Of real solutions

Activity ax is termed the rational activity and coefficient yx is the rational activity coefficient This activity is not directly given by the ratio of the fugacities, as it is for gases, but appears nonetheless to be the best means from a thermodynamic point of view for description of the behaviour of real solutions. The rational activity corresponds to the mole fraction for ideal solutions (hence the subscript x). Both ax and yx are dimensionless numbers. 

The behaviour of real solutions approaches that of ideal solutions at high dilution. The molar conductivity at limiting dilution, denoted A0, is... 

To deal with the properties of real solutions, most workers determine the magnitude of a pure number that can be multiplied by the mole fraction to bring the equation of state back to an ideal form ... 

Obviously this picture might be supported and supplemented by according data from different experimental investigations, or it might be modified to fit these data. Interactions within the basic hydrated structures, as well as their energetics, are obtainable from gas-phase solvation experiments or from accurate MO calculations. For the simulation of real solutions, dynamic calculations will be inevitable. There is, however, a demand for acceptable effective potentials to be used in molecular dynamics, or in Monte Carlo calculations. 

We will begin, as we have in other chapters, with a discussion of the behavior of a hypothetical fluid known as an ideal solution. Then a study of the factors which cause real solutions to deviate from the behavior of ideal solutions will guide us in the development of methods to predict the behavior of real solutions. 

As in the case of ideal gases, ideal liquid solutions do not exist. Actually, the only solutions which approach ideal solution behavior are gas mixtures at low pressures. Liquid mixtures of components of the same homologous series approach ideal-solution behavior only at low pressures. However, studies of the phase behavior of ideal solutions help us understand the behavior of real solutions. 

Chemical Potentials of Real Solutions. Activity, a and Activity Coefficients, f... 

The activity a2 of an electrolyte can be derived from the difference in behavior of real solutions and ideal solutions. For this purpose measurements are made of electromotive forces of cells, depression of freezing points, elevation of boiling points, solubility of electrolytes in mixed solutions and other characteristic properties of solutions. From the value of a2 thus determined the mean activity a+ is calculated using the equation (V-38) whereupon by application of the analytical concentration the activity coefficient is finally determined. The activity coefficients for sufficiently diluted solutions can also be calculated directly on the basis of the Debye-Hiickel theory, which will bo explained later on. 

In this brief review of salt solutions, we start by examining ionic hydration. We then examine from the standpoint of ion-ion interactions the properties of real solutions and how these are affected by ionic hydration (Blandamer, 1970). 

We shall now proceed with the methodology for determining a, and we return later to the question of determining the extent of the departure of real solutions from Raoult s Law. 

The real solutions used to study the characteristics of macromolecular solutes are rarely ideal even at the highest dilutions that can be used in practice. The expressions derived earlier for ideal solutions arc therefore invalid in the experimental range. It is useful, however, to retain the form of the ideal equations and express the deviation of real solutions in terms of empirical parameters. Thus the usual practice in micromolecular thermodynamics is to retain Eq. (2-62) but substitute fictitious concentrations, called activities, for the experimental solute concentrations. In polymer science, on the other hand, the measured concentrations are taken as accurate and deviations from ideality are expressed in the coefficients of the concentration terms. 

Linear viscoelastic behavior is actually observed with polymers only in very restricted circumstances involving homogeneous, isotropic, amorphous specimens subjected to small strains at temperatures near or above Tg and under test conditions that are far removed from those in which the sample may be broken. Linear viscoelasticity theory is of limited use in predicting service behavior of polymeric articles, because such applications often involve large strains, anisotropic objects, fracture phenomena, and other effects which result in nonlinear behavior. The theory is nevertheless valuable as a reference frame for a wide range of applications, just as the thermodynamic equations for ideal solutions help organize the observed behavior of real solutions. 

To Buckingham et al. is due the theory of the Kerr effect in dilute solutions, whereas Kielich developed a statistical theory of the effect for multi-component systems of an arbitrary degree of concentration and showed the Kerr constant of real solutions to be a non-additive quantity. 

This occurs because solutions of real substances do not necessarily conform to the theoretical relationships predicted for dilute solutions of so-called ideal solutes. It is often necessary to take account of the non-ideal behaviour of real solutions, especially at high solute concentrations (see Tide (2000) for appropriate data). 

THERMODYNAMIC DESCRIPTION OF REAL SOLUTIONS IN THE CONDENSED STATE 163... 

Thermodynamic Description of Real Solutions in the Condensed State... 

Since then further progress has extended the field of applicability of Gibbs chemical thermodynamics. Thus the introduction of the ideas of fugacity and activity by G. N. Lewis enabled the thermodynamic description of imperfect gases and of real solutions to be expressed with the same formal simplicity as that of perfect gases and ideal solutions. These results were completed when N. Bjerrum and E. A. Guggenheim introduced osmotic coefficients. 

The concept of an ideal solution is important in the development of an understanding of the properties of real solutions. In a liquid solution, molecules are in intimate contact with one another so that the question of ideality is determined by the nature of the intermolecular forces. Suppose a solution is formed by mixing two liquids, A and B. Then, the solution is ideal if the intermolecular forces between A and B molecules are no different from those between A and A, or B and B molecules. 

Some liquid mixtures obey Raoult s law, but most of the solutions deviate from this. Thus, the name ideal liquid solutions is defined for solutions that obey Raoult s law. Similarly to real gases, real solutions that do not obey Raoult s law should also be expressed by thermodynamical equations. Since we can still measure the vapor pressure of real solutions, instead of the mole fraction XA term in Equation (164), we may write... 

Activity coefficient is a function of the state of a mixture. An activity-coefficient equation is required to calculate the fugacities of real solutions. The interrelationship of the activity coefficients through the Gibbs-Duhem equation implies that the activity-coefficient equations of aU components are derivatives of a common thermodynamic function. Since the activity coefficient is an expression of the nonideal behavior of a component, a thermodynamic function is needed to express the nonideality of the total solution and then to obtain from it the activity-coefficient equation. 

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