Solution ideal diluted

There are ideal solutions, ideally dilute solutions, and nonideal solutions. Ideal solutions are solutions made from compounds that have similar properties. In other words, the compounds can be interchanged within the solution without changing the spatial arrangement of the molecules or the intermolecular attractions. Benzene in toluene is an example of a nearly ideal solution because both compounds have similar bonding properties and similar size. In an ideally dilute solution, the solute molecules are completely separated by solvent molecules so that they have no interaction with each other. Nonideal solutions violate both of these conditions. On the MCAT, you can assume that you are dealing with an ideally dilute solution unless otherwise indicated however, you should not automatically assume that an MCAT solution is ideal. 

Solute, ideal-dilute solution, mole fraction basis /if = -I- T In xb... 

Solute, ideal-dilute solution, molality basis... 

An additional option allows the user to fit data for binary mixtures where one of the components is noncondensable. The mixture is treated as an ideal dilute solution. The solute... 

In analogy to the gas, the reference state is for the ideally dilute solution at c, although at the real solution may be far from ideal. (Teclmically, since this has now been extended to non-volatile solutes, it is defined at... 

The situation for electrolyte solutions is more complex theory confimis the limiting expressions (originally from Debye-Htickel theory), but, because of the long-range interactions, the resulting equations are non-analytic rather than simple power series.) It is evident that electrolyte solutions are ideally dilute only at extremely low concentrations. Further details about these activity coefficients will be found in other articles. 

The standard state of an electrolyte is the hypothetical ideally dilute solution (Henry s law) at a molarity of 1 mol kg (Actually, as will be seen, electrolyte data are conventionally reported as for the fonnation of mdividual ions.) Standard states for non-electrolytes in dilute solution are rarely invoked. 

Substances at high dilution, e.g. a gas at low pressure or a solute in dilute solution, show simple behaviour. The ideal-gas law and Henry s law for dilute solutions antedate the development of the fonualism of classical themiodynamics. Earlier sections in this article have shown how these experimental laws lead to simple dieniiodynamic equations, but these results are added to therniodynaniics they are not part of the fonualism. Simple molecular theories, even if they are not always recognized as statistical mechanics, e.g. the kinetic theory of gases , make the experimental results seem trivially obvious. 

The McMillan-Mayer theory offers the most usefiil starting point for an elementary theory of ionic interactions, since at high dilution we can incorporate all ion-solvent interactions into a limitmg chemical potential, and deviations from solution ideality can then be explicitly coimected with ion-ion interactions only. Furthemiore, we may assume that, at high dilution, the interaction energy between two ions (assuming only two are present in the solution) will be of the fomi... 

For example, the measurements of solution osmotic pressure made with membranes by Traube and Pfeffer were used by van t Hoff in 1887 to develop his limit law, which explains the behavior of ideal dilute solutions. This work led direcdy to the van t Hoff equation. At about the same time, the concept of a perfectly selective semipermeable membrane was used by MaxweU and others in developing the kinetic theory of gases. 

At the end of the 1930s, the only generally available method for determining mean MWs of polymers was by chemical analysis of the concentration of chain end-groups this was not very accurate and not applicable to all polymers. The difficulty of applying well tried physical chemical methods to this problem has been well put in a reminiscence of early days in polymer science by Stockmayer and Zimm (1984). The determination of MWs of a solute in dilute solution depends on the ideal, Raoult s Law term (which diminishes as the reciprocal of the MW), but to eliminate the non-ideal terms which can be substantial for polymers and which are independent of MW, one has to go to ever lower concentrations, and eventually one runs out of measurement accuracy . The methods which were introduced in the 1940s and 1950s are analysed in Chapter 11 of Morawetz s book. 

Equation 13 has an important implication a clathrate behaves as an ideally dilute solution insofar as the chemical potential of the solvent is independent of the nature of the solutes and is uniquely determined by the total solute concentrations 2K yK1.. . 2x yKn in the different types of cavities. For a clathrate with one type of cavity the reverse is also true for a given value of fjiq (e.g. given concentration of Q in a liquid solution from which the clathrate is being crystallized) the fraction of cavities occupied 2kVk s uniquely determined by Eq. 13. When there are several types of cavities, however, this is no longer so since the individual occupation numbers 2k2/ki . ..,2k yKn, and hence the total solute concentration... 

When a small amount of a strong molten electrolyte is dissolved in another strong molten electrolyte, the laws of ideal dilute solutions are obeyed until relatively high concentrations are attained, assuming occurrence of a virtually complete dissociation. 

First approaches at modeling the viscoelasticity of polymer solutions on the basis of a molecular theory can be traced back to Rouse [33], who derived the so-called bead-spring model for flexible coiled polymers. It is assumed that the macromolecules can be treated as threads consisting of N beads freely jointed by (N-l) springs. Furthermore, it is considered that the solution is ideally dilute, so that intermolecular interactions can be neglected. 

In most cases polymer solutions are not ideally dilute. In fact they exhibit pronounced intermolecular interactions. First approaches dealing with this phenomenon date back to Bueche [35]. Proceeding from the fundamental work of Debye [36] he was able to show that below a critical molar mass Mw the zero-shear viscosity is directly proportional to Mw whereas above this critical value r 0 is found to be proportional to (Mw3,4) [37,38]. This enhanced drag has been attributed to intermolecular couplings. Ferry and co-workers [39] reported that the dynamic behaviour of polymeric liquids is strongly influenced by coupling points. 

These classical molecular theories may be used to illustrate good agreement with the experimental findings when describing the two extremes of concentration ideally dilute and concentrated polymer solutions (or polymer melts). However, when they are used in the semi-dilute range, they lead to unsatisfactory results. 

Relaxation Time Behaviour in Ideally Dilute and Concentrated Solutions... 

First approaches to approximating the relaxation time on the basis of molecular parameters can be traced back to Rouse [33]. The model is based on a number of boundary assumptions (1) the solution is ideally dilute, i.e. intermolecular interactions are negligible (2) hydrodynamic interactions due to disturbance of the medium velocity by segments of the same chain are negligible and (3) the connector tension F(r) obeys an ideal Hookean force law. 

The ideality of the solvent in aqueous electrolyte solutions is commonly tabulated in terms of the osmotic coefficient 0 (e.g., Pitzer and Brewer, 1961, p. 321 Denbigh, 1971, p. 288), which assumes a value of unity in an ideal dilute solution under standard conditions. By analogy to a solution of a single salt, the water activity can be determined from the osmotic coefficient and the stoichiometric ionic strength Is according to,... 

However, a detailed model for the defect structure is probably considerably more complex than that predicted by the ideal, dilute solution model. For higher-defect concentration (e.g., more than 1%) the defect structure would involve association of defects with formation of defect complexes and clusters and formation of shear structures or microdomains with ordered defect. The thermodynamics, defect structure, and charge transfer in doped LaCo03 have been reviewed recently [84],... 

Activity coefficient — 1 when solution — ideal solution, i.e. very dilute solution. 

If the activity coefficients jj for all ions and electrons are constant, i.e. Henry s or Raoult s law or the law of ideally diluted solutions holds, Eqn (8.27) reads... 

Equation (15.13) can describe either an ideal solution [see Equation (14.7)] or a solution sufficiently dilute that Henry s law is followed [see Equation (15.5)]. In either case, it follows that... 

In what follows we shall always write A, = fC. We assume that the ligand is provided from either an ideal gas phase or an ideal dilute solution. Hence, A, is related to the standard chemical potential and is independent of the concentration C. On the other hand, for the nonideal phase, A will in general depend on concentration C. A first-order dependence on C is discussed in Appendix D. Note also that A, is a dimensionless quantity. Therefore, any units used for concentration C must be the same as for (Aq) . 

It should be noted that estimating Hemy s law constant assumes the gas obeys the ideal gas law and the aqueous solution behaves as an ideally dilute solution. The solubility and vapor pressure data inputted into the equations are valid only for the pure compound and must be in the same standard state at the same temperature. 

The solute and the solvent are not distinguished normally in such ideal mixtures, which are sometimes called symmetric ideal mixtures. There are, however, situations where such a distinction between the solute and the solvent is reasonable, as when one component, say, B, is a gas, a liqnid, or a solid of limited solubility in the liquid component A, or if only mixtures very dilute in B are considered (xb 0.5). Such cases represent ideal dilute solutions. 

Although Pb tends to - °o as Xb tends to 0 (and In Xb also tends to - °o), the difference on the right-hand side of Eq. (2.18) tends to the finite quantity pi, the standard chemical potential of B. At infinite dilution (practically, at high dilution) of B in the solvent A, particles (molecules, ions) of B have in their surroundings only molecules of A, but not other particles of B, with which to interact. Their surroundings are thus a constant environment of A, independent of the actual concentration of B or of the eventual presence of other solutes, C, D, all at high dilution. The standard chemical potential of the solute in an ideal dilute solution thus describes the solute-solvent interactions exclusively. 

Fig. 2.4 The vapor pressure diagram of a dilute solution of the solute B in the solvent A. The region of ideal dilute solutions, where Raoult s and Henry s laws are obeyed by the solvent and solute, respectively, is indicated. Deviations from the ideal at higher concentrations of the solute are shown. (From Ref. 3.)...

From Fig.7 the calculated 3 -values of 1i1 CgSOC-CjFNa solution at different surface tension are shown in Table B together with the X g- obtained from the adsorption data by the Gibbs theorem. For the 1i1 mixed solution, assuming ideal (as the solution is dilute), then ... 

For ideal (dilute) solutions the activity is replaced by the mole fraction x]s, which, for a two-component surface solution, equals (1 — x ). With the customary expansion of the logarithm as a power series (see Appendix A), these substitutions yield... 

Equation (1) may be applied to the equilibrium between vapor and liquid of a pure substance (X = vapor pressure) or to the equilibrium between an ideal dilute solution and the pure phase of a solute X = solubility) or to the equilibrium of a chemical reaction (X = equilibrium constant). 

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