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Why is the solid product washed with ice-cold solvent during in the last stages of recrystallisation? Is this to remove soluble impurities? (for example) Well, what if the impurities were also insoluble in the cold solvent?

Recrystallisation is weird in the sense that we have to make some assumptions in order for the process to fulfill the 'ideal' purification of the solid product that we're trying to get to.

For example, we have to assume that all soluble impurities are washed off during suction filtration, and that no impurities manage to creep up within the molecules of the crystals when they form. Would I be correct in saying this?

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    $\begingroup$ Recrystallisation may be done in a multitude of ways, depending on your particular situation; the product may be washed with ice-cold solvent, or with another solvent that would supposedly dissolve the impurities but not the product, or not washed at all. You may call it weird, but then again, pretty much all chemistry is weird in the same sense, or worse. It is an experimental science, after all. $\endgroup$ – Ivan Neretin May 15 '17 at 15:06
  • $\begingroup$ So is the main goal of this step to kind of 'clean off' the surface of the crystals? $\endgroup$ – Mathematician May 15 '17 at 15:11
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    $\begingroup$ Yeah, kind of. See, at this stage the crystals are wet with mother solution (admittedly, a tiny amount of it, but it is still there), which contains the very impurities we wanted to get rid of in the first place. $\endgroup$ – Ivan Neretin May 15 '17 at 15:15
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Possible sources of impurities in the recrystallization process can be described in terms of phenomena occuring during coprecipitation and which are the basis of gravimetry:

  • inclusion (impurity occupies positions in the crystal lattice);
  • occlusion (impurity is physically captured within the crystal as it has been growing);
  • adsorption (impurity is adsorbed on the surface layer of the crystal);
  • postprecipitation (impurity forms secondary solid phase once recrystallization of the target stopped/slowed down).

Washing crystals with a fluid only addresses the last two phenomena, adsorbance and postprecipitation. Postprecipitation is rarely a problem as it occurs on a large time scale or when a really poor solvent has been chosen.

Properties of the washing liquid vastly depend on the properties of the compound being recrystallized. In the simplest case it's the same solvent (as in your example), but it can also be an electrolyte, hydrolysis suppressor or another solvent (e.g. distilled water) altogether.

As for the temperature of the washing liquid, it's actually better to use many small portions of the hot solvent as filtration of the hot solutions happens much faster, surface adsorption decreases with the temperature and removal of mother solution from the surface is faster. However, if solubility of the recrystallized product is significantly increasing with the temperature (and this is typically the case), then one has to sacrifice the efficiency of the washing process for the better yield and use cold solvent instead.

Impurities, insoluble in the cold solvent, are practically not an issue. First, recrystallization starts from a homogeneous solution. Second, before crystals are washed, they are separated from the mother solution so that only minor amount of it is left on the crystals' surface, and if there were any impurities, they don't get a chance to nucleate as their concentration in washing solvent is going to be negligible.

As for your perception of the recrystallization as of a "weird" process, I'd say it's probably more complicated than one would expect from looking at the beaker with some crystalline mess. In fact, underlying processes are described with more or less appropriate models, and once a person gets experienced enough, it all starts to make much more sense.

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