Match the LIST-I with LIST-II.
| LIST-I Property | LIST-II Unit | ||
| A. | Conductivity | I. | m−1 |
| B. | Resistivity | II. | S m2 mol-1 |
| C. | Cell constant | III. | Ω m |
| D. | Molar conductivity | IV. | S m−1 |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → A-IV, B-III, C-I, D-II
All four quantities come from the resistance of a column of solution of length l and area of cross-section A:
\( \displaystyle R=\rho\,\frac{l}{A} \)
\( \displaystyle \kappa=\frac{1}{\rho} \)
\( \displaystyle \Lambda_m=\frac{\kappa}{C} \)
Each unit follows from these definitions (resistance in Ω, conductance in S = Ω−1).
A. Conductivity — This matches IV. S m−1. Conductivity is the reciprocal of resistivity, so its unit is (Ω m)−1 = S m−1.
B. Resistivity — This matches III. Ω m. From R = ρl/A, ρ = RA/l, whose unit is Ω × m2/m = Ω m.
C. Cell constant — This matches I. m−1. The cell constant is l/A, a length divided by an area, so its unit is m/m2 = m−1.
D. Molar conductivity — This matches II. S m2 mol-1. Dividing conductivity by concentration in mol m−3 gives:
\( \displaystyle \frac{\mathrm{S\,m^{-1}}}{\mathrm{mol\,m^{-3}}}=\mathrm{S\,m^{2}\,mol^{-1}} \)
Shortcut: A–IV appears only in Options (2) and (4), and B–III then leaves only Option (2).