Partial specific quantity

A partial specific quantity of a substance is the partial molar quantity divided by the molar mass, and has dimensions of volume divided by mass. For example, the partial specific volume vb of solute B in a binary solution is given hy 

Although this book makes little use of specific quantities and partial specific quantities, in some applications they have an advantage over molar quantities and partial molar quantities because they can be evaluated without knowledge of the molar mass. For instance, the value of a solute s partial specific volume is used to determine its molar mass by the method of sedimentation equilibrium (Sec. 9.8.2). 

The general relations in Sec. 9.2.4 involving partial molar quantities may be turned into relations involving partial specific quantities by replacing amounts by masses, mole fractions by mass fractions, and partial molar quantities by partial specific quantities. Using volume as an example, we can write an additivity relation V = and Gibbs- 

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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]

The expression (2-4) provides the definition of a partial molal quantity if the gram-molecular weight (mole) is the unit of mass and of a partial specific quantity if the gram is the unit of mass. In the future, the symbol i will denote a partial molal quantity defined by the relation... 

Analogues of (4.269), (4.270) for expressing the partial specific quantities through mixture properties in independent variables temperature and densities (4.213) are... 

The diameter d of a polymer chain can be estimated from (1) hydrodynamic quantities such as intrinsic viscosity and sedimentation coefficient, (2) the partial specific volume vgp of the polymer, and (3) X-ray crystallographic data of the polymer. Table 2 lists the values of d for liquid-crystalline polymers estimated by different methods. Those determined from hydrodynamic data are close to but slightly larger than those from vsp and crystallographic data, though this may not always be the case. 

With additional information, including the heat capacity of the buffer solvent, the partial specific volumes (volume per gram of the solute), and the specific volume of the solvent, one can extract the partial specific heat capacity (J K 1g I) of the solute. Privalov has summarized these calculations.8 Because the solutions are studied at very low concentrations, it is assumed that the contribution to the total heat capacity from the solvent cancels out when one calculates the excess heat capacity. With only minor exceptions, the procedures used to calculate parameters associated with the transformations in nucleic acids and in proteins are the same and yield quantities that are interpreted in similar ways, although researchers in these two fields may use a different notation for the same quantity. 

The populations of other intermediate states are very small and can be neglected. For larger more complex proteins made up of multiple subunits, and in many fibrous proteins, this conclusion cannot be supported. Complex globular proteins appear to melt cooperatively in domains in which the smaller units melt independently, and the melting in fibrous proteins is even more complex. While the molar quantities for the heat capacity are dependent upon the size of the protein, the partial specific heat capacities of many proteins are very nearly the same. 

The partial molar properties are not measured directly per se, but are readily derivable from experimental measurements. For example, the volumes or heat capacities of definite quantities of solution of known composition are measured. These data are then expressed in terms of an intensive quantity—such as the specific volume or heat capacity, or the molar volume or heat capacity—as a function of some composition variable. The problem then arises of determining the partial molar quantity from these functions. The intensive quantity must first be converted to an extensive quantity, then the differentiation must be performed. Two general methods are possible (1) the composition variables may be expressed in terms of the mole numbers before the differentiation and reintroduced after the differentiation or (2) expressions for the partial molar quantities may be obtained in terms of the derivatives of the intensive quantity with respect to the composition variables. In the remainder of this section several examples are given with emphasis on the second method. Multicomponent systems are used throughout the section in order to obtain general relations. 

Here, is termed the specific chemical enthalpy, B, the specific thermal enthalpy and Bp the specific pressure enthalpy. The combination of the specificrthermal enthalpy, Bp, and the specific pressure enthalpy, Bp, may he named the specific physical enthalpy. When the material species is one of the components in a solution, Equations A-l through A-7 are valid, provided that the specific quantities are changed to the partial molar quantities. Note that superscript 0 refers to the standard state, and subscript 0 refers to the dead state cp is the specific heat, and v is the specific volume. 

How well do the sedimentation coefficients and densities predicted by the model match the values actually observed for LDL Excellent agreement with the experimental points is shown by the solid curve of Fig. 2, which is a plot of the values for 525,1.20 given in Table II. However, this agreement was achieved by selecting a value for the partial specific volume of the cholesteryl esters to make the best fit, yielding the value of 1.058 ml/g for this this quantity. [If a value of 1.044 ml/g were employed for the partial specific volume of the cholesteryl esters, as was used by Sata et al. (1972), the values of 525,1.20 listed in Table II would have decreased by about 3,5%. The values of S[ in Table II would have dropped by 1 to 2 Svedbergs.]... 

E4. Edelstein, S. J., and Schachman, H. K., The simultaneous determination of partial specific volumes and molecular weights with microgram quantities. /. Biol. Chem. 242, 306-311 (1967). 

To characterize the thermodynamic behavior of the components in a solution, it is necessary to use the concept of partial molar or partial specific functions. The partial molar quantities most commonly encountered in the thermodynamics of polymer solutions are partial molar volume Vi and partial molar Gibbs free energy Gi. The latter quantity is of special significance since it is identical to the quantity called chemical potential, pi, defined by... 

For convenience, we generalize the concept of the partial molal quantity defined in Eq. (2-5) to include the specification of constant electric field. Thus, we write... 

We denote by y all specific partial thermodynamic quantities of constituents and by y corresponding specific total (or for mixture) thermodynamic quantities ... 

A change of independent variables from mixture invariant r, py to mixture invariant T, P, wp, may be done also for primed quantities, specifically for (4.224) fa = a(T, P, u)p) and therefore (4.216) is valid also for primed partial thermodynamic quantities (see (4.226))... 

Results (4.265) and (4.211) permit to obtain partial specific thermodynamic quantities ya (fulfilling Gibbs-Duhem equations (4.263) of course) from specific thermodynamic quantities y = y(T, P, vop) of the mixture (measurable in accord with then-mixture invariance) and their dependence on composition as follows... 

Relations (4.283)-(4.286) in uniform mixture permit to express the partial specific thermodynamic quantities from extensive (4.283) as ([59], i.e. as an analogue of the molar classical definition [138, 141])... 

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