Solutions truly ideal

The term solubility thus denotes the extent to which different substances, in whatever state of aggregation, are miscible in each other. The constituent of the resulting solution present in large excess is known as the solvent, the other constituent being the solute. The power of a solvent is usually expressed as the mass of solute that can be dissolved in a given mass of pure solvent at one specified temperature. The solution s temperature coefficient of solubility is another important factor and determines the crystal yield if the coefficient is positive then an increase in temperature will increase solute solubility and so solution saturation. An ideal solution is one in which interactions between solute and solvent molecules are identical with that between the solute molecules and the solvent molecules themselves. A truly ideal solution, however, is unlikely to exist so the concept is only used as a reference condition. 

Monomer added at the end of polymerizations linked to chains already present and molecular weights were determined solely by the monomer/initiator ratio. However, dispersity ratios, MJMn, do not approach the values (1.02-1.05) attained in truly ideal living polymerizations. The molecular weight distributions of polymer formed when monomer is added slowly to initiator solutions were even broader suggesting that initiation is slower than propagation. 

Very few mixtures form truly ideal solutions in which both components follow the equation Hi — h + RTlnXi over all the composition range and over a range of temperatures. The total free energy of a solution is given by... 

Though few solutions are truly ideal, essentially all show the characteristics of ideality when dilute. Fig. 6.6 illustrates that in a dilute solution the partial... 

When we looked at the solubility of naphthalene in various solvents (Section 6.4), we found that in benzene the actual solubility was close to the truly ideal value, as predicted on the basis of Raoult s Law, but in both hexane and methanol it was considerably lower. The chemical potential of the solid solute (and hence its activity in the solid state) is the same in all cases the activity of the naphthalene in solution must also be identical, for at equilibrium... 

Thus for hexane y — 0.30/0.12 = 2.5. The activity coefficient greater than unity indicates that a smaller quantity of naphthalene in solution is necessary for it to attain the chemical potential of solid naphthalene than if the solution were truly ideal. We could say that as the naphthalene does not like being in the solution its tendency to stay in the solid state is greater. 

Although no real mixture is truly ideal, we can often use the concept of an ideal solution to reduce the labor needed to compute property values for real mixtures. To do so we introduce, for each property f, an excess property/. ... 

An interesting question, which is closely related to the VPIE, is the deviation of isotopic mixtures from the ideal behavior. Isotopic mixtures, that is, mixtures of isotopic molecules (e.g., benzene and deuterated benzene), have long been considered as textbook examples of ideal solutions statistical theory predicts that mixtures of very similar species, in particular isotopes, will be ideal the only truly ideal solutions would thus involve isotopic species molecules which differ only by isotopic substitution... form ideal solutions except for isotope mixtures, ideal solutions will occur rather rarely we expect binary solutions to have ideal properties when the two components are isotopes of each other. ... 

In practice, few solutions are truly ideal. They involve energies of mixing. In the lattice model, the total energy of mixing is the sum of the contact interactions of noncovalent bonds of all the pairs of nearest neighbors in the mixture. For a lattice solution of A and B particles. Figure 15.4 shows the three possible types of contact an AA bond, a BB bond, or an AB bond. There are no other options, because the lattice is completely filled by A s and B s. 

On the other hand, the theoretical or hypothetical osmotic pressure ( rth) that we would have calculated if the system had been a truly ideal dilute solution is... 

There are essentially two problems concerning the LIP, which we will consider in turn. Firstly, what is the concentration of iron in the LIP And secondly, what is its nature Perhaps, we should add a codicil, namely how can we measure either of these without provoking a redistribution of iron which totally distorts the subsequent picture. In order to circumvent this problem, in vivo approaches have been developed, which we will now discuss - however, the ideal solution to resolving the problem raised in our codicil would be to use truly non-invasive analytical methods, which do not perturb subtle intracellular equilibria. 

The ideal HPLC detector should have the same characteristics as those required for GC detectors, i.e. rapid and reproducible response to solutes, a wide range of linear response, high sensitivity and stability of operation. No truly universal HPLC detector has yet been developed but the two most widely applicable types are those based on the absorption of UV or visible radiation by the solute species and those which monitor refractive index differences between solutes dissolved in the mobile phase and the pure mobile phase. Other detectors which are more selective in their response rely on such solute properties as fluorescence, electrical conductivity, diffusion currents (amperometric) and radioactivity. The characteristics of the various types of detector are summarized in Table 4.14. 

This paper shows that the conditions of thermodynamic equilibrium in a mix-tine of chemically reacting ideal gases always have a solution for the concentrations of the mixture components and that this solution is unique. The paper has acquired special significance in the last few years in connection with the intensive study of systems in which this uniqueness does not occur. Such anomalies may be related either to nonideal components, or to treatment of stationary states, rather than truly equilibrium ones, in which the system exchanges matter or energy with the surrounding medium. 

Thus, for a given value of the relative composition of the feed, the intensity of the tag-along effect, like the intensity of the displacement effect, depends strongly on the ratio of the two column saturation capacities. Note, however, that the solution of the ideal model for a binary mixture that is discussed in this chapter assumes that the Langmuir competitive model is valid. But the Langmuir competitive model is truly valid only if 5,1 = qsg-... 

There are numerous variations on free solution CE (FSCE), such as micellar electrokinetic capillary chromatography (MECC or MEKC), where a moving, pseudostationary phase is added to the CE buffer, and secondary chemical equilibria or interactions ensue that effect separations of even neutral compounds, as well as ionic analytes. However, in general, CE utilizes truly homogeneous, solution phase separation approaches, without a stationary (permanent, fixed) phase, making it perhaps ideally suited for molecular recognition in searching combinatorial libraries. 

At this point we can write out the defining equations of a truly non-ideal solution (equations (15.3)). This would be one for which all properties in addition to the enthalpy differ from the ideal values. Here again, the subscript non-ideal dissol n refers to the difference between a non-ideal solution and a mechanical mixture of its pure components ... 

Aqueous solutions can be modeled by writing a virial equation such as (17.37) in which osmotic pressure replaces pressure. Friedman (1962) describes applications of cluster expansion theory, which include long-range Coulombic potentials as well as short-range square-well potentials that operate when unlike ions approach within the diameter of a water molecule. These models are mathematically quite cumbersome and are not easily used for routine calculations. They do predict the non-ideal behavior of simple electrolytes such as NaCl quite admirably at moderate concentrations however, they use the square-well potential as an adjustable parameter and so retain some of the properties of the D-H equation with an added adjustable term. For this reason these are not truly a priori models. 

In many respects, liquids represent a nearly ideal specimen type. If all elements are in solution, the sample is truly homogeneous and obviously no particle size effects are present. Standards are easily prepared and excellent quantitative results are possible. The major drawbacks arise from the dilution factor with resulting decreased intensities and the difficulty of analyzing low-atomic-number elements whose radiations must pass through the window of the sample cell. On the other... 

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