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When a salt solution is evaporated (bunsen burner, evaporating dish/beaker), for example CuSO4 aq, there will be residue left over, as with all salt solutions.

However, the common form of copper (II) sulfate is in copper II sulfate pentahydrate (and I'm sure some other ones that are less common which I am not familiar of). It has a bluish tint.

Pure copper II sulfate is white.

When the copper II sulfate solution ( for example 1 L, 0.5M) is evaporated, is there a mathematical way to work out at which points copper II sulfate pentahydrate would be the residue, as well when the pentahydrate would evaporate as well to form pure copper II sulfate.

Furthermore, is there such case with a salt solution where hydrated salt version would not occur as the residue after evaporation, or vice versa with the anhydrous version?

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    $\begingroup$ Yes there is a mathematical way, and quite simple at that. When the solubility limit is reached, you will have a solid precipitate. When a certain temperature is reached, your hydrated salt will dehydrate. $\endgroup$ Commented Aug 15, 2023 at 7:15

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You're asking about a number of points..

  • "Massive" copper sulfate pentahydrate is blue. However it can have a white coating if partially dehydrated.

  • In geology there is a streak test where a mineral is rubbed on a alumina plate to create microscopic particles. The streak test often yields colors that are different than that of the "massive" specimen. In this case copper sulfate pentahydrate will have a white steak because of the small particle size and light coloring.

  • If you try to dry a solution of copper sulfate over a Bunsen burner it will splatter. Whether it will be the anhydrous form or the pentahydrate depends on how hot you heat the residue as you evaporate the solution.

  • As you evaporate the solution you'll reach the solubility limit and copper sulfate pentahydrate will start to crystalize. The solubility limit does depend on temperate. Copper sulfate behaves "normally" in that it is more soluble in hot solutions than cold. You can look up the solubility as a function of temperature.

  • If you just air dry the copper sulfate solution you'll get the pentahydrate unless you're in an unusually dry climate.

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  • $\begingroup$ I'll add that growing a large copper II sulfate pentahydrate crystal from a supersaturated solution using a seed crystal on a string is a common experiment. I don't know about now but copper sulfate used to be sold in drug stores to treat infected (fungus?) toes. $\endgroup$
    – MaxW
    Commented Aug 19, 2023 at 5:25
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Wikipedia references https://en.wikipedia.org/wiki/Copper(II)_sulfate with:

Copper(II) sulfate pentahydrate decomposes before melting. It loses two water molecules upon heating at 63 °C (145 °F), followed by two more at 109 °C (228 °F) and the final water molecule at 200 °C (392 °F).

A quote from the question:

Furthermore, is there such case with a salt solution where hydrated salt version would not occur as the residue after evaporation, or vice versa with the anhydrous version?

I had a related question about Aluminum Chloride https://en.wikipedia.org/wiki/Aluminium_chloride:

Reactions with water

Anhydrous aluminium chloride is hygroscopic, having a very pronounced affinity for water. It fumes in moist air and hisses when mixed with liquid water as the Cl− ligands are displaced with H2O molecules to form the hexahydrate [Al(H2O)6]Cl3. The anhydrous phase cannot be regained on heating the hexahydrate. Instead HCl is lost leaving aluminium hydroxide or alumina (aluminium oxide):

$$\ce{[Al(H2O)6]Cl3 → Al(OH)3 + 3 HCl + 3 H2O}$$

The point being that the Bunsen burner may not be hot enough (or there alternatively may be too much humidity in the room) to completely drive out the water at "200 °C (392 °F)" for Copper(II) sulfate pentahydrate. After all, the water solvent boils nearly at 100 °C and after that, additional heating results in popping of the salt from the beaker.

Has a different oven than the Bunsen Burner been possible to use to get the Copper(II) sulfate pentahydrate decomposition temperature after full evaporation of the solvent, and slow heating to the required temperature (with some additional margin) to prevent popping of the Copper(II) sulfate pentahydrate at a lower temperature from the Bunsen Burner?

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