Component Distance travelled by the component (cm)

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How can I cite this page? I can't find the name of author or publishing date etc. It would be really helpful if I could cite the Khan Academy website!

You can cite Khan Academy as the author I think haha

In regards to gas chromatography, isn't it better to say that the separation is based on the samples interaction with the stationary phase of the column rather than the samples boiling point?

Yes to you and the article. The thing is, polarity and bp. are related, so they will both affect separation.

Extraction...is it considered one of the types of partition chromatography ?

No. Extraction is based on two liquid phases where they are separated based on an organic layer (nonpolar) and an aqueous layer (polar). One layer is the organic layer that floats on top of the other; the bottom layer is polar and can be bound to a solvent. IN the case of mixing oil and water, the oil floats (nonpolar organic phase) and the water sinks (aqueous polar phase). This is clearly different than "partition chromatography" because the latter is based on a solid phase (that one compound has some affinity or attraction to) and a liquid phase (that another compound has some affinity or attraction to). In extraction, the inside of the beaker would have to be coated with a stationary phase, but it is not. So, extraction is not partition chromatography. Also, we can tell by the out-right definition from the Meriam Webster Medical Dictionary: Partition Chromatography: "a process for the separation of mixtures in columns or on filter paper based on partition of a solute between two solvents one of which is immobilized by the substance in the column or by the paper." In extraction, one is not immobilized, but they separate based on exclusion from one another.

For ion-exchange chromatography, (specifically cation exchange) would raising the pH of the buffer will cause the beads to become more negatively charged thereby strengthening the ionic interactions between cations and the beads? and conversely for anion exchange chromatography?

In ion exchange, you don't change the charge on the beads of the resin. You change the charge on the analyte (for example a protein that you want to purify). So in a cation exchange where the beads are negatively charged, raising the pH causes deprotonation of the protein. The result depends on the pH of the buffer and isoelectric point of the protein.

Let's say the protein has a pI of 6.5 (it's neutral at this pH).
If your column is originally at a pH of 4, the protein will be protonated, so it has a +ve charge and sticks to the -ve beads in the column. Raising the buffer pH to 6.5 or higher deprotonates the protein, so now it's neutral (or negatively charged if you raised the pH a lot), which causes it to stop being attracted to the -ve beads. Now the protein will elute.

Had this been an anion exchange, then you would start at a very high pH so that your protein is in its anionic form, and you slowly lower the pH to 6.5 so that it becomes neutral (or below 6.5 so it becomes positively charged) which causes it to not be attracted to the the positive beads.

Is it possible to calculate the Rf for the techniques other than paper and thin layer chromatography? For example, for liquid column chromatography the solvent and compounds travel the full length of the column. Would you do something like (time for solvent to reach the end of the column)/(time for the compound to reach the end)?

Difference between gas and column chromatography?

A big one is execution: most column techniques are (as far as I know) done by hand, maybe attached to an automatic solvent dispenser, but relatively small scale.