Lewis-Randall ideal solution

In 4.5.5 we computed residual properties for gaseous mixtures of methane and sulfur hexafluoride mixtures at 60°C and 20 bar. In 5.3.1 and 5.3.2 we computed excess properties for this same mixture. We can also compute residual properties for the ideal solution (Lewis-Randall standard state). Comparisons of these three kinds of difference measures are shown in Table 5.1 for equimolar mixtures. We see that the equimolar mixture of methane and sulfur hexafluoride exhibits positive deviations... 

You will recognize Equation (8.3) as Raoult s law, which you have undoubtedly seen before. It directly results from the criteria for equilibrium [Equation (8.1)] under the special circumstances described above (ideal gas, ideal solution, Lewis/Randall reference state). This equation is convenient, since the saturation pressure of species i depends only on the temperature of the system. The relation between Pf and T is commonly fit to the Antoine equation. Appendix A.l provides Antoine equation parameters for several species. 

The fugacity of species B in an ideal solution of gases is given by the Lewis and Randall rule... 

This equation, known as the Lewis-Randall rule, applies to each species in an ideal solution at all conditions of temperature, pressure, and composition. It shows that the fugacity of each species in an ideal solution is proportional to its mole fraction the proportionality constant is the fugacity of pure species / in the same physical state as the solution and at the same T and P. Ideal solution behavior is often approximated by solutions comprised of molecules similar in size and of the same chemical nature. 

The excess Gibbs energy is of particular interest. Equation 160 may be written for the special case of species / in an ideal solution, with fSidt replaced by xj in accord with the Lewis-Randall rule ... 

Equation 22 is a special application of the general Lewis-Randall ideal solution model (3,10) that is typically used for near-ambient pressures and... 

Criteria for ideal solution behaviour The criteria for ideal solution behaviour are discussed in most chemical thermodynamic texts (e.g., Lewis and Randall, 1961, p. 130 Nordstrom and Munoz, 1986, p. 401). The conditions may be summarized as follows. 

The straight dashed line in Fig. 12.18 that represents the Lewis/Randall is the only model of ideal-solution behavior so far considered. Alternative me also express the direct proportionality between /, and x, represented by (11.61), but with different proportionality constants. We may express this... 

Equations (12.46) and (12,47) imply two models of solution ideality. first is based on the Lewis/ Randall rule, for which the standard-state fuga... 

Figure 12.18 is drawn for a species that shows positive deviations from ideality in the sense of the Lewis/ Randall rule. Negative deviations from ideality are also common, and in this case the /j-vs.-x, curve lies below the Lewis/Randall line. In Fig. 12.19 we show the composition dependence of the fugacity of acetone in two different binary solutions at 50°C. When the second component is methanol, acetone shows positive deviations from ideality. On the other hand, when the second component is chloroform, acetone shows negative deviations from ideality. The fugacity of pure acetone f—<— is of course the same regardless of the second component. However, Henry s constants, represented by the slopes of the two dotted lines, are very different for the two cases. 

When Henry s law is taken as the model of ideality for the solute (species 1) and the Lewis/ Randall rule provides the model of ideality for the solvent... 

This equation relates the excess Gibbs energy based on the asymmetric treatme of solution ideality to the excess Gibbs energy based entirely on the Lewis Randall rule. 

In Sec. 10.4 we wrote down equations for an ideal solution by analogy to for an ideal gas. We wish here to formalize development of the equations f ideal solution. We define an ideal solution as a fluid which obeys Eq. (11 the Lewis/ Randall rule,... 

A mixture of ideal gases is a special case ofan ideal solution for which the Lewis/Randall rule [Eq. (11.61)] simplifies to f a = y,P. Equation (11.58) then reduces to... 

Figure 12.21 Plot of/, vs. x, showing extrapolation to x, = 1. The straight lines represent ideal-solution models based on Henry s law and the Lewis/Randall rule.

Related Calculations. If the gas is not ideal, the fugacity coefficients , will not be unity, so the activities cannot be represented by the mole fractions. If the pressure is sufficient for a nonideal solution to exist in the gas phase, , will be a function of y, the solution to the problem. In this case, the y, value obtained for the solution with Lewis-Randall rule for... 

The fugacities are plotted in Fig. 12.2 as solid fines. The straight dashed lines represent Eq. (11.80), the Lewis/Randall rale, wliich expresses the composition dependence of the constituent fugacities in an ideal solution ... 

If, over the interval from 0 to P, the partial molar volume V for component i is equal to the molar volume v for pure component i (that is V = v then the Lewis and Randall rule holds for component / over the pressure interval 0 to P. (Note that for the ideal solution behavior to exist over the interval 0 to P, it is necessary that the Lewis-Randall rule hold for each component of the mixture over the interval 0 to P.) Thus, if V = then Eq. (14-49) reduces to... 

The concept of ideal solution signifies no interactions between molecules. The only information regards pure component properties and mixture composition. Following the Lewis Randall rule, the component fugacity in an ideal solution is obtained by multiplying the pure species fugacity at given T and P by its molar fraction. Thus, for the vapour phase we may write ... 

For an ideal solution we may apply the Lewis-Randall rule and write the fugacity as fi =. It follows that ... 

Another reference-state for the solute / may be its pure liquid fugacity, fj. This state is a virtual one, because in practice x, 1. If the actual liquid mixture has as reference an ideal solution obeying the Lewis-Randall rule, we may define the reference-state f- as the limit of component fugacity at jc, 1 ... 

Ideal solution is often chosen as reference in analysis. In this case we may write for the fugacity of a component the relations f/ (HL) = XjHj and fj LR) = X/fk vhere HL stands for Henry law and L-R for Lewis-Randall assumption. The problem is now how to express the phase equilibrium A possible approach would be to use Henry law for solute, and Lewis-Randall rule for solvent. For this reason such definition of Ai-values is considered asymmetric. 

In the case of ideal solutions the Lewis-Randall approximation can be used ... 

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