Thermodynamics partial molal quantities

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. 

Aside from adsorption isotherm data one can use calorimetric techniques to obtain information on the thermodynamic properties of materials adsorbed on surfaces. The experimental techniques are now more involved but they do supply direct information on the heats liberated during the adsorption process. Here the use of partial molal quantities is imperative since increments of the heats of adsorption diminish with successive amounts of gas transferred to the adsorbed phase. Here we follow the systematic treatment furnished by Clark. ... 

One should always remember that it is difficult to proceed from thermodynamic measurements to molecular properties. This is particularly true in multicomponent systems. That is, water-water and water-protein interactions are inextricably mixed with protein-protein interactions when one measures partial molal quantities. Assumptions and experiments beyond those yielding thermodynamic information are needed to determine what is happening at the molecular level. The major cause... 

Composition Thermodynamic Data for the Formation of FeTiH Relative Partial Molal Quantities, 298 K ... 

In this section we describe two methods for determining partial molal quantities for two-component systems from experimental data. In both cases the experimental data necessary are the behavior of the extensive property G or, equivalently, the intensive property as a function of the mole fraction of one of the components. (More details can be found in the book Gilbert Newton Lewis and Merle Randall, Thermodynamics and the Free Energy of Chemical Substances, pp. 36-41, McGraw-Hill Book Company, Inc., New York, 1923.)... 

In thermodynamics of solutions, the partial molal quantity and the apparent molal quantity for a component are usually defined [66]. In the properties of enthalpy, one deals with quantities which cannot be measured in an absolute sense. It is thus necessary to use a reference state from which to make the evaluations. Since the state of infinite dilution of the solute in the solvent is taken as reference, the specification of the composition of the solution by means of the molality m2 of the solute is consequently most convenient for the calculation of enthalpy. 

In order to obtain thermodynamic properties of hydride compositions other than the hydrogen-deficient dihydride phase (which is normally in equilibrium with the metal phase), it is necessary to use partial molal quantities of hydrogen in the hydride, as illustrated for the calculation of enthalpy (n the following expression ... 

An extremely useful quantity in the thermodynamic treatment of multicomponent phase equilibria is the chemical potential. The chemical potential for component /, is the partial molal Gibbs free energy with respect to component i at constant pressure and temperature ... 

The partial molal free energy of a spray of finely dispersed droplets is not so simply related to escaping tendency as it is in systems usually treated by thermodynamic methods. Even the definition of the partial molal free energy is not entirely devoid of difficulty. To discuss equilibrium we wish to think of the transfer of a small amount of adsorbent from each droplet in the spray to another phase— e.g., the gas phase (16). If a little material leaves each droplet, there must be a concomitant decrease in surface area, A, and an increase in specific area, quantity related to escaping tendency of material is not the derivative of free energy with respect to n, the number of moles in the spray at either constant area or constant specific area. The condition is that the number of droplets, v, be constant. (This means that area divided by mass to the 2/3 power is nearly invariant.)... 

The above equations again correlate partial molal and molar energies and enthalpies only when all intensive variables are held fixed is the partial molal and molar enthalpy the same. In most cases one may drop the term involving Vs - One may also use Eqs. (5.2.2) to access other thermodynamic functions of interest in terms of differential quantities. 

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. 

The standard partial molal heat capacity of electrolytes, is probably the best thermodynamic property for providing information on ion-solvent interactions, but until very recently only two publications reported this quantity for electrolytes in non-aqueous systems. The reasons for the scarcity of data become obvious when one considers the formidable experimental and theoretical problems in obtaining this function. 

There has been much discussion in the literature about the volume of a molecule and its role in the interpretation of hydrodynamic properties. Therefore, before considering the question of the relation between the size and shape of the effective hydrodynamic eUipsoid and that of the dissolved protein particle, it is worthwhile to discuss this thermodynamic variable, i.e., volume, and a related quantity, the partial molal (or the partial specific) volume. 

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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