Partial molal quantities

The summation is taken over all species (including inerts) present in the system. For gaseous mixtures that follow ideal solution behavior the partial molal quantities may be replaced by the pure component values. 

A SLIGHTLY MORE RIGOROUS APPROACH. In the above description, the system was treated as though the reactants were ideal gases. A better approach is to account for the free energy of the system as a function of added reactants, and for solutions, the most technically correct action is to use partial molal quantities. Because free energy, G(T, P, ni, H2,. ..), is a state function depending on temperature, pressure, and the moles of... 

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... 

Fig. 1.6 Extensive variable (IF) versus composition at fixed temperature. By drawing tangent XY to the curve at arbitrary composition N, the partial molal quantities and can be obtained.

Herasymenko (6) has observed sharply varying partial molal heats and entropies of solution of cadmium in gold or in silver. Although he calculated continuous partial molal quantities, he noted that his changes appeared almost discontinuous. ... 

Note that, if the system is not ideal, then partial molal quantities A, aS, and aS must be used instead of the above. 

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 ... 

Partial molal quantity Written over small 1 - (Bar)... 

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... 

The relation (2-15) is of great significance, and it shows that the changes of partial molal quantities with composition are not mutually independent at constant temperature and pressure. 

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.)... 

The symbol Pi was first used by Gibbs and called by him the chemical potential of component i. It can be seen from Eq. (6-52) and the definition of partial molal quantities [Eq. (2-5)] that Pi is the partial molal free energy /( and is an intensive property. 

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... 

In all of these arguments, one must keep in mind that partial molal quantities of ions reflect not so much the absolute amount of structure around the ion, but rather the amount of structure around the ion relative to that of the pure solvent at that temperature. Thus, while the net amount of order in a solution decreases as the temperature increases, the effect of the ion on ordering the system, through ion-dipole interactions, relative to the pure solvent at that temperature continues to increase. 

Now we formally define a partial molal quantity represented by M as... 

Where reactions are carried out in solution, two situations are possible the solution can be dilute or concentrated. For dilute solutions, the concentration can be used directly as an exact measure of its activity. This is often justified in organic synthesis because normally solvents are used in large excess. But where the reactant concentration is high, its activity in solution cannot be replaced by concentration without an appropriate correction factor. Note that in both cases we would be dealing with partial molal quantities. 

Partial molar quantities are intensive properties of the solution since they depend only on the composition of the solution, not upon the total amount d each component. If we add the several components simultaneously, keeping their ratios constant, the partial molal quantities remain the same. We can thus integrate the above expression keeping nj, n2,. .. in constant proportions and find, while holding temperature and pressure constant, that... 

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