The average thermal energy of a particle in an ideal gas depends on temperature. We can pull average velocity out of the energy if we know the mass of the gas particle.

Thermal energy = kinetic energy

3/2 k_b T = 1/2 m v^2

Rearrange:

v = sqrt( 3 k_b T / m)

• k_b = boltzmann constant = 1.4e-23 J/K
• m for a nitrogen molecule = 28 amu = 4.6e-26 kg
• T in the stratosphere is around 220-270K, lets pick 250 arbitrarily

Plugging in yields v = 477 m/s. Oxygen would be slightly slower due to being more massive.

At sea level, the speed of sound is around 340m/s, and it decreases as you go up. In other words, the average air molecule is already bouncing around in the stratosphere at supersonic speeds. A collision with a supersonic aircraft would be absolutely unremarkable in terms of accelerating a gas molecule out of the atmosphere.

UV photochemistry and solar wind are the main ways gas is able to escape the atmosphere. Also, the above velocity is the average velocity. There are rare gas particles going much faster such that some gas can escape the atmosphere just by bouncing off other gas molecules ("thermal escape").