# What volume is occupied by a 7*g mass of dinitrogen gas at a temperature of 300*K, and a pressure of 750*mm*Hg?

Jul 10, 2017

$V \cong 6 \cdot L$

#### Explanation:

Given $V = \frac{n R T}{P}$, we know that nitrogen (LIKE most of the elemental gases) is a DIATOM, i.e. ${N}_{2}$. We also know that $760 \cdot m m \cdot H g \equiv 1 \cdot a t m .$ This is a key point, as we can use the height of a mercury column as an accurate representation of pressure.

So $V = \frac{\frac{7.0 \cdot g}{28.0 \cdot g \cdot m o {l}^{-} 1} \times 0.0821 \cdot \frac{L \cdot a t m}{K \cdot m o l} \times 300 \cdot K}{\frac{750 \cdot m m \cdot H g}{760 \cdot m m \cdot H g \cdot a t {m}^{-} 1}}$

All units EXCEPT $\text{litres}$ cancel, so...........

$\cong 6 \cdot L \ldots \ldots .$