Apparent molar quantities

Some authors (4,5,6,9,10) have used the apparent molar quantity d>/2, where... 

When a solute particle is introduced into a liquid, it interacts with the solvent particles in its environment. The totality of these interactions is called the solvation of the solute in the particular solvent. When the solvent happens to be water, the term used is hydration. The solvation process has certain consequences pertaining to the energy, the volume, the fluidity, the electrical conductivity, and the spectroscopic properties of the solute-solvent system. The apparent molar properties of the solute ascribe to the solute itself the entire change in the properties of the system that occur when 1 mol of solute is added to an infinite amount of solution of specified composition. The solvent is treated in the calculation of the apparent molar quantities of the solute as if it had the properties of the pure solvent, present at its nominal amount in the solution. The magnirndes of quantities, such as the apparent molar volume or heat content, do convey some information on the system. However, it must be realized that both the solute and the solvent are affected by the solvation process, and more useful information is gained when the changes occurring in both are taken into account. 

If the concentration of solute 3 Is sufficiently low, relative to Its CMC, the transfer functions become Identical for partial and apparent molar quantities and are said to approach the standard state. 

The densities and volumetric heat capacities of the binary systems, which are required for the calculation of the transfer functions, were measured at the same time as those of the ternary systems. The derived apparent molar quantities of the binaries were In excellent agreement with those In the literature (11,16). 

From these data It Is possible to calculate the transfer functions of BE from water to a solution of NaDec. In general, for any transfer function defined In terms of apparent molar quantities,... 

APPARENT MOLAR QUANTITY. For a solution containing i moles of solvent and n% moles of solute, an apparent molar quantity is defined as... 

It can be shown by starting with the definition of the apparent molar property and differentiating that the apparent molar quantities are related by the same equations as the molar quantities. Thus if,... 

Apparent molar quantities (sometimes called apparent molal quantities) are used primarily for binary systems, and are usually expressed as functions of the molality. These quantities are used because in many cases their values are readily obtained by experiment. The general apparent molar quantity, (f>X, is defined as... 

Apparent molar quantities for multicomponent systems, other than binary systems, have been used to only a limited extent because of the difficulty of dealing with more than two mole numbers. Actually, there is no single definition of an apparent molar quantity for such systems. If we limit the discussion to the volume and refer to the definition of the apparent molar volume of the binary system (Eq. 6.53)), then we see that for multicomponent systems we must consider the difference between the volume of the solution and some other volume, and the meaning of the molar quantity. There appear to be two possible cases for these definitions. In the first case we could choose... 

We might proceed by plotting versus m, drawing a smooth curve through the points, and constructing tangents to the curve at the desired concentrations in order to measure the slopes. However, for solutions of simple electrolytes, it has been found that many apparent molar quantities such as tp vary linearly with yfm, even up to moderate concentrations. This behavior is in agreement with the prediction of the Debye-Hiickel theory for dilute solutions. Since... 

Although partial molar quantities are in principle measurable from slopes or intercepts as in Figures 9.3 and 9.5, they are not actually measured in this way. In practice, apparent molar quantities are determined, and the corresponding partial molar quantities are calculated from these. It is standard practice to let component 1 refer to the... 

Conductance measurements on dilute solutions are of special interest for electrolyte theory. These measurements can be carried out at high precision for almost all electrolytes in almost all solvents at various temperatures and pressures and thus provide an efficient method for determining the basic data of electrolyte solutions, i.e. A , and R, under various conditions. Values of and R are found to be compatible with the values obtained from thermodynamic methods. The enthalpies and volumes of ion-pair formation, AH and AV, as determined from temperature- and pressure-dependence of conductance, are compatible with the corresponding relative apparent molar quantities, ii (IP) and Ov (IP), from thermodynamic measurements, cf. Section 5.2. R-vahies are found to be almost independent of temperature. 

FIGURE 1 Determination of partial molar quantities Z2 and apparent molar quantities z from measurements of extensive thermodynamic quantities Zpj n n2) (also AZ2 from AZ see Section III.B). 

Solution chemistry also makes use of another type of molar quantity, the so-called apparent molar quantity 4>z of the solute Y, according to... 

Yi being the solvent. The apparent molar quantity 4>z is also shown in Fig. 1. The advantage of apparent molar quantities is their direct access from experimental data, z = (Z — n Z )lYi2 Comparison of Eqs. (52) and (53) yields the relations... 

Besides partial molar and apparent molar quantities, thermodynamics makes use of relative quantities such as (Zi — Zp, (Zi — Z ), or (Oz - resulting from mixing or solution processes. 

Another useful formulation of the extensive property Z is based on the definition of apparent molar quantities Oz of the solute, which yields... 

The advantage of using apparent molar quantities is the direct accessibility of d>z from experimental results, < z = (Z-nsZp/ny [Eq. (41)]. 

In a recent study of the a, co-amino acids, Chalikian et al. [93C] determined apparent molar quantities over the concentration range 1 - 3 mg mL Within the limits of the experimental errors, the results obtained were considered to be the same as partial molar compressibilities at infinite dilution. 

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