Molar volume of mixing

The volume of mixing for one mole of solution is termed the molar volume of mixing, A mixFm, and is derived by dividing eq. (3.14) by the total number of moles ( A + wb) in the system... 

The molar volume of mixing of two binary systems is shown in Figure 3.2. Pb-Sn shows positive deviation from the ideal behaviour at 1040 K [1] while the volume of mixing of Pb-Sb at 907 K is negative, with a minimum at Xpb 0.5 and asymmetric with respect to the composition [2],... 

If, however, site interactions of atoms on energetically equivalent sites are equal and the standard molar volumes of mixing components are not dissimilar (i.e., within 5 to 10% difference), equation 3.157 may be simplified and the activity of any component i in the mixture (a,) may be expressed in a generalized fashion as shown by Helgeson et al. (1978) ... 

The excess molar volume is also called the molar volume of mixing. 

AH and AV are molar enthalpy and molar volume of mixing, respectively. The heat of mixing is negligible in most cases. In an isobaric system the second term vanishes, and the Gibbs-Duhem equation takes the form ... 

One important solute is water, which is completely miscible in imidazolium salts with short alkyl side chains and hydrophilic anions such as d, but is only partially miscible with ionic liquids with longer side chains and less hydrophilic anions. Extraction into an aqueous phase is important for product recovery from an ionic liquid medium. Hanke and Lynden-BeU [143] used simulation to investigate thermodynamic properties and local structure in mixtures of water with [MMIM]Q and [MMIM][PF6] liquids. They found that the excess energy of solvation was negative for the chloride and positive for the [PF ]" liquid, as shown in Fig. 4.2-12. There is a similar difference in the molar volumes of mixing shown in Fig. 4.2-13. This is consistent with the perception of the [PFe]" anion as being more hydrophobic than the chloride anion. 

Fig. 4.2-13 Molar volumes of mixing for water with [MMI M]Cl (bottom curve with filled circles) and [MMIM][PFe] (middle curve with filled squares). The open circles show the experimental volumes of mixing for [BMIM][PF6] and water.

The molar volume of mixing, also equal to the excess molar volume, is... 

This concept is also often applied to the volume of the solution even though absolute molar volumes of mixing can be determined quite easily. Other standard states are possible. The most common alternative involves an infinitely dilute solute, also known as the Henry s law standard state. 

Table 9.7 Molar volumes of mixing of binary mixtures of 1-hexanol (A) and 1-octene (B) at 25 °C. ...

Show that for a perfect solution the molar volume of mixing AV ux = 0. 

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