black)("bar"))) × "146.06 g"·color(red)(cancel(color(black)("mol"^"-1"))))/("0.083 14" color(red)(cancel(color(black)("bar")))·"L"·color(red)(cancel(color(black)("K"^"-1""mol"^"-1"))) × 273.15 color(red)(cancel(color(black)("K")))) = "6.43 g/L"`