Question

The hydrated metal ion that has the largest size is:

• A. Na\(^+\)
• B. Cs\(^+\)
• C. Li\(^+\)
• D. K\(^+\)

Hint:

Smaller cations with higher charge density form larger hydration shells, giving the largest effective hydrated radius.

Answer 1

The Correct Option is C

Step 1: Separate bare ionic radius from hydrated ionic radius.
The bare ionic radius grows down a group: $Li^{+} \lt Na^{+} \lt K^{+} \lt Cs^{+}$. But the question asks about the hydrated radius, which includes the shell of water molecules clinging to the ion, and that shell depends on charge density, not on the bare size alone.

Step 2: Recall approximate bare ionic radii.
\[ Li^{+} \approx 76 \, \text{pm}, \quad Na^{+} \approx 102 \, \text{pm}, \quad K^{+} \approx 138 \, \text{pm}, \quad Cs^{+} \approx 170 \, \text{pm} \]

Step 3: Work out charge density from these radii.
Charge density is roughly charge divided by volume, so for ions carrying the same $+1$ charge, the smallest ion packs the highest charge density. $Li^{+}$, with the smallest radius, has the strongest electric field at its surface.

Step 4: Connect charge density to the size of the hydration shell.
A stronger electric field pulls in and holds onto more water dipoles, more tightly and in more layers. So the ion with the highest charge density, $Li^{+}$, ends up dragging around the largest hydration shell, even though its bare radius is the smallest.

Step 5: Reverse the bare-radius order.
Since hydration shell size runs opposite to bare radius here, the hydrated radius order mirrors the bare radius order:
\[ \text{Hydrated radius: } Li^{+} \gt Na^{+} \gt K^{+} \gt Cs^{+} \]

Step 6: Confirm the answer.
$Cs^{+}$, despite being the biggest bare ion, holds the weakest hydration shell and ends up with the smallest hydrated radius, the opposite of what its bare size would suggest.

Final Answer:
\[ \boxed{Li^{+} \text{ has the largest hydrated radius}} \]