# How to calculate the mass of a layer of an atmosphere?

In a problem I'm working on, I need to derive what fraction of molecules in the Earth's atmosphere are found in the troposphere (the bottom layer extending from the surface to approx. 12 km). I have a basic idea to solve the problem, which involves the mass of the whole atmosphere/troposphere, but I'm not exactly sure how to go about calculating the mass of the troposphere. It's easy to (sorry for the painful phrase) look up the mass of the entire atmosphere, but I couldn't really find a good explanation as to how that value came about. Can anyone shed some light on this, or even more usefully, how to calculate the mass of a layer in the atmosphere (criteria below)?

Problem criteria: We'll establish the troposphere in this problem as extending from the surface (Z=0 km) to Z=12 km and pressure coordinates from 1000 mb at the surface to 200 mb at the top of the layer (the tropopause, in this case). The atmosphere is also isothermal at 255 K.

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The force of gravity on the air just another way of looking at the force exerted on the surface of the earth by atmospheric pressure. So:$$M g= PA$$ where M is the mass of the atmosphere, g is the acceleration of gravity, P is the atmospheric pressure, and A is the surface area of the earth.

Warning: watch your units. Better use $kilograms, metre/second^2, pascals, metres^2$

Repeat for the reduced pressure at the level of the tropopause. Or simply note that if the pressure there is one fifth of the surface pressure, the mass above that level is one fifth of the total mass...

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+1 for the observation in the last sentence. – Neal Jan 24 '13 at 2:42
Ah yes, makes sense to me. And wow, yeah that is quite the helpful hint there! Makes complete sense! – Devin Jan 24 '13 at 3:11

This may rather be physics than math, but the mass can be obtained from the weight.

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