Three-suffix Margules equation

The Wilson equation is superior to the familiar Van-Laar and Margules equations (see Volume 2, Chapter 11) for systems that are severely non-ideal but, like other three suffix equations, it cannot be used to represent systems that form two phases in the concentration range of interest. 

These equations become identical to the three-suffix Margules equations when = 21, and the functional form of these two types of equations is not greatly different unless the constants i2 and differ by more than about 50 per cent. 

These equations are known as three suffix Margules equations. 

In the A-B binary solution the activity coefficients are given by the three-suffix Margules equations ... 

P13.8 In the free DDBSP Explorer Version, search for all data for the system water-acetic acid and regress these data simultaneously using the Three-Suffix Margules equation and binary parameters with quadratic temperature dependence. The Three-Suffix Margules g -model is very seldom... 

Fig. 3.6. Partial pressures (o), activities (6), and activity coefficients (c) for the system acetone-chloroform at 35.17 C. [Data of Zawidzki, Z. Physik. Chem. 35,129 (1900).] Activity coefficients fitted by three-suffix Margules equations Aab log 0.39, Aba log 0.51...

For liquids and solids, determine the activity coefficients for binary and multicomponent mixtures through activity coefficient models, including the two-suffix Margules equation, the three-suffix Margules equation, the van Laar equation, and the Wilson equation. Identify when the symmetric activity coefficient model is appropriate and when you need to use an asymmetric model. 

The three-suffix Margules equation is equivalent in function to Equation (7.60) ... 

From these data, estimate the parameters in the three-suffix Margules equation. At equilibrium, the fugacities in each liquid phase must be equal, that is. 

Your supervisor has assigned you to obtain parameters A and B for the three-suffix Margules equation to input in the company s phase equilibrium computer database. The binary mixture of interest is benzene (a) in 1-propanol b) at 75°C. You cannot find any values in the literature for the three-suffix Margules equation, but you do find the following values from the van Laar (vL) equation ... 

A binary vapor mixture contains 48% ethanol a) in water (b) at 70°C. Determine the pressure at which this vapor develops the first drop of liquid. What is the fiquid composition The excess Gibbs energy can be described by the three-suffix Margules equation with parameters ... 

At high pressures, both the vapor and liquid phases may be nonideal. Consider a binary mixture of a and b with vapor-phase mole fraction and T known. Develop a set of equations and a solution algorithm to determine the composition in the liquid phase and the system pressure. Use the van der Waals equation to quantify deviations from ideality in the vapor and the three-suffix Margules equation to model the nonideal liquid. Assume that critical properties, liquid volumes, and Antoine coefficients for each species are readily available and that the three-suffix Margules parameters have been determined. 

Using the three-suffix Margules equation for activity coefficients gives ... 

In Examples 8.9 and 8.10, we explore different ways to fit model parameters of the two-suffix and three-suffix Margules equations, respectively, using experimental VLE data. We will use an entire data set to find the best value for the two-suffix Margules parameter A or the three-suffix Margules parameters A and B. When a model equation can be written in a linear form, a least-squares linear regression can be employed to determine the model parameters. Example 8.11 uses this method on the same data as used in Examples 8.9 and 8.10. This latter method is restricted to simpler activity coefficient models that can be written in linear form. 

However, we now use the three-suffix Margules equation to write the activity coefficients in terms of the Margules parameters, A and B. Applying the expressions in Table 7.2 ... 

Determine the model parameters for the two-sufflx and the three-suffix Margules equations using the Hquid-vapor equilibrium data for a binary system of benzene (l)-cyclohexane (2) at 10°C. Mole fractions of liquid vs. total pressure are reported in Table E8.0A. 

We can rewrite the two-suffix and three-suffix Margules equations by dividing g by (xiXa). The two-suffix Margules equation becomes ... 

Again, we will consider the case when the nonideality is described by the three-suffix Margules equation with parameters given in Example 8.19. We can write the Gibbs energy according to Equation (E8.20B) ... 

A binary mixture exhibits vapor-liquid-liquid equilibrium at 300 K. The excess Gibbs energy is described by the two-suffix Margules equation with A = 6235 [j/mol]. Determine the composition of the three phases and the total pressure. The saturation pressures are given by Pf = 100 [kPa] andP = 50 [kPa]. 

VLE data can be used to obtain best-fit values of activity coefficient model parameters. A general approach appficable to any model is through the use of objective functions. An objective function takes account of the entire measured data set. It is written in terms of the difference between the calculated value of a given property and the experimental value of the same property. The model parameters are determined when the objective function is minimized. Alternatively, equations such as the two-suffix and three-suffix Margules equations can be rewritten to find model parameters through averages and linear regression. 

Consider a mixture of 1-propanol (a) and water (h) in vapor-liquid equilibrium at 25°C. For a liquid with mole fraction Xa = 0.2, answer the following questions. The three-suffix Margules equation parameters are ... 

At a 300 K and 1 bar, a binary mixture of species a and b form two partially miscible liquid phases. The following activity coefficients at infinite dilution are reported 7 = Sandy = 15. Using the three-suffix Margules equation, determine the composition of two liquid phases in equilibrium. 

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