Question

A cylinder contains gas at a pressure of $2.0atm$and a number density of$4.2\times {10}^{25}{m}^{-3}$. The rms speed of the atoms is $660m/s$. Identify the gas.

Short answer

The gas isNeon

Step-by-step solution

Given information and formula used

Given : Gas is at a pressure : $2.0atm$

Number density : $4.2\times {10}^{25}{m}^{-3}$

rms speed of the atoms : $660m/s$

Theory used :

To identify a gas, we must first determine its molar mass. The mass of one mole, $M$or the Avogadro number of molecules . That is, if the mass of a single molecule is $m$, $M=m{N}_A$will result.

Remember that the pressure may be defined in terms of molecular mass, number density, and rms speed as $p=\frac{1}{3}\frac{N}{V}m{v^2}_{rms}$to express the mass of one atom.

Identifying the gas 

$m=\frac{3p}{N/V{v^2}_{rms}}$As a result, we can write the molecular mass as .

We get role="math" localid="1649059712027" $M=m{N}_A=\frac{3p{N}_A}{N/V{v^2}_{rms}}$by plugging this result into the preceding one.

$M=\frac{3\times 2\times {10}^5\times 6.02\times {10}^{23}}{4.2\times {10}^{25}\times {660}^2}=\boxed{0.0197kg}$will be the result.

In gram terms, this is $19.7g$.

We can find periodic tables in periodic tables. We can find the molar mass of neon in periodic tables at $20.1$, thus we can say our gas is Neon within a little margin of error.