# What is the density of neon gas given a pressure of 505*mm*Hg, and a temperature of 318*K?

## What is the density of neon gas given a pressure of $505 \cdot m m \cdot H g$, and a temperature of $318 \cdot K$?

Mar 14, 2017

We assume a litre volume of gas under these conditions.

And get $\rho = 0.5 \cdot g \cdot {L}^{-} 1$

#### Explanation:

Now, we know $P V = n R T$, for an Ideal Gas, and we ASSUME that neon will approximate Ideal Gas behaviour.

From the equation: $\frac{P}{R T} = \frac{n}{V} = \frac{\text{mass"/"molar mass}}{V}$

P/(RT)=("mass"/"molar mass")/V=rhoxx1/"molar mass"

And thus, (FINALLY!): $\rho = \frac{P}{R T} \times \text{molar mass}$

And we plug in the given numbers:

$\rho = \frac{\frac{505 \cdot m m \cdot H g}{760 \cdot m m \cdot H g \cdot a t {m}^{-} 1} \times 20.18 \cdot g \cdot m o {l}^{-} 1}{0.0821 \cdot \frac{L \cdot a t m}{{K}^{-} 1 \cdot m o {l}^{-} 1} \times 318 \cdot K} \cong 0.51 \cdot g \cdot {L}^{-} 1$

The units are appropriate for density, as we require. Please check my figures and assumptions; there is a lot of 'rithmetic here.