2024.9.04
Chemistry at pirika.com > Chemistry > Chemical engineering > Reprint: gas-liquid equilibrium estimation by ASOG. > Chapter 1: Basic equations of solution theory
1.8 How to obtain activity and activity coefficients
It was explained that the active volume is the ‘effective molar concentration’.
Using this, Raoult’s law equation P=P1*a1+P2*a2 can be used as it is in real solutions.
So how can we obtain these activity coefficients?
It is said that there are more than 10,000 different compounds used in chemical engineering, and it is impossible to obtain activity coefficients for all such compound pairs (10,000*9,999).
When it comes to further multi-component mixtures, the combination of activity coefficients increases exponentially.
The same pure component pair will have different activity coefficients when measured at constant pressure and constant temperature, or even at different pressures and temperatures. So it is important to know how to estimate the activity coefficient under the required conditions.
Here, the idea of Analytical Solutions of Groups (ASOG) was born 50 years ago.
Let me explain the basic concept of the ASOG Act.
For example, when it comes to the alcohol and water mentioned earlier, there are as many types of combinations as there are types of alcohols. Starting with methanol, there are various alcohols with larger or branched carbon chains. Sometimes they contain things like double or triple bonds, or carbon chains wrapped around rings. We do not know how many such alcohols there are, but if we divide them into the groups that make up an alcohol, they can be expressed as a combination of five groups: hydroxyl group, CH2 group, CH2= group, CH2 (ring) and water. In other words, if the interaction parameters between the five groups (0 for the same group) are known, the activity coefficient can be calculated for any combination of alcohol and water using 5*4=20 parameters. This means that small data can be used to predict big data. In the field of chemical engineering, the rational handling of big data started 50 years ago.
So how many groups should we define?’ is the difficult part. With each additional group, the number of parameters that have to be determined increases to the power of two. If 100 groups are defined, 100*99 parameters have to be determined.
However, if there are only 10,000 precise experimental data series to determine the parameters, it is not possible to determine all of them. Therefore, ASOG uses a special way of counting groups.
To illustrate with the alcohol with branches mentioned earlier, there are four different groups of molecules: CH3-, -CH2-, >CH- and >C<. The more detailed the classification, the more accurate the calculation, but the more parameters that have to be determined. Therefore, ASOG uses the same parameters for -CH2- as for CH3-. >CH- is treated as 0.8 CH3- and >C< as 0.5 CH3-. (There is also a special counting scheme for water, which counts as 1.6)
Using such techniques, any branching structure can be calculated by determining CH3-1 parameters, where originally four groups of parameters had to be determined. Using such techniques to reduce the number of groups, the ASOG method makes it possible to use small data to predict big data.
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