BPSC 70th CCE Re-exam Prelims General Studies · Question 106 of 142

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.

• (a)Increases slightly on dilution — 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)Does not changes with dilution — 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)None of the above — 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.

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.

The habit that answers this question is to read the noun before reasoning about the trend, because chemistry gives conductance three names with three different behaviours and an examiner will always offer at least two of them. Once the noun is fixed as conductivity, ask what it is defined per: per unit volume. Then dilution obviously thins out the carriers and the answer follows in one step. Keep the paired result attached, because the same paper elsewhere may ask it: molar conductivity increases on dilution, slightly for a strong electrolyte such as potassium chloride or sulphuric acid, and steeply for a weak electrolyte such as acetic acid, where dilution actually increases the degree of dissociation and creates new ions rather than merely freeing existing ones. That contrast is the discriminator between strong and weak in every question on this topic, and it is also how the strength of a weak acid is measured — the sharp rise in molar conductivity on dilution is the experimental signature of an equilibrium shifting towards dissociation.

• Conductivity (specific conductance, kappa) is the conductance of a unit volume of solution, SI unit siemens per metre; it always decreases as concentration decreases, for both strong and weak electrolytes
• Molar conductivity lambda-m = kappa ÷ concentration, the conductance of the volume containing one mole of electrolyte; it increases on dilution
• For a strong electrolyte the increase in molar conductivity on dilution is small and follows lambda-m = lambda-zero − A√c, the Debye–Hückel–Onsager relation, because dissociation is already complete and only ionic mobility improves
• For a weak electrolyte such as acetic acid the increase is steep, because dilution raises the degree of dissociation and creates additional ions
• Limiting molar conductivity for a weak electrolyte cannot be found by extrapolation; it is obtained from Kohlrausch's law of independent migration of ions

• Reading 'conductivity' as 'molar conductivity' — the two move in opposite directions on dilution, and the option set will contain both answers
• Believing conductivity behaves differently for strong and weak electrolytes; it falls on dilution for both, and only the molar conductivity curves differ in shape
• Confusing conductance (sample-dependent) with conductivity (a property of the solution)

BPSC lifts a single line from the chapter and offers the neighbouring line as the distractor, so the mark is won by reading the exact term in the stem rather than by deeper chemistry. UPSC rarely asks conductance theory at all; when electrochemistry appears in the General Studies paper it is applied — dry cells, lead-acid batteries, fuel cells, electroplating — so the same chapter has to be revised once for the definition and once for the application.

• practice — not a real PYQ

  On dilution, the molar conductivity of a weak electrolyte such as acetic acid

  • (a)decreases sharply
  • (b)increases sharply
  • (c)remains constant
  • (d)first decreases and then increases

  Answer(b) increases sharply — because dilution increases the degree of dissociation, producing more ions per mole of electrolyte, unlike a strong electrolyte where the rise is only slight.

• practice — not a real PYQ

  The SI unit of conductivity (specific conductance) is

  • (a)ohm metre
  • (b)siemens per metre
  • (c)siemens square metre per mole
  • (d)siemens

  Answer(b) siemens per metre — siemens alone is the unit of conductance, and siemens square metre per mole is the unit of molar conductivity.