Question

Correct order of limiting molar conductivity for cations in water at 298 K is :

• A. \( H^+>K^+>Ca^{2+}>Mg^{2+} \)
• B. \( H^+>Ca^{2+}>Mg^{2+}>K^+ \)
• C. \( Mg^{2+}>H^+>Ca^{2+}>K^+ \)
• D. \( H^+>Na^+>Ca^{2+}>Mg^{2+}>K^+ \)

Hint:

The limiting molar conductivity depends on the size and charge of the ion. Smaller and highly charged ions are more hydrated, leading to lower mobility and thus lower conductivity. However, \(H^+\) has exceptionally high conductivity due to its movement through a proton hopping mechanism.

Answer 1

The Correct Option is B

Limiting Molar Conductivities of ions :

$\lambda^0_{H^+} : 349.8 \text{ Sem}^2 \text{mol}^{-1}$

$\lambda^0_{Na^+} : 50.11 \text{ Sem}^2 \text{mol}^{-1}$

$\lambda^0_{K^+} : 73.52 \text{ Sem}^2 \text{mol}^{-1}$

$\lambda^0_{Ca^{2+}} : 119 \text{ Sem}^2 \text{mol}^{-1}$

$\lambda^0_{Mg^{2+}} : 106.12 \text{ Sem}^2 \text{mol}^{-1}$

Therefore correct order of limiting molar conductivity of cations will be -

$H^+>Ca^{2+}>Mg^{2+}>K^+>Na^+$

Answer 2

The question asks for the correct order of limiting molar conductivity for cations in water at 298 K. Limiting molar conductivity (\(\Lambda_m^0\)) is the conductivity of an ion when it is at infinite dilution, and no further dissociation occurs.

Among the given options, the correct order is determined by understanding the mobility of ions in water. The mobility and consequently the limiting molar conductivity of ions mainly depend on the size of the hydrated ions and the charge on the ions. Higher mobility results in higher conductivity.

• \(H^+\) ion: The proton (\(H^+\)) has the highest limiting molar conductivity. This is primarily because of its ability to move quickly through the Grotthuss mechanism, a unique chain mechanism of proton transfer.
• \(Ca^{2+}\) and \(Mg^{2+}\): These ions are divalent, which can affect their hydration and mobility. However, calcium generally has higher conductivity than magnesium due to larger ionic radius and less hydration.
• \(K^+\): As a monovalent cation, potassium has lower limiting molar conductivity compared to \(H^+\), \(Ca^{2+}\), and \(Mg^{2+}\) due to its larger size and higher degree of hydration.

Thus, the order based on the limiting molar conductivity is:

\(H^+ > Ca^{2+} > Mg^{2+} > K^+\)

Therefore, the correct answer is: \( H^+ > Ca^{2+} > Mg^{2+} > K^+ \)