between a solution containing solute and pure water. We can write the left hand side as: , where is the activity coefficient of the solvent. The product is also known as the activity of the solvent, which for water is the water activity . The addition to the pressure is expressed through the expression for the energy of expansion: where is the molar volume (m³/mol). Inserting the expression presented above into the chemical potential equation for the entire system and rearranging will arrive at: If the liquid is incompressible the molar volume is constant, , and the integral becomes . Thus, we get The activity coefficient is a function of concentration and temperature, but in the case of dilute mixtures, it is often very close to 1.0, so The mole fraction of solute, , is , so can be replaced with , which, when is small, can be approximated by . The mole fraction is . When is small, it may be approximated by . Also, the molar volume may be written as volume per mole, . Combining these gives the following. For aqueous solutions of salts, ionisation must be taken into account. For example, 1 mole of NaCl ionises to 2 moles of ions. See also Gibbs–Donnan effect References External links What is Osmosis? Explanation and Understanding of a Physical Phenomenon Amount of substance Cell biology Membrane biology Solutions Jacobus Henricus van 't Hoff