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The thermal stability of alkaline earth metals increases down the group for hydroxides i-e., Be(OH)2 is less stable than Ba(OH)2. The solubility also increases down the group for these compounds i-e., Be(OH)2 is less soluble in water as compared to Ba(OH)2. Hence for Hydroxides of group 2 elements the solubility and thermal stability trends are same i-e. Both increases down the group. But the solubility and thermal stability trends become inverse of each other for the "sulphates of group 2 elements". Does this mean that there is no relation between solubility and thermal stability?

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    $\begingroup$ There's no reason to think there would be such relation, imo. $\endgroup$ – Mithoron Dec 31 '19 at 16:41
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Nobody is able to foresee the solubility of a product. There are some experimental rules, but they all have exceptions, that nobody is able to explain.

Just have a look on the Calcium salts made with the halogens (F, Cl, Br, I). There is a nice analogy among Cl, Br and I, but not F. Look ! The Calcium chloride $\ce{CaCl2}$, bromide $\ce{CaBr2}$ and iodide $\ce{CaI2}$ are all extremely soluble in water. They are all soluble in less than their weight of water. But calcium fluoride $\ce{CaF2}$ is among the least soluble product on Earth. The principal mineral for Fluoride is $\ce{CaF2}$, and it can be found everywhere at the surface of the Earth. If this mineral would have been at least a little soluble in water, the rains would have washed away this mineral in the geological times. Why is there such a huge difference between calcium fluoride and the other halogenides ? Nobody knows !

Another example. Potassium perchlorate is the only potassium salt which is very weakly soluble in water. By comparison, Sodium perchlorate is extremely soluble in water. Why? Another example: the number of Silver compounds which are soluble in water is limited. In organic solvents, it is even worse. But the Handbook of Chemistry and Physics says that Silver perchlorate is soluble in toluene. Why? Nobody knows.

From time to time there are articles published in journals like the Journal of Chemical Education. The author is proud of displaying a theory filled with new parameters, for explaining the solubility of quite a lot of chemicals. But there are always exceptions, that he regrets not to be able to explain.

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While solubility, thermal stability and density are pretty hard to explain as @maurice said. But, there is good logic for the solubility of group 2 hydroxides. The lattice energy of a solid is inversely proportional to the radius ratio (as lower the radius ratio greater the packing efficiency). So, hydroxide being a small ion, makes a more stable aqueous solution with beryllium than barium. Similarly for the sulphates, sulphate is a large ion, hence, beryllium has more stable sulphate. This radius ratio logic can explain solubility of nearly all group 1 and group 2 salts (I say nearly because of carbonates and hydrogen-carbonates, which follow a reverse trend) For a more detailed explaination see this (1)

(1) https://chem.libretexts.org/Bookshelves/Inorganic_Chemistry/Supplemental_Modules_(Inorganic_Chemistry)/Descriptive_Chemistry/Elements_Organized_by_Block/1_s-Block_Elements/Group__2_Elements%3A_The_Alkaline_Earth_Metals/1Group_2%3A_Chemical_Reactions_of_Alkali_Earth_Metals/The_Solubility_of_the_Hydroxides%2C_Sulfates_and_Carbonates

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