Solutions, ideal nonideal

A solution which obeys Raoult s law over the full range of compositions is called an ideal solution (see Example 7.1). Equation (8.22) describes the relationship between activity and mole fraction for ideal solutions. In the case of nonideal solutions, the nonideality may be taken into account by introducing an activity coefficient as a factor of proportionality into Eq. (8.22). 

Solntions in which the concentration dependence of chemical potential obeys Eq. (3.6), as in the case of ideal gases, have been called ideal solutions. In nonideal solntions (or in other systems of variable composition) the concentration dependence of chemical potential is more complicated. In phases of variable composition, the valnes of the Gibbs energy are determined by the eqnation... 

An important attribute of Equation 5.16 is that the pressure exerted on both phases, Ptot, is common to both isotopomers. The important difference between Equations 5.16 and 5.9 is that the isotopic vapor pressure difference (P/ — P) does not enter the last two terms of Equation 5.16 as it does in Equation 5.9. Also isotope effects on the second virial coefficient AB/B = (B — B)/B and the condensed phase molar volume AV/V are significantly smaller than those on AP/P ln(P7P). Consequently the corrections in Equation 5.16 are considerably smaller than those in Equations 5.9 and 5.10, and can sooner be neglected. Thus to good approximation ln(a") is a direct measure of the logarithmic partition function ratio ln(Qv Q7QvQcO> provided the pressure is not too high, and assuming ideality for the condensed phase isotopomer solution. For nonideal solutions a modification to Equation 5.16 is necessary. 

Otherwise, the solution is nonideal, and the deviation from the ideal is described by means of the activity coefficient... 

Like gases, solutions can also be thought of as ideal. Raoult s law only works for ideal solutions. Ideal solutions are described as those solutions that follow Raoult s law. Solutions that deviate from Raoult s law are nonideal. What makes a solution deviate from ideal behavior The main reason is intermolecular attractions between solute and solvent. When the attraction between solute and solvent is very strong, the particles attract each other a great deal. This makes it more difficult for solute particles to enter the vapor phase. As a result, fewer particles will enter that state and the vapor pressure will be lower than expected. Remember, Raoult s law operates on the assumption that the reason for a decrease in the number of particles leaving the solution is that fewer can be on the surface in order to leave. If, in addition to this, the solute particles are also holding more tightly to the solvent particles, then fewer will leave the surface than expected. The most ideal solutions are those where the solvent and solute are chemically similar. 

This equation is good for ideal solutions. For an ionic surfactant solution, the solution is nonideal even at very low surfactant concentration and gives a highly nonlinear dependence of osmotic pressure on concentration. This is expected because ionic surfactants have a high affinity for the interfaces of solution-vapor, solution-solid, and solution-membrane as well as for themselves (i.e., micellization). 

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. 

Fropi this equation we see that the infinite dilution panial molar property 02(7. P,. v 0> fs the amount by which the total property 0 changes as a result of the addition of one mole of species 2 to an infinitely large amount of species 1 (so that, V2 remains about zero). Note that if the solution were ideal, the total property 0 would change by an amount equal to the pure component molar property 0, however, since most solutions are nonideal, the change is instead equal to 02-... 

However, we know that the use of equilibrium constants based on concentration is correct only for ideal systems. For reactions at high pressure or in solution, the nonideality of the reaction mixture becomes important and equilibrium constants... 

The diffusion coefficients of ionic solutes show nonideal behavior with variation of composition of the solvent mixture in water-methanol binary mixtures. The degree of non-ideality of the solute diffusion is found to be similar to the nonideality that is observed for the diffusion of water and methanol molecules in these mixtures and is attributed to the enhanced stability of the HBs and formation of interspecies complexes in the mixtures. The diffusion coefficient of water is found to be minimum at 0-5 and that of methanol shows the minimum at = 0.7. However, the observed deviation from linear behavior with composition is found to be a bit weaker than that found in simulations of water-DMSO mixtures [11,12],... 

The first term in parenthesis on the right-hand side of eg. fi2.42l reflects entropic effects that arise from the number of possible ways that macromolecules and solvent can be arranged in space this term is also known as the combinatorial contribution. The second term on the right-hand side is the enthalpic contribution and arises from differences between polymer-polymer and polymer-solvent interactions this term is also referred to as the residual contribution (not to be confused with the residual properties introduced earlier, which measure deviations from the ideal-gas state). Even if this term is zero (i.e., x = o), the solution is nonideal due to the size difference between polymer and solvent. 

Thus, Pick s Second Law can be rigorously applied for the case of ffie interdiffusion of ideal solutions. For nonideal solutions, the simultaneous soittffon of Eqs. (D) and (B) can be carried out if density versus composition data ate available for the tysiem. ... 

Essentially, the activity of a species is its effective mole fraction. It is introduced in order to preserve the form of equations derived from ideal solution in nonideal situations. All of the deviations from ideality are contained within the activity. For nonideal solutions, we can further isolate this deviation from ideahty by invoking the activity coefficient ()/a)> which relates the activity and the mole fraction of the solute (5) ... 

The other term [i T ln(a,)] accounts for the influence of concentration on chemical potential. It is intuitively imderstandable that the concentration of a component, as well as its molecular structure, should influence the chemical potential of that component (and the free energy of the mixture). A very important feature of this term is the notion that chemical potentials vary linearly with the logarithm of concentration, in ideal or nearly ideal solutions. Although many solutions are nonideal and phase separation may dramatically alter the dependence of chemical potential on composition (eliminating its influence altogether under some circumstances), it is, nevertheless, useful to become very familiar with this important equation. 

Clearly if Ya is unity then the solution is ideal. Otherwise the solution is nonideal and the extent to which ya deviates from unity is a measure of the solution s non-ideality. In any solution we usually know [A] but not either a a or Ya- However we shall see in this chapter that for the special case of dilute electrolytic solutions it is possible to calculate ya- This calculation involves the Debye-Hdckel theory to which we turn in Section 2.4. It provides a method by which activities may be quantified through a knowledge of the concentration combined with the Debye-Huckel calculation of ya- First, however, we consider some relevant results pertaining to ideal solutions and, second in Section 2.3, a general interpretation of Ya-... 

The activity coefficients in Vieland s equation account for deviations from ideality in the properties of solutions. For solutions with ideal behavior, for brevity ideal solutions , they have a value of unity. For solutions with nonideal behavior ( nonideal solutions ) there exist numerous models for the calculation of activity coefficients, physically more or less grounded and more or less sophisticated. 

For solutions with nonideal behavior, the energies of the three different types of bonding between nearest neighbors in the solution, Eaa, bb and Eab, differ from each other, resulting in a nonzero enthalpy of mixing. The entropy of mixing can, but needs not necessarily, be conserved as for an ideal solution. 

Figures 7.4 and 7.5. One may show (Problem 7.17) that Eq 7.x is equivalent to an ideal solution of nonideal gases. (For ideal gases, z = 1.00 for all P and T.) For this mixing rule...

The simplest mixing rule leads to the L-R rule, an ideal solution of nonideal gases, which is very widely used and fairly reliable for modest pressures. 

C. Show that this is equivalent to an ideal solution of nonideal gases. 

In Raoult s law-type formulations, we normally take = ,-, (the L-R rule, and ideal solution of nonideal gases), but Chao and Seader retained and computed it from the Redlich and Kwong (RK) EOS, as described in detail in the next section and in Appendix F. For the liquid they departed radically from Raoult s law by replacing pt with (<))i)pure liquid r-P. Substituting this value in Equation 10.2 produces... 

We rarely have data on gas-phase nonideality, so we normally make the L-R assumption (an ideal solution of nonideal gases. Section 8.6.2), changing to K. ... 

Raoult s law is, of course, valid for mixtures of very similar compounds, i.e. ideal solutions. For nonideal solutions ... 

Intermolecular Forces and the Solution Process—Predictions about whether two substances will mix to form a solution involve knowledge of intermolecular forces between like and unlike molecules (Figs. 14-2 and 14-3). This approach makes it possible to identify an ideal solution, one whose properties can be predicted from properties of the individual solution components. Most solutions are nonideal. 

This chapter presents quantitative methods for calculation of enthalpies of vapor-phase and liquid-phase mixtures. These methods rely primarily on pure-component data, in particular ideal-vapor heat capacities and vapor-pressure data, both as functions of temperature. Vapor-phase corrections for nonideality are usually relatively small. Liquid-phase excess enthalpies are also usually not important. As indicated in Chapter 4, for mixtures containing noncondensable components, we restrict attention to liquid solutions which are dilute with respect to all noncondensable components. 

Condensed phases of systems of category 1 may exhibit essentially ideal solution behavior, very nonideal behavior, or nearly complete immiscibility. An illustration of some of the complexities of behavior is given in Fig. IV-20, as described in the legend. 

In general, one should allow for nonideality in the adsorbed phase (as well as in solution), and various authors have developed this topic [5,137,145-149]. Also, the adsorbent surface may be heterogeneous, and Sircar [150] has pointed out that a given set of data may equally well be represented by nonideality of the adsorbed layer on a uniform surface or by an ideal adsorbed layer on a heterogeneous surface. 

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