Suppose you want to dissolve some \(\mathrm{MgCl}_{2}\) in water. (a) How do we know that magnesium cations have a \(+2\) charge? (b) \(\Delta E_{\text {solute separation }}\) for \(\mathrm{MgCl}_{2}\) is much more positive than \(\Delta E_{\text {solute separation }}\) for \(\mathrm{NaCl}\). Explain what this means and why it might be so. (c) \(\mathrm{MgCl}_{2}\) is more soluble in water than \(\mathrm{NaCl}\). Explain how this is possible in light of the information given in (b).

Magnesium (Mg) is an alkaline earth metal, and it is in the second group in the periodic table. Elements in Group 2 generally lose two electrons to achieve a stable octet electron configuration which is the fully filled s and p orbitals of the previous energy level. When magnesium loses two electrons, it forms a cation with a charge of +2, which we can represent as Mg²⁺. Therefore, magnesium cations have a +2 charge.

The positive value of solute separation energy for MgCl₂ than that of NaCl means that the energy required to separate Mg²⁺ and Cl⁻ ions in the MgCl₂ lattice is higher compared to the energy needed to separate Na⁺ and Cl⁻ ions in the NaCl lattice. This is because Mg²⁺ has a higher charge compared to Na⁺, which leads to stronger electrostatic attraction between Mg²⁺ and Cl⁻ ions. Therefore, more energy is needed to separate the MgCl₂ ions in the lattice.

Despite the higher solute separation energy for MgCl₂, it can still be more soluble in water than NaCl. This is because the hydration energy of MgCl₂, or the energy released when Mg²⁺ and Cl⁻ ions interact with water molecules, is also higher than the hydration energy of NaCl. The hydration energy comes from the electrostatic attraction between the charged ions and the oppositely charged ends of the water molecules (Oxygen end being negative and hydrogen end being positive). The higher charge of Mg²⁺ compared to Na⁺ results in stronger interaction with water molecules, leading to higher hydration energy. The overall energy change for the dissolution process is the difference between the hydration energy and solute separation energy. If the hydration energy is significantly larger than the solute separation energy, more negative overall energy change will occur, promoting dissolution. In the case of MgCl₂, the higher hydration energy compensates for the higher solute separation energy, making it more soluble in water than NaCl.