Apparent molar property

In thermodynamics, an apparent molar property of a solution component in a mixture or solution is a quantity defined with the purpose of isolating the contribution of each component to the non-ideality of the mixture. It shows the change in the corresponding solution property (for example, volume) per mole of that component added, when all of that component is added to the solution. It is described as apparent because it appears to represent the molar property of that component in solution, provided that the properties of the other solution components are assumed to remain constant during the addition. However this assumption is often not justified, since the values of apparent molar properties of a component may be quite different from its molar properties in the pure state. For instance, the volume of a solution containing two components identified as solvent and solute is given by where V_0 is the volume of the pure solvent before adding the solute and \tilde{V}_{0} its molar volume (at the same temperature and pressure as the solution), n_0 is the number of moles of solvent, {}^\phi\tilde{V}_1, is the apparent molar volume of the solute, and n_1 is the number of moles of the solute in the solution. By dividing this relation to the molar amount of one component a relation between the apparent molar property of a component and the mixing ratio of components can be obtained. This equation serves as the definition of {}^\phi\tilde{V}_1,. The first term is equal to the volume of the same quantity of solvent with no solute, and the second term is the change of volume on addition of the solute. {}^\phi\tilde{V}_1, may then be considered as the molar volume of the solute if it is assumed that the molar volume of the solvent is unchanged by the addition of solute. However this assumption must often be considered unrealistic as shown in the examples below, so that {}^\phi\tilde{V}_1, is described only as an apparent value. An apparent molar quantity can be similarly defined for the component identified as solvent {}^\phi\tilde{V}_0,.