THE IDEAL SOLUTION

The ideal solution is defined thermodynamically as one in which the dependence of the chemical potential of each component on the composition is expressed by 

The standard state for the chemical potential of each component in the solution is thus defined as the pure component at the same temperature and pressure and in the same state of aggregation as the solution. We say that the chemical potential of the fcth component in a solution at the temperature T, pressure P, and composition x referred to the pure fcth component at the same T and P and in the same state of aggregation is equal to RT In xk. This difference is also known as the change of the chemical potential on mixing at constant temperature and pressure, so 

The quantity AGM is called the change of Gibbs energy on mixing at constant temperature and pressure or, more briefly, the Gibbs energy of mixing. 

By appropriate differentiation of Equations (8.57), (8.59), and (8.60), we obtain the corresponding expressions for the entropy. Thus, 

A large number of chemical processes are carried out in solution and the application of chemical thermodynamics to solutions is an important part of the subject. Solutions can be gaseous, liquid, or solid. In this chapter we shall be concerned largely with solutions that are in the liquid state, for instance, mixtures of two liquids or the solution of a solid in a liquid. It is often convenient to refer to the substance which predominates in a solution as the solvent and to the minor constituent as the solute. In some solutions the components are miscible in all proportions. Thus ethanol and water will mix to form a homogeneous mixture whatever the relative quantities of ethanol and water. Other components will show limited mutual solubility. For example, only a limited amount of sodium chloride can be dissolved in water at any particular temperature. However much NaCl we add to a beaker of water the concentration of the salt will not exceed the value corresponding to a saturated solution. Some pairs of non-ionic substances, such as phenol and water, also show limited mutual solubility. 

The concept of an ideal solution is of great value in thermodynamics. We shall define it, for the moment, as a solution in which the total vapour pressure is given by Raoult s Law, 

The term in the square brackets is constant at any temperature and is in fact the chemical potential of the pure liquid i, fif (l), as for a pure liquid in equilibrium with its vapour 

We must note when we write, for the perfect gas, the equation 

The PV term is generally small and unless many atmospheres pressure are involved it is usually safe to ignore it (for instance when the vapour pressure of a liquid is not 1 atm). To simplify the notation for the standard states when applied to solutions we shall continue to use the standard states defined at 1 atm. We shall assume that the approximate equation 

Historically, an ideal solution was defined in terms of a liquid-vapor or solid-vapor equilibrium in which each component in the vapor phase obeys Raoult s law. 

Chemical Thermodynamics Basic Concepts and Methods, Seventh Edition. By Irving M. Klotz and Robert M. Rosenberg 

If the vapor does not behave as an ideal gas, the appropriate equation corresponding to Equation (14.1) is 

Equation (14.2) clearly reduces to the historical form of Raoult s law [Equation (14.1)] when the vapors are an ideal mixture of ideal gases. 

The ideal gas is a useful model of tlie behavior of gases, and serves as a standard to wliich real-gas belravior can be compared. Tliis is formalized by the introdnction of residual properties. Another useful model is tire ideal solution, wliich serves as a standard to wliich real-solution behavior can be compared. We will see in the following section how tliis is formalized by introdnction of excess properties. 

Equation (11.26) establishes tire belravior of species i m an ideal-gas mixture  

Tliis equation takes on a new dimension when G f, the Gibbs energy of pure species i m the ideal-gas state, is replaced by Gj, tire Gibbs energy of pure species i as it actually exists at tire mixhire T and P and hr tire same physical state (real gas, liquid, or solid) as the mixture. It then applies to species in real solutions. We therefore define an ideal solution as one for which  

All otlier themiodynamic properties for an ideal solution follow from Eq. (11.72). The partial entropy results from differentiation with respect to temperature at constant pressure and composition and then combination with Eq. (11.18) written for an ideal solution  

The summability relation, Eq. (11.11), applied to the special case of an ideal solution is written  

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Various functional forms for / have been proposed either as a result of empirical observation or in terms of specific models. A particularly important example of the latter is that known as the Langmuir adsorption equation [2]. By analogy with the derivation for gas adsorption (see Section XVII-3), the Langmuir model assumes the surface to consist of adsorption sites, each having an area a. All adsorbed species interact only with a site and not with each other, and adsorption is thus limited to a monolayer. Related lattice models reduce to the Langmuir model under these assumptions [3,4]. In the case of adsorption from solution, however, it seems more plausible to consider an alternative phrasing of the model. Adsorption is still limited to a monolayer, but this layer is now regarded as an ideal two-dimensional solution of equal-size solute and solvent molecules of area a. Thus lateral interactions, absent in the site picture, cancel out in the ideal solution however, in the first version is a properly of the solid lattice, while in the second it is a properly of the adsorbed species. Both models attribute differences in adsorption behavior entirely to differences in adsorbate-solid interactions. Both present adsorption as a competition between solute and solvent. 

The entropy of mixing of very similar substances, i.e. the ideal solution law, can be derived from the simplest of statistical considerations. It too is a limiting law, of which the most nearly perfect example is the entropy of mixing of two isotopic species. 

The ideal solution is a model fluid which serves as a standard to which teal solution behavior can be compared. Equation 151, which characterizes the... 

In the past, for many air pollution control situations, a change to a less polluting fuel offered the ideal solution to the problem. If a power plant was emitting large quantities of SO2 and fly ash, conversion to natural gas was cheaper than instaUing the necessary control equipment to reduce the pollutant emissions to the permitted values. If the drier at an asphalt plant was emitting 350 mg of particulate matter per standard cubic meter of effluent when fired with heavy oil of 4% ash, it was probable that a switch to either oil of a lower ash content or natural gas would allow the operation to meet an emission standard of 250 mg per standard cubic meter. 

The ideal solution law, Henry s Law, also enters into the establishment of performance of ideal and non-ideal solutions. 

Consider now the non-ideal solution of a completely dissociated uni-divalent salt, and its comparison with the corresponding ideal solution. In choosing the ideal solution, if we denote the two solute species by B and C, we must obviously take a solution that contains twice as many... 

Figure 6.5 Vapor pressures for x,c-C6HnCH +. v c-C(,Hi2 at T= 308.15 K. The symbols represent the experimental vapor pressures as follows , vapor pressure of c-C6Hi2 , vapor pressure of c-C6HnCHi , total vapor pressure. The dashed lines represent the ideal solution prediction.

We repeat that ideal solutions, like ideal gases, do not exist. But like the ideal gas, the ideal solution has an application as a reference state, and it is important to know the conditions under which Raoult s law is a good... 

Figure 6.10 Representative deviations from ideal solution behavior allowed by the Duhem-Margules equation. The dotted lines are the ideal solution predictions. The dashed lines giveP2IP2 (lower left to upper right), and p jp (upper left to lower right).

Figure 6.12 Activity (ai and a ) for. yi(C4H9)20 +. V2CCI4 at 7= 308.15 K. The dashed lines are the ideal solution predictions.

Equation (7.6) is the starting point for deriving equations for Amix2[j[, the change in Zm for forming an ideal mixture. For the ideal solution, 7r.( = 1 and equation (7.6) becomes... 

Figure 8.20 (Solid + liquid) phase equilibria for [.viQHf, +. yl.4-C6H4(CH,)2 - The circles are the experimental results the solid lines are the fit of the experimental results to equation (8.31) the dashed lines are the ideal solution predictions using equation (8.30) the solid horizontal line is at the eutectic temperature and the diamonds are (.v, T) points referred to in the text.

Figure 8.21 gives the ideal solution prediction equation (8.36) of the effect of pressure on the (solid + liquid) phase diagram for. yiC6H6 + xj 1,4-C6H4(CH3)2. The curves for p — OA MPa are the same as those shown in Figure 8.20. As... 

Figure 8.23 (Solid + liquid) phase diagram for (. 1CCI4 +. yiCHjCN), an example of a system with large positive deviations from ideal solution behavior. The solid line represents the experimental results and the dashed line is the ideal solution prediction. Solid-phase transitions (represented by horizontal lines) are present in both CCI4 and CH3CN. The CH3CN transition occurs at a temperature lower than the eutectic temperature. It is shown as a dashed line that intersects the ideal CH3CN (solid + liquid) equilibrium line.

Any convenient model for liquid phase activity coefficients can be used. In the absence of any data, the ideal solution model can permit adequate design. 

Eq. (29) is closely related to the classical melting point depression and solubility expression for solutions of simple molecules. In the case of the ideal solution, for example, m2 m2= In N2, N2 being the... 

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. 

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