Problem 33 - Chemistry in 30 days

Question

Which of the following has the highest ionic conductivity in solution? (a) \(\mathrm{Rb}^{+}\) (b) \(\mathrm{K}^{+}\) (c) \(\mathrm{Li}^{+}\) (d) \(\mathrm{Na}^{+}\)

Step-by-Step Solution

Answer

(b) \(\mathrm{K}^{+}\) has the highest ionic conductivity in solution.

Step 1: Define Ionic Conductivity

Ionic conductivity is the measure of an ion's ability to carry an electrical current in a solution. It depends on the ion's size and mobility.

Step 2: Analyze Ion Size

In general, larger ions tend to have lower mobility in a solution and hence lower ionic conductivity. Order in size from smallest to largest: \(\mathrm{Li}^{+} < \mathrm{Na}^{+} < \mathrm{K}^{+} < \mathrm{Rb}^{+}\). Smaller ions tend to be more mobile.

Step 3: Consider Ion Mobility

Smaller ions are more strongly solvated (surrounded by solvent molecules), which can impede their mobility. Therefore, there is a balance between the size of the ion and solvation effects. \(\mathrm{Li}^{+}\) is highly solvated, reducing its conductivity.

Step 4: Summarize Conductivity Trends

The most mobile and least solvated larger ions generally have higher conductivity in solution. Even though \(\mathrm{Li}^{+}\) is the smallest, \(\mathrm{K}^{+}\) usually exhibits higher ionic conductivity due to a balance between mobility and solvation.

Key Concepts

Ion Mobility

Ion mobility refers to the speed at which an ion moves through a solution when an electric field is applied. It is a crucial factor in determining ionic conductivity. When ions can easily move through the solution, they can carry electrical current more efficiently.
Several factors can affect ion mobility:

• Viscosity of the solution - thicker solutions can slow down ion movement.
• Strength of the electric field - stronger fields can increase mobility.
• Temperature - higher temperatures often enhance mobility by reducing solution viscosity.

However, ion size also plays a significant role, which leads to the next important factor: the size of the ion.

Ion Size

The size of an ion can significantly impact its mobility within a solution. Smaller ions, although they might seem like they'd move faster, often face a unique challenge. They tend to attract a tight shell of solvent molecules that affects their mobility.
Larger ions experience less of this solvation effect, allowing them to move more freely, depending on the balance between size and solvation.

• Small ions (like  ext{Li}^{+}) get solvated more heavily, reducing mobility.
• Larger ions (like  ext{K}^{+} or  ext{Rb}^{+}) usually face less solvation hindrance, potentially enhancing mobility.

This interaction between ion size and solvation significantly influences ionic conductivity in solutions.

Solvation Effects

Solvation effects describe the interaction between ions and the solvent molecules surrounding them. This phenomena greatly impacts both the ion's mobility and its ability to conduct electricity through a solution.
Solvent molecules create a shell around ions in a process called solvation. For smaller ions, this shell is typically denser, which can:

• Decrease ion mobility, as the ions drag along more solvent molecules.
• Impact overall conductivity due to added resistance.

The balance between being small enough to be easily solvated yet large enough to minimize solvation hindrance is crucial. This balance is why some larger ions, like  ext{K}^{+}, can sometimes outperform smaller ions like  ext{Li}^{+} in terms of ionic conductivity.