2024.9.04
Chemistry at pirika.com > Chemistry > Chemical engineering > Reprint: gas-liquid equilibrium estimation by ASOG. > Chapter 1: Basic equations of solution theory
1.5 Coefficient of activity equation
However, this is unwieldy, so it is usual to take it to the form of an activity coefficient equation, such as the Antoine vapour pressure equation, which returns an activity coefficient when the composition is entered. The Wilson equation used in the ASOG method is briefly introduced here.
Wilson’s equation: the activity coefficient equation applicable to homogeneous liquid phase systems, where the activity coefficient of component i in an N-component system is given by
ln γi = -ln [∑(j=1)N xjΛij ] + 1 – ∑(k=1)N (xk Λkl) / (∑(j=1)N xj Λkj ) (1-6)
Λij ≡ (υj/υi ) exp[ -((λij -λii))/RT] (λij = λji ) (1-7)
xj：Mole fraction of pure component j υj：Liquid molar volume of pure component j
The (λij-λii ), (λij-λjj )are called Wilson parameters for components i and j. However, in some literature, Λij and Λji are also called Wilson parameters, which is confusing. Sometimes(λij-λii ) is called the Small Wilson parameter and Λij the Large Wilson parameter, but the magnitudes of the absolute values of the parameters themselves are reversed, so there is confusion there too.
This Large Wilson activity coefficient equation (1-6) is a non-linear equation, so the parameters are not easy to find. Using the Marquardt method or similar, convergence calculations are made from the activity coefficient values for the mole fractions obtained earlier.
Once the Large Wilson parameter is obtained, it is substituted into equation (1-7) to obtain the Small Wilson parameter.
In this case, the liquid molar volume of the pure component is needed. More precisely, we need the molar volume at the temperature at which Λij is obtained. However, because it is difficult to obtain the molar volume at an arbitrary temperature, and because the ratio of the i and j components in (1-7) does not change significantly, the molar volume at 25°C, which has the most data, is often used as a substitute.
Ethanol/water would be a very important separation process in chemical engineering, such as distilling to make spirits (distilling beer to make whisky, distilling wine to make brandy) or distilling alcohol made from sugar cane fermentation to make anhydrous fuel alcohol (to be mixed with petrol). There are so many areas of chemical engineering where activity factors are required, such as distillation, liquid-liquid extraction and solid-liquid extraction.
Next section: 1.6 Basic equations for gas-liquid equilibrium
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