Question

It is possible to prepare short x-ray pulses via a process called “high harmonic generation” wherein a short pulse of visible light from a laser is focused into flowing gas. The efficiency of x-ray generation depends strongly on the density of the gas.
You are working in a lab that uses Xenon gas to produce x-rays. However, a colleague of yours mistakenly filled a gas cylinder you use with Argon rather than Xenon.
If the volume of your cylinder is 50 L and the pressure of the gas in it is 150 bar, how much does the density of the gas in the tank differ due to it being filled with Argon rather than Xenon at a temperature of 873K?
For Ar, B2V(873 K) = 19.48 cm3/mol. For Xe, B2V(873 K) = 7.95 cm3/mol.

Answer 1

Given

For Ar, B2V(873 K) = 19.48 cm3/mol.

For Xe, B2V(873 K) = 7.95 cm3/mol.

The molar volume of argon is19.48 cm3/mol and molar mass of argon is 39.948 g/mol Density of argon can be calculated by using following formula.

Density of argon = molar mass of argon/ molar volume of argon

                             =   39.948 g/mol/19.48 cm³/mol = 2.05 g/cm³

Density of argon at 873K and 150 bar = 2.05 g/cm³

The molar volume of xenon is7.95 cm3/mol and molar mass of xenon is 131.293 g/mol

Density of xenon = molar mass of xenon/ molar volume of xenon

                             =   131.233 g/mol/7.95 cm³/mol = 16.514 g/cm³

Density of xenon at 873K and 150 bar = 16.514 g/cm³

The density of the gas in the tank is lower, when filled with Argon rather than Xenon.

Difference = 16.514 g/cm3 -2.05 g/cm³ = 14.509 g/cm³