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How does the solubility of hydroxides of the alkaline earth metals change when we move from Be to Ba?

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Hint :Alkaline earth metals elements of group 2 in the periodic table. The elements include beryllium $ \left( {Be} \right),\; $ magnesium $ \left( {Mg} \right),\; $ calcium $ \left( {Ca} \right),\; $ strontium $ \left( {Sr} \right),\; $ barium $ \left( {Ba} \right), $ and radium $ \left( {Ra} \right). $ . They are called alkaline earth metals because of two reasons: first Their oxides remain in the crust of the earth and are water soluble and second is that they are very heat-stable.

Complete Step By Step Answer:
The alkaline-earth elements are highly metallic and are good conductors of electricity. Their melting point and boiling point are comparatively higher than those of alkali metals. They all are strong reducing agents. Most alkaline earth metals produce a characteristic color when exposed to a flame because of the emission or reabsorption spectrum. The colors that they show are Ca – Brick Red color, Sr – Crimson Red color, and Ba – Apple Green color. Beryllium and magnesium do not show color. Alkaline earth metals form hydroxides also. Whenever oxides react with water it yields hydroxides. There is a proper trend that these metals follow when it comes to the solubility of their hydroxides. When we move down the group they become more soluble, that is solubility increases from Be to Ba. Magnesium hydroxide is almost insoluble and forms suspension with water, calcium hydroxide is sparingly soluble, strontium hydroxide is more soluble and barium hydroxide produces a strongly alkaline solution. Therefore the trend of solubility of hydroxides is as follows:
 $ Be{(O\;H)_2} < \;Mg{(O\;H)_2} < \;Ca{(O\;H)_2}\; < \;Sr{(O\;H)_2}\; < \;Ba{(O\;H)_2} $

Note :
Metal hydroxides are strong bases. Some of them are weak electrolytes as they are partially soluble in water. Alkaline earth metals hydroxides are also basic. Alkaline earth metals have numerous uses: for manufacturing of alloys, $ Mg{(O\; H)_2} $ is used as an antacid in medicine, radium for the treatment of cancer, etc.