Ascending chain condition on principal ideals

An apparent molar property is a quantity that can be used to calculate a property of a solution. For instance, the volume of the solution is given by

$V={\tilde {V}}_{0}n_{0}+{}^{\phi }{\tilde {V}}_{i}n_{i}\,$

where V₀ is the molar volume of the solvent, n₀ is the number of moles of solvent, ${}^{\phi }{\tilde {V}}_{i}\,$ is the apparent molar volume of solute i, and n_i is the number of moles of solute i in the solution. (The apparent molar volume can also be denoted V_φ.) This equation applied to a single-solute solution serves as the definition of the apparent molar volume of the solute. For multicomponent solutions, the equation does not give an unambiguous definition of the apparent molar properties.

Apparent molar properties are not in fact constants (even at a given temperature), but are functions of the composition. At infinite dilution, they are equal to the partial molar property.

Some apparent molar properties that are commonly used are apparent molar enthalpy, heat capacity, and volume.

Properties

The sum of the extensive apparent quantities/volumes is given by:

$\sum _{i}{}^{\phi }{V}_{i}=qV-(q-1)\sum _{i}V_{i}\,$

where q is the number of the components of the mixture.

Electrolytes

The apparent molar volume of a salt is usually less than the molar volume of the solid salt. For instance, solid NaCl has a volume of 27 cm³ per mole, but the apparent molar volume at low concentrations is only 16.6 cc/mole. In fact, some aqueous electrolytes have negative apparent molar volumes: NaOH -6.7, LiOH -6.0, and Na₂CO₃ -6.7 cm³/mole. This means that their solutions in a given amount of water have a smaller volume than the same amount of pure water. The physical reason is that nearby water molecules are strongly attracted to the ions so that they occupy less space.

See also

• Volume fraction
• Ideal solution
• Regular solution
• Solvation shell
• Partial molar property
• Excess molar quantity
• Thermodynamic activity

External links

• Apparent Molar Properties: Solutions: Background
• The (p,ρ,T) Properties and Apparent Molar Volumes of ethanol solutions of LiI or ZnCl2
• Apparent molar volumes and apparent molar heat capacities of Pr(NO3)3(aq), Gd(NO3)3(aq), Ho(NO3)3(aq), and Y(NO3)3(aq) at T = (288.15, 298.15, 313.15, and 328.15) K and p = 0.1 MPa