Clarification on osmotic pressure

In today's lecture, we came used the following equation:

Pi = kB T x_solute / v

Then, we substituted in to get

Pi = kB T x_solute * N_solvent / V_solvent

Here, N_solvent and V_solvent apply to the right hand side of the osmotic pressure experiment; that is, the solution (non pure) phase. Since v is for the pure phase, here we are making the approximation that the molar volume of the solvent is the same on the left and right hand side of the experiment. This is almost certainly the case for small, dilute amounts of solvent.

MSS