What determines salt solubility?

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A short background. I am tutoring a student and we got to analytical chemistry and detection of various cation groups. It’s a bunch of reagents and reactions to memorize and most of them rely to a salt of certain ion combination being insoluble while the rest are soluble. Now the student asked me why is that so and is there any rhyme or reason and I must say that I don’t have an answer. I know that solubility depends on polarity, but, for example if you add HCl in cation solution, only Ag, Hg and Pb cations will drop out of the solution as a precipitate. Why those? What is different between say AgCl2 and CuCl2 that silver chloride will precipitate while copper one won’t? Same thing for any further steps (eg why Fe(OH)3 will precipitate while Ba2+ will stay)? Is there any underlying system/logic behind it or is it just a bunch of memorisation? Any way to explain that to highschooler?

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Imagine you have a toy box with lots of different toy animals in it. Some of the toy animals are small and round, while others are big and flat. If you try to fit the small, round toy animals into a box that is too small, they might not fit and will stay on top of the box. But if you try to fit the big, flat toy animals into the same box, they might be able to squeeze in and fit inside.

In a similar way, certain chemicals might be able to dissolve in a solution because they are small and have a certain shape, while other chemicals might not dissolve because they are too big or have a different shape.

For example, if you mix a solution of silver ions (Ag+) with a solution of hydrochloric acid (HCl), the silver ions will react with the hydrochloric acid to form a compound called silver chloride (AgCl). Silver chloride is a solid, and it will not dissolve in the mixture. This is why you might see a white precipitate (a solid that has settled out of the solution) form when you mix these chemicals together.

On the other hand, if you mix a solution of copper ions (Cu+) with hydrochloric acid, the copper ions will not react with the hydrochloric acid and will stay in the solution. This is because copper ions are different from silver ions and have different properties, so they do not form a solid when they are mixed with hydrochloric acid.

So, the reason why certain chemicals dissolve in a solution while others form a precipitate has to do with their size, shape, and the types of atoms they are made of. It’s a bit like trying to fit different toy animals into a box – some will fit, while others will not.

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