Chemistry - Ideal Gas Question with Solution | TestHub

Density of a gas is given by: $d=\frac{PM}{RT}$

Therefore, for Neon (Ne) and Argon (Ar), we have:

$d_{Ne}=\frac{P_{Ne}{M}_{Ne}}{R{T}_{Ne}}$ And $d_{Ar}=\frac{P_{Ar}{M}_{Ar}}{R{T}_{Ar}}$

The ratio of their densities is:

$$\frac{d_{Ar}}{d_{Ne}}=\left(\frac{P_{Ar}}{P_{Ne}}\right)\left(\frac{M_{Ar}}{M_{Ne}}\right)\left(\frac{T_{Ne}}{T_{Ar}}\right)$$

Given that the ratio is $2:1$, and the molar masses are $M_{Ar}=40$ and $M_{Ne}=20$:

$$\frac{2}{1}=\left(\frac{P_{Ar}}{P_{Ne}}\right)\left(\frac{40}{20}\right)\left(\frac{T_{Ne}}{T_{Ar}}\right)$$

$$\frac{P_{Ar}}{P_{Ne}}=\frac{1}{2}$$