Question

Consider the ionic compound magnesium chloride, \(\mathrm{MgCl}_{2}\). Do you think the hydration energy for this compound is greater than, less than, or about equal to that of \(\mathrm{NaCl}\) ?

Short answer

The hydration energy of magnesium chloride (MgCl2) is greater than that of sodium chloride (NaCl), because the magnesium ion (Mg2+) is smaller and has a higher charge than the sodium ion (Na+), resulting in stronger electrostatic attraction between Mg2+ and water molecules.

Step-by-step solution

Understand the concept of hydration energy

Hydration energy is the amount of energy released when a specific amount of ions get surrounded by water molecules. The smaller and more charged an ion is, the larger its hydration energy, because the electrostatic attraction between the ion and the polar water molecules is stronger.

Determine the size and charge of Mg2+ and Na+

In MgCl2, magnesium ions (Mg2+) have a charge of +2, while in NaCl, sodium ions (Na+) have a charge of +1. Let's compare the size (ionic radius) of these two ions. The ionic radius of Mg2+ is 72 pm, and the ionic radius of Na+ is 102 pm. We can see that Mg2+ is smaller and has a higher charge than Na+.

Compare hydration energies

Now let's compare the hydration energies of MgCl2 and NaCl based on the size and charge of their ions. Since Mg2+ is smaller and has a higher charge than Na+, the electrostatic attraction between Mg2+ and water molecules is stronger than that between Na+ and water molecules. Therefore, the hydration energy of MgCl2 is greater than that of NaCl. In conclusion, the hydration energy of magnesium chloride (MgCl2) is greater than that of sodium chloride (NaCl).

Key concepts

Ionic Compounds

Ionic compounds are substances formed by the combination of positively and negatively charged ions. These compounds are typically solid and exhibit a crystalline structure.
These ions are held together by strong ionic bonds that result from the electrostatic forces between oppositely charged particles.
When these compounds dissolve in water, the ionic bonds are broken, and the individual ions are surrounded by water molecules, a process known as hydration. The energy change associated with this process is the hydration energy.
Ionic compounds play crucial roles in various biological processes and industrial applications. For example, sodium chloride ( NaCl) is an essential dietary component, while magnesium chloride ( MgCl_2) is often used in ice control and as a source of magnesium in supplements. Understanding their properties can lead to better use of these important compounds.

MgCl2 vs NaCl

When comparing magnesium chloride ( MgCl_2) and sodium chloride ( NaCl) , one of the key considerations is their hydration energy. This is the energy released when the ions in these compounds interact with water molecules.
Magnesium chloride is composed of Mg^{2+} ions and Cl^{-} ions, while sodium chloride is made of Na^{+} ions and Cl^{-} ions. Due to the charge difference and sizes of Mg^{2+} and Na^{+} , the impact on hydration energy differs significantly.
Due to its smaller size and higher charge, the magnesium ion exerts a much stronger attraction with water molecules compared to the sodium ion. Thus, the hydration energy for MgCl_2 is greater than NaCl . This difference affects how these salts dissolve in water, with magnesium chloride interacting more intensely with water.

Electrostatic Attraction

Electrostatic attraction is a fundamental force in chemistry that describes the pull between charged particles. In ionic compounds, this force is what binds the cations and anions together in a stable arrangement.
The strength of electrostatic attraction depends on the magnitude of the charges involved and the distance separating them. The equation governing this behavior is Coulomb's Law, where the force is proportional to the product of the charges and inversely proportional to the square of the distance between them:\[ F = k \frac{{q_1 q_2}}{{r^2}} \]Where F is the force of attraction, q_1 and q_2 are the charges, r is the distance between the charges, and k is Coulomb's constant.
In the context of hydration energy, smaller ions with higher charges, like Mg^{2+}, have stronger electrostatic attractions with water molecules compared to larger ions with lower charges, like Na^{+}. This property leads to higher hydration energy for compounds like MgCl_2.

Ionic Radius

The ionic radius is a measure of the size of an ion in an ionic compound. It plays a crucial role in determining how ions interact with each other and with solvents like water.
Smaller ions tend to have higher charge densities, meaning the charge is concentrated over a smaller area. This results in stronger interactions with other ions and polar molecules, leading to increased hydration energy.
For example, the ionic radius of Mg^{2+} is smaller at 72 pm compared to Na^{+} , which has an ionic radius of 102 pm. This smaller size leads to a higher density of the positive charge on Mg^{2+} , causing a stronger attraction with the negative dipole of water molecules. Thus, MgCl_2 has a greater hydration energy than NaCl , primarily due to the smaller ionic radius of the magnesium ion.