Read the passage carefully and answer the Questions.
Molar conductivity (\( Λ_m \)) of a solution at a given concentration (c) is the conductance of volume, V of solution, containing one mole of electrolyte kept between the two electrodes with area of cross-section A and at a distance of unit length. It increases with the decrease in concentration and when the concentration approaches zero, the molar conductivity is called limiting molar conductivity (\( Λ^0_m \)). For a strong electrolyte, \( Λ_m \) increases linearly with dilution and is given by \( Λ_m = Λ^0_m -Ac^{1/2} \). The value of the constant A for a given solvent depends on the type of electrolyte along with temperature. According to Kohlrausch law, the value of \( Λ^0_m \) for an electrolyte is \( Λ^0_m=v_+λ^0_+ + v_-λ^0_- \), where \( v_+ \) and \( v_- \) are the number of cations and anions, respectively, per molecule of the electrolyte and \( λ^0_+ \) and \( λ^0_- \) are limiting molar conductivities of cation and anion, respectively. Kohlrausch law finds many applications, like determining the solubility of a sparingly soluble salt, determining the degree of dissociation (\( Λ_m/Λ^0_m \)) and the dissociation constant of a weak electrolyte.
Which one of the following has a different value of constant A in water?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \(CaCl_2\)
In the equation \( \Lambda_m = \Lambda^{0}_m - A\,c^{1/2} \), the constant A depends, for a given solvent and temperature, on the type of electrolyte, that is, on the charges on the cation and anion it gives. Electrolytes are grouped as 1-1, 2-1, 2-2 and so on, and all electrolytes of one type have the same value of A. Count the charges from the dissociation of each salt:
\( \ce{CaCl2 -> Ca^2+ + 2Cl-} \): a doubly charged cation with singly charged anions, a 2-1 electrolyte.
\( \ce{KCl -> K+ + Cl-} \): a 1-1 electrolyte.
\( \ce{NaCl -> Na+ + Cl-} \): a 1-1 electrolyte.
\( \ce{LiCl -> Li+ + Cl-} \): a 1-1 electrolyte.
KCl, NaCl and LiCl are all 1-1 electrolytes and share one value of A in water. So the salt with a different value of A is \( \ce{CaCl2} \).
NCERT (2026-27 edition):
Strong Electrolytes
