# Osmotic Pressure: Comparing Solutes and Ideal Gases

The equation describing osmotic pressure is

$\Pi=\frac{n}{V} RT$

which is just like the ideal gas equation law

$PV=nRT$

So how much of an analogy is there between ideal gases and solutes? Is there a extended version of the equation for osmotic pressure that matches the van der Waals equation of state?

If solutes can be in a state like a gas, can they also be in a state like a liquid? Is this distinct from a precipitate which would be the analog of a solid?

The van t'Hoff equation for the osmotic pressure can be expanded by a virial expansion similarly to the extension of ideal gas equation. In the gas case, the coefficients of the virial expansion are related to the van der Waals constants a and b. Thus you can probably also obtain a similar equation of state for the osmotic pressure $\Pi$ of a solute. However, their interpretation will probably be different.