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I'm trying to understand an observed reaction from a chem practical:

You have a solution of ammonium sulfate, which you add to a bovine serum albumin solution. The proteins precipitate, and the solution becomes cloudy. w/v % of $\ce{(NH4)2SO4}$ at this point is 57%.

When you add water (in a ratio of 2 parts water: 1 part serum solution)to the mix, the process reverses, and the solution becomes clear again.

This can be explained by the ammonium sulfate solution 'stealing' water from the proteins, which causes them to precipitate, and then the process reversing once more water is added. (Right?)

Question: Does the ammonium sulfate 'steal' the water because it wants to reach equilibrium, or because it's supersaturated, or what?

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Well, I wouldn't know how to sum it up better than chemwiki.ucdavis:

To achieve this conformation the molecule folds in such a way that all of the hydrophobic parts of a molecule are aggregated together and the hydrophillic groups are left to interact with the water. In the case of proteins it is the charged amino acids that allow selective salting out to occur. Charged and polar amino acids such as glutamate, lysine, and tyrosine require water molecules to surround them to remain dissolved. In an aqueous environment with a high ionic strength, the water molecules surround the charges of the ions and proteins. At a certain ionic strength, the water molecules are no longer able to support the charges of both the ions and the proteins. The result is the precipitation of the least soluble solute, such as proteins and large organic molecules.

If you ask what the aminoacid content of bovine serum albumin is, I'll cite:

Glycine, illanine, Valine, Leucine, Isoleucineh, Proline, Phenylalanine, Tyrosine, Tryptophan, Serine, Threonine, Half-cystinee, Methionine, Arginine, Histidine, Lysine, Aspartic acid and Glutamic acid. Source

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