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.