https://doi.org/10.1351/goldbook.O04344
Excess pressure required to maintain osmotic equilibrium between a solution and the pure solvent separated by a @MT06878@ permeable only to the solvent: \[\mathit{\Pi} = -\frac{R\ T}{V_{\text{A}}}\ \ln a_{\text{A}}\] where \(V_{\mathrm{A}}\), \(a_{\mathrm{A}}\) are the partial molar volume and activity of solvent \(\text{A}\) for an incompressible fluid. For ideal dilute solutions, \(\mathit{\Pi} = c_{\text{B}}\ R\ T=\rho _{\text{B}}\ \frac{R\ T}{M_{\text{B}}}\), where entities \(\text{B}\) are individually moving solute molecules, ions, etc., regardless of their nature, \(c_{\text{B}}\), \(\rho _{\mathrm{B}}\) are the amount and mass concentration of the solutes, and \(M_{\mathrm{B}}\) is the mass average molar mass of the solutes. The amount is sometimes expressed in osmol (meaning a @M03980@ of osmotically active entities), but this usage and the corresponding term @O04343@ are discouraged.