Excess pressure required to maintain osmotic equilibrium between a solution and the pure solvent separated by a membrane permeable only to the solvent: \[\mathit{\Pi} = -\frac{R\ T}{V_{\rm{A}}}\ \ln a_{\rm{A}}\] where \(V_{\mathrm{A}}\), \(a_{\mathrm{A}}\) are the partial molar volume and activity of solvent \(\rm{A}\) for an incompressible fluid. For ideal dilute solutions, \(\mathit{\Pi} = c_{\rm{B}}\ R\ T=\rho _{\rm{B}}\ \frac{R\ T}{M_{\rm{B}}}\), where entities \(\rm{B}\) are individually moving solute molecules, ions, etc., regardless of their nature, \(c_{\rm{B}}\), \(\rho _{\mathrm{B}}\) 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 mole of osmotically active entities), but this usage and the corresponding term osmolarity are discouraged.