Question

As you increase altitudes on Earth, how does the composition of the air change? I suppose that the heavier and larger molecules would be less prevalent higher up. Is there an equation to describe the change?

Answer 1

As the gases go higher in the atmosphere they start to compose or join together at some point which causes them to change since there is mixture of more than one gas, sometimes they form a different element when certain gases form.

Answer 2

Certainly. You want what's often called the "barometric law" or "exponential atmosphere law." This is readily derivable from many approaches, and is only valid for atmospheres in equilibrium everywhere (e.g. where the temperature is the same everywhere). its usefulness for an actual atmosphere is somewhat limited.

\[P_i = P_i^0 e^{-\frac{M g h}{R T}}\]

Here P_i is the partial pressure of the i^th gas, P_i^0 is its partial pressure at your reference altitude (e.g. sea level), M is the molar mass of the gas, g is the acceleration due to gravity, h is the altitude above your reference altitude, R is the gas constant, and T is the absolute temperature.

As you can see, the partial pressures of heavier gases (those with larger M) will fall off faster with increasing altitude (increasing h).

Note that this formula also doesn't take into account the fact that the strength of gravity falls off with altitude, that is, g is not constant.