# Question f2a59

May 6, 2017

The density of nitrogen at NTP is 1.16 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 $n = \frac{m}{M}$, we can substitute this to get

$p V = \left(\frac{m}{M}\right) R T$

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(brown)(bar(ul(|color(white)(a/a)ρ = (pM)/(RT)color(white)(a/a)|)))" "

NTP — Normal Temperature and Pressure — is defined as 20 °C and 1 atm.

$p = \text{1 atm}$
$M = \text{28.01 g/mol}$
$R = \text{0.082 06 L·atm·K"^"-1""mol"^"-1}$
$T = \text{20 °C" = "293.15 K}$
ρ = (1color(red)(cancel(color(black)("atm"))) × 28.01color(white)(l) "g"·color(red)(cancel(color(black)("mol"^"-1"))))/("0.082 06" "L"·color(red)(cancel(color(black)("atm·K"^"-1""mol"^"-1"))) × 293.15color(red)(cancel(color(black)("K")))) = "1.16 g/L"#