The conductivity of an electrolytic solution is measured with a conductivity cell, which has two electrodes a fixed distance l apart, each with an area of cross-section A. The resistance R of the cell is given by R = ρl/A = l/(κA), where ρ is the resistivity and κ the conductivity of the solution.
The quantity l/A is constant for a given cell; it is denoted by G* and is called the cell constant. It is found by measuring the resistance of the cell filled with a KCl solution whose conductivity is known accurately at various concentrations: G* = l/A = Rκ.
The molar conductivity of a solution, Λm, is its conductivity divided by its molar concentration (Λm = κ/c). Its SI unit is S m2 mol−1 when c is expressed in mol m−3. Conductivity always decreases with decrease in concentration, for both strong and weak electrolytes, because the number of ions per unit volume that carry the current in the solution decreases.
Which of the following statements is incorrect?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → The unit of the cell constant is cm s−1
The passage defines the cell constant as G* = l/A, the distance between the electrodes divided by their area of cross-section. Its unit is therefore length divided by area:
\( \displaystyle G^*=\frac{l}{A}=\frac{\mathrm{cm}}{\mathrm{cm^2}}=\mathrm{cm^{-1}} \)
Option (1) The conductivity of a solution in S cm−1 is the conductance of a column of the solution 1 cm long with an area of cross-section of 1 cm2 — A correct statement. Since κ = G × l/A, putting l = 1 cm and A = 1 cm2 gives κ = G: conductivity is the conductance of a unit cube of the solution.
Option (2) The SI unit of conductivity (specific conductance) is Ω−1 m−1 — A correct statement. The SI unit of conductivity is S m−1, and 1 S = 1 Ω−1.
Option (3) The unit of the cell constant is cm s−1 — An incorrect statement. The unit of l/A is cm−1; cm s−1 is a unit of speed.
Option (4) The conductivity of a solution decreases with decrease in concentration — A correct statement. On dilution the number of ions per unit volume that carry the current decreases, for both strong and weak electrolytes.
NCERT (2026-27 edition):
2.4.1 Measurement of the Conductivity of Ionic Solutions – “The quantity l/A is called cell constant denoted by the symbol, G*. It depends on the distance between the electrodes and their area of cross-section and has the dimension of length–1 and can be calculated if we know l and A.”