# Barometric law for hard sphere sedimentation

1. Apr 13, 2014

### KayDee01

So I have the equation for Barometric law in terms of density as: $\frac{\phi(z)}{\phi_{0}}$=exp($-g.M.z/R.T$) where R=Universal gas constant, z=height of sedimentation, T=Standard temperature, g=Gravitational acceleration, M=Molar mass.

When this equation is used to calculate the height of the universe, the molar mass is the molar mass of the atmosphere. But if you're using it to calculate the height of a colloid sedimentation when you have a colloid solution, is the molar mass referring to the mass of the colloid, the average mass of the colloid and solvent, or the relative mass of the colloid (i.e. buoyant mass of the colloid in the given solvent)??

This isn't a homework question, I'm just wondering what factors are being taken into account when calculating the height of a colloid sediment.

2. Apr 13, 2014

### abitslow

The height of the Universe? LOL.
This is not a law. A Law is a physical principle which has very broad utility and has been extensively tested. The Barometric equation qualifies under neither requirement. It applies ONLY to ideal gasses, AND, can only apply near sea-level (as given here). I don't know ANY colloids that do not settle given sufficient time in an unstirred isothermal container (which turns out to be extremely difficult to actually construct). Yet, your "Law" contains no time dependence. How do you have sedimentation without time? You are correct to suspect that talking about colloids as if their density is irrelevant is a fools errand. Packing of a sediment is usually characterized as hard or soft, but obviously must depend on particle to particle interactions, as well as particle volume and shape.
I would never use this to predict sediment volume (height). But then, perhaps it's "good enough" for geology/hydrology?
I think you're right, that the difference in density between the solvent and the solute (as it exists in solution) is the correct parameter to use to predict Φ/Φ₀.

Last edited: Apr 13, 2014