Problem 44 - Chemistry: An Atoms-Focused Approach

Question

In an aqueous solution containing \(\mathrm{Na}^{+}, \mathrm{Mg}^{2+}, \mathrm{K}^{+},\) and \(\mathrm{Ca}^{2+}\) salts, which cation would you expect to experience the strongest ion-dipole interactions?

Step-by-Step Solution

Answer

Answer: Mg2+

Step 1: Comparing Charges of the Ions

Let's compare the charges of given ions: Na+ has a charge of +1, Mg2+ has a charge of +2, K+ has a charge of +1, and Ca2+ has a charge of +2. Notice that Mg2+ and Ca2+ have higher charges compared to Na+ and K+. So, we can eliminate Na+ and K+ from our options since they experience weaker ion-dipole interactions due to their lower charge.

Step 2: Comparing Sizes of the Ions

Next, let's compare the sizes of the remaining ions, Mg2+ and Ca2+. The ionic radii of Mg2+ is approximately 72 pm, while Ca2+ has an ionic radius of about 100 pm. The smaller ion, Mg2+, will have a stronger ion-dipole interaction due to its smaller size, as it allows the water molecules to come in closer proximity.

Step 3: Determining the Ion with Strongest Ion-Dipole Interactions

Based on the comparison of both charges and sizes of the ions, we have determined that Mg2+ has a higher charge and smaller size compared to the other ions in the aqueous solution. Therefore, Mg2+ would experience the strongest ion-dipole interactions.

Key Concepts

Cation Charges

Understanding cation charges is essential to predicting chemical behavior in solutions. Cations are positively charged ions, and their charge is determined by the number of electrons they lose. In the given exercise, we are dealing with four cations:

• Na⁺ has a charge of +1.
• Mg²⁺ has a charge of +2.
• K⁺ also has a charge of +1.
• Ca²⁺ has a charge of +2.

When considering ion-dipole interactions, the strength of the interaction is affected by the charge of the ion. More charged ions exert a stronger attractive force on the opposite charges of the dipoles in surrounding water molecules. This means that ions with higher charges, such as Mg²⁺ and Ca²⁺, would typically form stronger ion-dipole interactions than Na⁺ and K⁺ with their +1 charge.
Therefore, in solutions, divalent cations (like Mg²⁺ and Ca²⁺) are generally expected to have more potent interactions with water molecules compared to monovalent cations.

Ionic Radii Comparison

Ionic radii can significantly influence the strength of ion-dipole interactions in solutions. The ionic radius is the measure of an ion's size.

• Mg²⁺ has an estimated ionic radius of 72 picometers (pm).
• Ca²⁺ has a larger ionic radius of approximately 100 pm.

Smaller ions, such as Mg²⁺, can draw water molecules closer due to less steric hindrance, enhancing the electrostatic attraction between the oppositely charged regions.
In this exercise, although both Mg²⁺ and Ca²⁺ have the same charge, the smaller ionic radius of Mg²⁺ allows it to participate in stronger ion-dipole interactions than the larger Ca²⁺.
Therefore, in the presence of polar solvents like water, smaller cations will generally form stronger ion-dipole interactions due to their ability to closely approach the solvent molecules, maximizing the attractive forces.

Aqueous Solutions

An aqueous solution is primarily water, and this polar solvent facilitates unique interactions with charged species like cations. Water's dipolar nature, with a partial negative charge near its oxygen atom and a partial positive charge near its hydrogen atoms, allows it to interact with ions through ion-dipole interactions.
In water, cations are stabilized by these interactions as the oxygen atom, carrying a negative partial charge, aligns itself toward the positively charged cation.
Such alignment reduces the net potential energy of the system, stabilizing the solution. For instance, in an aqueous solution, cations like Mg²⁺ and Ca²⁺ not only dissolve but also influence the structure and dynamics of the water around them significantly compared to monovalent ions.
Overall, aqueous solutions provide an essential medium for many chemical reactions where ion behavior is crucial, affecting everything from solubility to conductivity.