# What is the density of hydrogen gas using the ideal gas law?

Jun 2, 2018

Of course, for $\text{density}$ we need to SPECIFY....$\text{temperature}$ and $\text{pressure....}$

#### Explanation:

And, using standard conditions of $P = 1 \cdot a t m$...and $T = 298 \cdot K$, we address the Ideal Gas equation...(at least near standard conditions....)

$P V = n R T$...$\frac{n}{V} = \frac{P}{R T} = \frac{\text{mass"/"molar mass}}{V} = \frac{P}{R T}$

And so....

underbrace("mass"/V)_("density"=rho)=P/(RT)xx"molar mass"

And thus our working equation...${\rho}_{{H}_{2}} = \frac{P}{R T} \times 2.016 \cdot g \cdot m o {l}^{-} 1$

$= \frac{1 \cdot a t m \times 2.016 \cdot g \cdot m o {l}^{-} 1}{0.0821 \cdot \frac{L \cdot a t m}{K \cdot m o l} \times 298 \cdot K} \cong 0.1 \cdot g \cdot {L}^{-} 1$

We note that hydrogen gas, as are all elemental gases with any chemistry, is bimolecular, i.e. ${H}_{2}$...