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

May 1, 2016

The density of ${\text{SF}}_{6}$ at STP is 6.43 g/L.

#### Explanation:

We can use the Ideal Gas Law to solve this problem.

$\textcolor{b l u e}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} P V = n R T \textcolor{w h i t e}{\frac{a}{a}} |}}} \text{ }$

Since $\text{moles" = "mass"/"molar mass}$ or $n = \frac{m}{M}$, we can write

$P V = \frac{m}{M} R T$

We can rearrange this to

$P M = \frac{m}{V} R T$

But $\text{density"= "mass"/"volume}$ 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 ${\text{SF}}_{6}$ 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"