A gas in equilibrium has uniform density and pressure throughout its volume. This is strictly true only if there are no external influences. A gas column under gravity, for example, does not have uniform density (and pressure). As you might expect, its density decreases with height. The precise dependence is given by the so-called 'law of atmospheres' `n_2 = n_1 exp[-(mg)(H_2-H_1)/(kT)]` where `n_2,n_1` refer to number density at heights `h_2` and `h_1` respectively.Use this relation to derive the equation for sedimentation equilibrium of a suspension in a liquid column:
`n_2= n_1 exp[(-mgN_a)/(RT) (1-(rho)/(rho))(h_2-h_1)]` where `rho` is the density of the suspended particle, and `rho'` that of surrounding medium. `[N_A` is Avogadro's number, and R the universal gas constant].