Question
Nuclear attraction is often the deciding control factor for the association of neutral molecules to a given metal ion. Which one of the following represents the correct order of stability of the ions? $${\left[ {Be\left( {{H_2}{O_4}} \right)} \right]^{2 + }},{\left[ {Mg{{\left( {{H_2}O} \right)}_4}} \right]^{2 + }},$$ $${\left[ {Ca{{\left( {{H_2}O} \right)}_4}} \right]^{2 + }}\,{\text{and}}\,{\left[ {Sr{{\left( {{H_2}O} \right)}_4}} \right]^{2 + }}$$
A.
$${\left[ {Be{{\left( {{H_2}O} \right)}_4}} \right]^{2 + }} > \left[ {{{\left. {Sr{{\left( {{H_2}O} \right)}_4}} \right]}^{2 + }}} \right]$$ $$ > {\left[ {Mg{{\left( {{H_2}O} \right)}_4}} \right]^{2 + }} > {\left[ {Ca{{\left( {{H_2}O} \right)}_4}} \right]^{2 + }}$$
B.
$${\left[ {Ca{{\left( {{H_2}O} \right)}_4}} \right]^{2 + }} > {\left[ {Mg{{\left( {{H_2}O} \right)}_4}} \right]^{2 + }}$$ $$ > {\left[ {Be{{\left( {{H_2}O} \right)}_4}} \right]^{2 + }} > {\left[ {Sr{{\left( {{H_2}O} \right)}_4}} \right]^{2 + }}$$
C.
$${\left[ {Sr{{\left( {{H_2}O} \right)}_4}} \right]^{2 + }} > {\left[ {Ca{{\left( {{H_2}O} \right)}_4}} \right]^{2 + }}$$ $$ > {\left[ {Mg{{\left( {{H_2}O} \right)}_4}} \right]^{2 + }} > {\left[ {Be{{\left( {{H_2}O} \right)}_4}} \right]^{2 + }}$$
D.
$${\left[ {Be{{\left( {{H_2}O} \right)}_4}} \right]^{2 + }} > {\left[ {Mg{{\left( {{H_2}O} \right)}_4}} \right]^{2 + }}$$ $$ > {\left[ {Ca{{\left( {{H_2}O} \right)}_4}} \right]^{2 + }} > {\left[ {Sr{{\left( {{H_2}O} \right)}_4}} \right]^{2 + }}$$
Answer :
$${\left[ {Be{{\left( {{H_2}O} \right)}_4}} \right]^{2 + }} > {\left[ {Mg{{\left( {{H_2}O} \right)}_4}} \right]^{2 + }}$$ $$ > {\left[ {Ca{{\left( {{H_2}O} \right)}_4}} \right]^{2 + }} > {\left[ {Sr{{\left( {{H_2}O} \right)}_4}} \right]^{2 + }}$$
Solution :
The degree of hydration and the amount of hydration energy decreases as the size of the ion increases from $$B{e^{2 + }}$$ to $$S{r^{2 + }}.$$
\[\underset{\begin{smallmatrix}
\text{Hydration} \\
\text{Energy}\left( kJ\,\,mo{{l}^{-1}} \right)
\end{smallmatrix}}{\mathop{{}}}\,\underset{-2494}{\mathop{B{{e}^{2+}}}}\,<\underset{-1921}{\mathop{M{{g}^{2+}}}}\,<\underset{-1577}{\mathop{C{{a}^{2+}}}}\,<\underset{-1443}{\mathop{S{{r}^{2+}}}}\,\]
$${\text{Thus, stability of hydrated ion is}}$$
$${\left[ {Be{{\left( {{H_2}O} \right)}_4}} \right]^{2 + }} > {\left[ {Mg{{\left( {{H_2}O} \right)}_4}} \right]^{2 + }}$$ $$ > {\left[ {Ca{{\left( {{H_2}O} \right)}_4}} \right]^{2 + }} > {\left[ {Sr{{\left( {{H_2}O} \right)}_4}} \right]^{2 + }}$$