The conductivity of a strong electrolyte

Question

UnlockIAS · Accepted Answer

Correct — B, Decreases on dilution. Everything turns on the exact quantity the stem names. Conductivity, also called specific conductance and written as the Greek letter kappa, is the conductance of a solution held between two electrodes of unit area a unit distance apart — that is, the conductance of a unit volume of the solution, with SI units of siemens per metre. Because it is defined per unit volume, it depends on how many current-carrying ions are packed into that volume. Dilute the solution and you put the same number of ions into more water, so the number of ions per unit volume falls, and conductivity falls with it. This is true for strong and weak electrolytes alike, which is why the standard textbook statement is unqualified: conductivity always decreases with a decrease in concentration. The quantity that behaves the other way is molar conductivity, written as lambda-m and defined as the conductance of that volume of solution which contains one mole of the electrolyte — that is, kappa divided by concentration. Because the definition carries the whole mole of electrolyte with it however much water is added, dilution can only help: for a strong electrolyte the ions are already fully dissociated, so molar conductivity rises only slightly as inter-ionic attractions weaken and ionic mobility improves, following the square-root relation lambda-m = lambda-zero minus A times the square root of concentration. So the paper offers two true statements side by side and asks which belongs to the word it printed.

Why the other options are wrong — (a) True — but of the wrong quantity, and this is the whole design of the question. Molar conductivity of a strong electrolyte does increase slightly on dilution, because the ions are already completely dissociated and only their mobility improves as inter-ionic forces weaken. The word 'slightly' is even the giveaway that the option is quoting the strong-electrolyte molar-conductivity result; the stem, however, says conductivity.  (c) No conductance quantity is independent of dilution. Conductivity falls, molar conductivity rises, and only the limiting molar conductivity at infinite dilution is a fixed constant for a given electrolyte at a given temperature — and that is a limiting value, not a measurement at a working concentration.  (d) This escape option requires all three named statements to fail, and the second of them is exactly right. On a question where one option is the textbook sentence almost verbatim, a 'None of the above' is a trap for candidates who suspect a catch; the catch here is real but it is between (a) and (b), not beyond them.

Concept: Three related quantities have to be kept apart. Conductance is simply the reciprocal of resistance, measured in siemens, and depends on the size of the sample. Conductivity, kappa, removes that dependence by referring the conductance to unit length and unit cross-section — it is what a conductivity cell reports after its cell constant has been applied, and it is a property of the solution at that concentration. Molar conductivity, lambda-m, goes one step further and refers the conductance to one mole of dissolved electrolyte, so that solutions of different strengths can be compared fairly. The three are related by lambda-m = kappa divided by concentration, and that single equation explains the apparent paradox: when concentration falls, kappa falls too, but it falls more slowly than the concentration in the denominator, so the ratio rises. Extrapolating lambda-m to zero concentration gives the limiting molar conductivity, which for weak electrolytes cannot be measured directly and must be built up from ionic values using Kohlrausch's law of independent migration of ions.

State PCS 2025 Q106 — Science & Technology PYQ with Answer

State PCS 2025 Q106 — Science & Technology PYQ with Answer