How do the acidities of the aqueous solutions of the alkaline earth metal ions \(\left(\mathrm{M}^{2+}\right)\) change in going down the group?

Alkaline earth metals are found in Group 2 of the periodic table. They include Beryllium (Be), Magnesium (Mg), Calcium (Ca), Strontium (Sr), Barium (Ba), and Radium (Ra). As we go down the group, the atomic number and atomic size increase.

Acidity is a measure of the ability of a substance to donate hydrogen ions (H^+) in an aqueous solution. The more hydrogen ions a substance can donate, the higher its acidity. In the case of alkaline earth metal ions (M^2+), they react with water to form metal hydroxides and H^+ ions: \[M^{2+}(aq) + 2H_2O(l) \rightarrow M(OH)_2(s) + 2H^+(aq)\]

There are a few periodic trends that influence the acidity of a solution of alkaline earth metal ions: 1. Atomic Size: As we go down the group, the atomic size increases due to the addition of electron shells. This leads to a decrease in the charge density of the metal ions, making it easier for them to attract water molecules and form larger hydration shells. 2. Electronegativity: Electronegativity decreases down the group. As a result, the ability to attract electron pairs in the metal-ligand bond decreases, making it easier for the metal ions to donate H^+ ions. 3. Ionization Energy: Ionization energy decreases down the group, making it easier to remove electrons as we go down the group. This can increase the acidity of the solution as the metal ions can more easily form H^+ ions.

Considering the periodic trends stated above, as we go down the group, the acidity of alkaline earth metal ions' aqueous solutions increases. The increased atomic size and the decrease in electronegativity and ionization energy make it easier for the metal ions to form H^+ ions, thus increasing the acidity of their aqueous solutions. So, the order of acidity for aqueous solutions of alkaline earth metal ions is: \[ Be^{2+} < Mg^{2+} < Ca^{2+} < Sr^{2+} < Ba^{2+} < Ra^{2+} \] This means that the acidity of the aqueous solutions of alkaline earth metal ions increases as we go down the group.