Partial molal quantities example

Before the derivation of a general expression for the partial molal quantities, a simple example of partial molal quantity is treated. Consider liquids metal A and metal B, which form a complete solution of composition A Bj Let the volume of 1 g atom of liquid A and liquid B be and Pg, respectively. The volume of the solution, F(x), the mole fraction of which is x (1 — x), generally satisfies the following relation. 

Equation (1.16) is one example of the Gibbs-Duhem equation, which is one of the most useful formulae in thermodynamics. Thus, the partial molal quantity defined as the quantity satisfying the additive property is easily understandable. 

If duy moles of liquid metal j are added to a large quantity of the solution, the W increases by d IV at constant pressure and temperature. Considering the above mentioned example for the partial molal volume, the partial molal quantity Wj may be defined as... 

Parliai rnolal volumes and partial specific volumes are specific examples of a mucli more general Iheimodynamic rule thatextensivfe properties lor any system at equilibrium can always be expressed in terms of surris of the, partial molal (or partial specific) quantities of each of the individual,1 components in the [Pg.83]

Thermodynamic quantities which have the same value throughout a homogeneous compartment (temperature, T pressure, p) are called intensive. Those which are proportional to the amount of component i in that compartment are called extensive (enthalpy, H entropy. S free-energy, G). An extensive quantity may be converted to an intensive one by dividing by the amount of component i present. For example, the partial molal free-energy or chemical potential. 

It should be clear from the examples cited, and from the inapplicability of Eq. (1-32) to nonideal binary solutions, that the partial molal volume should not be interpreted as the molar volume. The.se are two different kinds of quantities and should not be confused with each other. Their numerical values happen to be equal only for a pure phase, or for an ideal solution. In hydrodynamic applications, as we shall see, the partial molal volume (or, as more commonly used, th( partial. specific volume) appears correctly in the Sv( dberg e< Uatioiis for sedimentation velocity and sedimentation eciuilibrium [e.g., lOq. (1-12)]. However, any attempt to identify... 

In Section 4 of Chapter 2, the strong ion-water interaction, in addition to the interionic interaction, was shown to be an influential factor in determining thermodynamic properties of polyelectrol3 e solutions. The hydration phenomenon of macroions is a typical example of the former type of interaction, but its quantitative aspect could not be discussed in terms of the mean activity coefficient. The measurement of the partial molal voliime of polyelectrol3 es is interesting because this volumetric quantity can furnish quantitative information on the hydration on one hand a because it is the pressure dernmtive of the mean activity coefficient on the other. In spite of its importance, however, only a few measurements have so far b n reported for synthetic polyelectrofytes (75, 79, 50). [For a review of the volumetric study of proteins, amino acids, and peptides, an earlier work by Cohn and Edsall should be consulted (5/)]. 

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