How do you determine the pKa values of novel bases?

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In a discussion about extracting a product from a reaction with a 50% yield, the focus is on separating the desired product from unwanted byproducts using acid-base extraction. The key challenge is determining the pKa values of unknown molecules based solely on their structures. Knowing the pKa is essential for selecting the appropriate acid to form a salt with the desired product while leaving the unwanted product unaffected. The conversation explores methods for estimating pKa values without experimental data, emphasizing the need for computational tools that can analyze molecular structures to predict properties like phase changes and solubility. While Chemspider.com offers predictions for known molecules, participants express interest in finding programs that can analyze new, uncharacterized compounds. A resource from the University of Iowa is mentioned as a potential tool for estimating pKa values based on molecular structure.
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Imagine there is a reaction performed and it contains a product that is easily separable via an acid base extraction. This product is only formed in 50% yield. The other 50% formed unwanted products that are to be separated and done away with.

If all that is known is the structure of these unknown molecules, how can they be extracted? I figure knowing the pKa values would be useful. Assuming the unwanted molecule is also soluble in the organic layer like the wanted molecule, and neither can be distilled out, the right acid could be selected to cause a salt to form of the wanted molecule but not the unwanted molecule.

My question is, how does one determine the pKa value off a molecule with no experimental data when only the structure is known? I can post pictures of the molecule shortly, but regardless of that, is there a way to determine pKa value off structure?

What would be really useful is if there was some sort of program that could analyze the structure of a molecule and determine when it is a solid/liquid/gas and the related temperatures of phase change. Anyone know of such a thing? I know Chemspider.com has a way to predict these values of molecules that are already in their database, but I have found no way to allow it to predict new molecules.
 
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5 seconds googling, second link: http://www.uiowa.edu/~quantum/omtkypka.pdf
 
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