The Case of an Ideal Solution

This equation is also known as the Lewis-Randall rule. It can be used for the determination of the fugacity of a mixture component through its fugacity in the pure state - at the same P and 7 as the mixture and in the same phase. 

12 is applicable to ideal mixtures only, i.e. mixtures of similar compounds. It does provide, however, a good approximation for /j in nonideal systems at high mole fractions of component /, where - as we saw in Example 11.2 - ideal solution behavior with respect to component i is approached. The accuracy declines, of course, with decreasing mole fraction of component i and with increasing nonideality of the solution. 

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The reasons for distinguishing enantiomer excess and optical purity of a product are again practical. As will be discussed in Section A.3., optical purity and enantiomer excess are equivalent only in the case of an ideal solution, i.e., in general ee = op. Furthermore, reliable reference values of xmal are rarely available. Thus, the op value is often a fairly unreliable measurement, and this should be apparent. 

Consider the case of an ideal solution involving a solute, which is a crystalline material at the solution temperature, dissolved in a liquid solvent. Even though the partial molal enthalpy of mixing is still zero because it is an ideal solution, there is an enthalpy requirement to overcome the crystal structure interactions. The van t Hoff equation (Adamson, 1979) gives... 

There remains the problem of eliminating the dependence of the reference chemical potential on the properties of the solution. For this purpose we adopt a different procedure We return to Eq. (2.5.12a), and consider the case of an ideal solution, to which (2.5.10b) also applies, so that Cj/xi cf. Then... 

An alternative assumption is that the equilibrium mixture is an ideal solution. This requires application of Eq. (4-371). However, in the case of an ideal solution Eq. (4-218) indicates that = ([), in which case Eq. (4-371) for a single reaction becomes... 

Under conditions of low pressure when the fugacity coefficient for the vapor is nearly 1.00, then K becomes Eq. (16), which for the case of an ideal solution can... 

For a given solvent at a given temperature RT/V is a constant, and therefore P oc (w - Tr )jir This is the relation between the osmotic pressure P and the solvent pressure ir in the case of an ideal solution This view attributes the phenomenon of osmotic pressure to the solvent primarily... 

Relation between the Osmotic Pressure and the Vapour Pressure It is well known that the vapour pressure of the solvent over the pure solvent is greater than its vapour pressure over the solution In the case of an ideal solution, this is due to the fact that the solvent pressure in the interior of the solvent is greater than the solvent piessure inside the solution, for the greater the solvent pressure, the greater, cetens paribus, the vapour pressure Tinker assumes that they are related to one another by the Dieterici expression, viz —... 

Case 1 If the intermolecnlar forces between A and B molecules are weaker than those between A molecules and between B molecules, then there is a greater tendency for these molecules to leave the solution than in the case of an ideal solution. Consequently, the vapor pressure of the solution is greater than the sum of the vapor pressures as predicted by Raoult s law for the same concentration. This behavior gives rise to the positive deviation [Fignre 12.9(a)]. In this case, the heat of solution is positive (that is, mixing is an endothermic process). 

In the case of an ideal solution, = 0, and since A5m is always positive, the value of AG is negative. When the solution does not behave ideally, a simple relation for Mlm has been proposed the van Laar expression for any two-component system based on the cell model for a liquid mixture [8,9],... 

We note that relation [5.9] is reduced to relation [5.8] in the case of an ideal solution for which the coefficient of activity is 1 (or independent of the concentration). 

From a molecular standpoint, this result makes sense. At a given temperature, the molecules in the liquid have a fixed kinetic energy. However, the unlike interactions in the liquid are not as strong as the like interactions. Thus, the two species when mixed are not held as vigorously in the liquid phase. More molecules, therefore, escape to the vapor than in the case of an ideal solution, and the pressure exerted is higher. 

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