Question

Which among the following cations has the lowest molar ionic conductivity in water at infinite dilution and at 25 degree centigrade?

• A. Hydrogen ion
• B. Lithium ion
• C. Sodium ion
• D. Silver ion

Answer 1

The Correct Option is B

To answer the question of which cation has the lowest molar ionic conductivity in water at infinite dilution and at 25 degrees centigrade, we need to understand the concept of molar ionic conductivity. Molar ionic conductivity refers to the ability of an ion to conduct electricity in a solution and is influenced by the ion's size and charge mobility. Molar ionic conductivity (\(\lambda^0\)) at infinite dilution can be expressed as:

\(\lambda^0 = \frac{\kappa}{c}\)

where \(\kappa\) is the conductivity and \(c\) is the concentration. 

In general, smaller ions with higher charge density tend to have higher ionic conductivity because they move more rapidly through the solution. However, at infinite dilution, the size and the solvation of the ion significantly influence its mobility:

1. Hydrogen ion (\(H^+\)): Hydrogen ions bind with water to form hydronium ions (\(H_3O^+\)), which move very quickly through the solution via proton hopping, which makes them have high conductivity.
2. Lithium ion (\(Li^+\)): Although it is a small ion, its high degree of solvation in water makes it move more slowly, resulting in lower conductivity.
3. Sodium ion (\(Na^+\)): Sodium ions are larger and less solvated compared to lithium, leading to higher mobility and conductivity than lithium ions.
4. Silver ion (\(Ag^+\)): Similar to sodium ions, silver ions also have higher mobility than lithium ions.

From the above explanation, it is evident that lithium ions have a large solvation shell, which hinders their mobility and results in them having the lowest molar ionic conductivity among the given options.

Thus, the correct answer is lithium ion (\(Li^+\)).