Limiting Molar conductivities for some ions in water at 298 K areIonλ…

The correct answer is Option (1) → HCl , CaCl₂ , MgSO₄ , NaCl

By Kohlrausch’s law of independent migration of ions, the limiting molar conductivity of an electrolyte is the sum of the contributions of its ions. Each ion counts as many times as it appears in the formula: if one formula unit gives ν₊ cations and ν₋ anions,

    \( \displaystyle \Lambda^{\circ}_m=\nu_{+}\lambda^{\circ}_{+}+\nu_{-}\lambda^{\circ}_{-} \)

Using the given values (in S cm² mol⁻¹):

• HCl — first (highest). One H⁺ and one Cl⁻. H⁺ has by far the largest λ° of all the ions given.

      \( \displaystyle \Lambda^{\circ}_m(\ce{HCl})=349.6+76.3=425.9 \)

• CaCl₂ — second. \( \ce{CaCl2 -> Ca^2+ + 2Cl^-} \): one Ca²⁺ and two Cl⁻.

      \( \displaystyle \Lambda^{\circ}_m(\ce{CaCl2})=119.0+2(76.3)=271.6 \)

• MgSO₄ — third. One Mg²⁺ and one SO₄²⁻.

      \( \displaystyle \Lambda^{\circ}_m(\ce{MgSO4})=106.0+160=266.0 \)

• NaCl — last (lowest). One Na⁺ and one Cl⁻; Na⁺ has the smallest λ° in the table.

      \( \displaystyle \Lambda^{\circ}_m(\ce{NaCl})=50.1+76.3=126.4 \)

Note: It seems that there is a mistake in the original NTA paper, which prints the unit of λ° as S m² mol⁻¹ when it should read S cm² mol⁻¹.

NCERT (2026-27 edition):
Variation of Conductivity and Molar Conductivity with Concentration – “… On the basis of the above observations he enunciated Kohlrausch law of independent migration of ions. The law states that limiting molar conductivity of an electrolyte can be represented as the sum of the individual contributions of the anion and cation of the electrolyte. …

In general, if an electrolyte on dissociation gives ν₊ cations and ν₋ anions then its limiting molar conductivity is given by:

    \( \displaystyle \Lambda^{\circ}_m=\nu_{+}\lambda^{\circ}_{+}+\nu_{-}\lambda^{\circ}_{-} \)    (2.25)

Here, λ°₊ and λ°₋ are the limiting molar conductivities of the cation and anion respectively. The values of λ° for some cations and anions at 298 K are given in Table 2.4.”

Table 2.4: Limiting Molar Conductivity for some Ions in Water at 298 K