Barometric pressure can be understood using the Boltzmann distribution. The potential energy associated with being a given height above the Earth€™s surface is mgh, where m is the mass of the particle of interest, g is the acceleration due to gravity, and h is height. Using this definition of the potential energy, derive the following expression for pressure: 

Assuming that the temperature remains at 298 K, what would you expect the relative pressures of N₂ and O₂ to be at the tropopause, the boundary between the troposphere and stratosphere roughly 11 km above the Earth€™s surface? At the Earth€™s surface, the composition of air is roughly 78% N₂, 21% O₂, and the remaining 1% is other gases.

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P = P,emgh/kT