Kohlrausch examined the limiting molar conductivity (Λ°m) of a number of strong electrolytes and observed certain regularities. On the basis of these observations he enunciated the Kohlrausch law of independent migration of ions. The law states that the limiting molar conductivity of an electrolyte can be represented as the sum of the individual contributions of the anion and the cation of the electrolyte. Thus, for sodium chloride:
\(\Lambda^{\circ}_m(\text{NaCl}) = \lambda^{\circ}_{\text{Na}^+} + \lambda^{\circ}_{\text{Cl}^-}\)
Using the Kohlrausch law, it is possible to calculate Λ°m for any electrolyte from the λ° of its individual ions. For a weak electrolyte such as acetic acid, Λ°m can also be obtained from the Λ°m values of strong electrolytes:
\(\Lambda^{\circ}_m(\text{CH}_3\text{COOH}) = \Lambda^{\circ}_m(\text{CH}_3\text{COONa}) + \Lambda^{\circ}_m(\text{HCl}) - \Lambda^{\circ}_m(\text{NaCl})\)
Consider the following statements about weak electrolytes such as acetic acid.
(A) For a weak electrolyte, the molar conductivity increases steeply on dilution, especially near lower concentrations.
(B) At infinite dilution, a weak electrolyte dissociates completely, and the conductivity of its solution at such a low concentration can be measured accurately.
(C) At any concentration c, the degree of dissociation of a weak electrolyte can be approximated to the ratio of its molar conductivity at that concentration to its limiting molar conductivity.
(D) Weak electrolytes such as acetic acid have a higher degree of dissociation at higher concentrations.
Which of the statements given above are correct? Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → (A) and (C) only
A weak electrolyte is only partly dissociated, and its degree of dissociation (α) rises as the solution is diluted. This decides how its molar conductivity changes with concentration.
(A) For a weak electrolyte, the molar conductivity increases steeply on dilution, especially near lower concentrations. — True. On dilution α increases, so one mole of the electrolyte gives more ions; Λm therefore rises steeply, most of all at low concentrations.
(B) At infinite dilution, a weak electrolyte dissociates completely, and the conductivity of its solution at such a low concentration can be measured accurately. — False. Dissociation is complete (α = 1) at infinite dilution, but the conductivity is then so low that it cannot be measured accurately.
(C) At any concentration c, the degree of dissociation of a weak electrolyte can be approximated to the ratio of its molar conductivity at that concentration to its limiting molar conductivity. — True. This is the relation
\( \displaystyle \alpha = \frac{\Lambda_m}{\Lambda^{\circ}_m} \)
(D) Weak electrolytes such as acetic acid have a higher degree of dissociation at higher concentrations. — False. At higher concentrations a weak electrolyte has a lower degree of dissociation; α increases only as the solution is diluted.
NCERT (2026-27 edition):
2.4.2 Variation of Conductivity and Molar Conductivity with Concentration – “Weak electrolytes like acetic acid have lower degree of dissociation at higher concentrations and hence for such electrolytes, the change in Λm with dilution is due to increase in the degree of dissociation and consequently the number of ions in total volume of solution that contains 1 mol of electrolyte. In such cases Λm increases steeply … on dilution, especially near lower concentrations. Therefore, Λ°m cannot be obtained by extrapolation of Λm to zero concentration. At infinite dilution (i.e., concentration c → zero) electrolyte dissociates completely (α =1), but at such low concentration the conductivity of the solution is so low that it cannot be measured accurately.”
“…At any concentration c, if α is the degree of dissociation then it can be approximated to the ratio of molar conductivity Λm at the concentration c to limiting molar conductivity, Λ°m.”
\( \displaystyle \alpha = \frac{\Lambda_m}{\Lambda^{\circ}_m} \qquad (2.26) \)