Ascending chain condition on principal ideals: Difference between revisions

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An '''apparent molar property''' is a quantity that can be used to calculate a property of a [[solution (chemistry)|solution]]. For instance, the [[volume]] of the solution is given by
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:<math>  V= \tilde{V}_{0} n_{0} + {}^\phi\tilde{V}_i n_i \,</math>
 
where V<sub>0</sub> is the [[molar volume]] of the solvent, n<sub>0</sub> is the number of [[mole (unit)|mole]]s of solvent, <math> {}^\phi\tilde{V}_i \,</math> is the apparent molar volume of [[solution|solute]] i, and n<sub>i</sub> is the number of moles of solute i in the solution. (The apparent molar volume can also be denoted V<sub>φ</sub>.) 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 [[:wikt:dilution|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:
:<math> \sum_i {}^\phi{V}_i= q V - (q-1)\sum_i V_i \,</math>
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 cm<sup>3</sup> per mole, but the apparent molar volume at low concentrations is only 16.6 cc/mole. In fact, some aqueous [[electrolyte]]s have negative apparent molar volumes: [[NaOH]] -6.7, [[LiOH]] -6.0, and [[sodium carbonate|Na<sub>2</sub>CO<sub>3</sub>]] -6.7 cm<sup>3</sup>/mole.<ref>[[Herbert Harned]] and [[Benton Owen]], ''The Physical Chemistry of Electrolytic Solutions'', 1950, p. 253.</ref> 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]]
 
==References==
<references/>
 
==External links==
* [http://www.le.ac.uk/chemistry/thermodynamics/pdfs/500/Topic0250.pdf Apparent Molar Properties: Solutions: Background]
* [http://thermosymposium.nist.gov/archive/symp17/pdf/Abstract_199.pdf The (p,ρ,T) Properties and Apparent Molar Volumes of ethanol solutions of LiI or ZnCl2]
* [https://e-reports-ext.llnl.gov/pdf/309544.pdf 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]
 
[[Category:Physical chemistry]]
[[Category:Thermodynamics]]

Latest revision as of 13:33, 27 July 2014

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