# Question 7f3c3

Aug 20, 2017

$69.2$ ${\text{L N}}_{2}$

#### Explanation:

We're asked to find the volume (in liters) occupied by $86.5$ ${\text{g N}}_{2}$.

I'll assume the conditions are standard temperature and pressure.

If these conditions are $1$ $\text{atm}$ and $273.15$ $\text{K}$ ($0$ $\text{^"o""C}$), then one mole of an (ideal) gas occupies a volume of $22.4$ $\text{L}$.

With that in mind, let's first convert from grams of nitrogen to moles, using its molar mass:

86.5cancel("g N"_2)((1color(white)(l)"mol N"_2)/(28.013cancel("g N"_2))) = color(red)(ul(3.09color(white)(l)"mol N"_2

Now, we use the above conversion factor

ul(1color(white)(l)"mol" = 22.4color(white)(l)"L"

to convert from moles to liters:

$\textcolor{red}{3.09} \cancel{\textcolor{red}{\text{mol N"_2))((22.4color(white)(l)"L N"_2)/(1cancel("mol N"_2))) = color(blue)(ulbar(|stackrel(" ")(" "69.2color(white)(l)"L N"_2" }} |}$

Therefore, $86.5$ grams of nitrogen occupies a volume of color(blue)(69.2color(white)(l)"liters"#.