The question is copied from chromatography, though i have some views, but i want more views to support those that i have already.
Hint: Retention factor k = Phase ratio * Partition coefficient.
https://www.sciencedirect.com/topics/medicine-and-dentistry/distribution-constant
Beyond solubility what matters is the difference in interaction between the solute and the solvent and the solute and the stationaty phase.
Solubility determines the interaction of chemical constituents in your sample with those of the two phase (Mobile and stationary). The constituent more soluble in one phase will have more affinity towards that phase, thereby separating from each other
Until the compound is not soluble in the mobile phase it can't be eluted.
Interesting approach based on this fact is used in HIC (Hydrophobic Interaction Chromatography) - a "negative" gradient of salt concentration is used. At the beggining the highest concentration of the salt stops all proteins at the column start, when the concentration is decreased the proteins start to be separated and eluted from the column.
regards,
G
Your question is far too general. In liquid chromatography (HPLC, TLC, paper, column...) you are creating a concentration partition (solubility!) of the molecule between the mobile and stationary (HPLC column) phases. If the molecule is not soluble there is no partition and no analysis!
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