Consider a box with two compartments separated by a semipermeable membrane. The first compartment is initially at pressure $P_0$ and contains the solvent ; the second compartment is initially at pressure $P_1$ and contains the solvent and a solute.
In deriving the van't Hoff my textbook says that we consider the system at equilibrium , yet it says that the two pressures are different at equilibrium. Isn't equality of pressures of subsystems a condition for equilibrium?
In thermodynamics we can have partial equilibrium depending on the presence or absence of constraints. Suppose we divide a box into two parts: the equilibrium conditions between the two parts depend on the the properties of the wall:
If the wall is impermeable, fixed, and conducting, we only have thermal equilibrium. The pressure and chemical potentials in each part are not allowed to equilibrate.
If the wall is impermeable, movable and insulating, then we only have mechanical equilibrium. i.e., pressure is equalized but temperature and chemical potential are not.
In the osmotic experiment the wall is fixed, conducting and semipermeable. This leads to thermal and chemical equilibrium between two parts that are at different pressures.
