Which one of the following ions has highest limiting molar conductivity?

Options

A. `Na^(+)`
B. `Mg^(2+)`
C. `K^(+)`
D. `Ca^(2+)`

Explanation

To determine which ion has the highest limiting molar conductivity, we will follow these steps:

### Step 1: Understand Limiting Molar Conductivity
Limiting molar conductivity (\( \Lambda_m^0 \)) is a measure of the ability of an ion to conduct electricity in solution. It is defined as the conductivity of an infinitely dilute solution divided by the concentration of the electrolyte.

### Step 2: List the Given Ions and Their Limiting Molar Conductivities
We need to compare the limiting molar conductivities of the following ions:
- \( \text{Na}^+ \): 50.70 S cm²/mol
- \( \text{K}^+ \): 73.5 S cm²/mol
- \( \text{Mg}^{2+} \): 106.0 S cm²/mol
- \( \text{Ca}^{2+} \): 119.0 S cm²/mol

### Step 3: Compare the Values
By comparing the values:
- \( \text{Na}^+ \): 50.70 S cm²/mol
- \( \text{K}^+ \): 73.5 S cm²/mol
- \( \text{Mg}^{2+} \): 106.0 S cm²/mol
- \( \text{Ca}^{2+} \): 119.0 S cm²/mol

We can see that \( \text{Ca}^{2+} \) has the highest limiting molar conductivity.

### Step 4: Reasoning Behind the Trend
The trend in limiting molar conductivity can be explained by the size and hydration of the ions:
- Smaller ions tend to have higher limiting molar conductivities due to less hydration.
- \( \text{Ca}^{2+} \) is larger than \( \text{Na}^+ \) and \( \text{K}^+ \), which means it is less hydrated compared to smaller ions like \( \text{Na}^+ \).
- Therefore, despite being a divalent ion, \( \text{Ca}^{2+} \) has the highest limiting molar conductivity due to its size and lower hydration.

### Conclusion
The ion with the highest limiting molar conductivity is \( \text{Ca}^{2+} \).

---