Four different electrolyte solutions with the concentrations given below have the same molar conductivity value of \( 1.29 × 10^{-4}\, S\, m^2\, mol^{-1} \). Arrange them in increasing order of their conductivity values:
(A) 0.1 M
(B) 0.075 M
(C) 0.15 M
(D) 0.05 M
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → (D), (B), (A), (C)
Molar conductivity is the conductivity per unit molar concentration:
\( \displaystyle \Lambda_m = \frac{\kappa}{c} \quad \Rightarrow \quad \kappa = \Lambda_m \times c \)
All four solutions have the same molar conductivity, so their conductivity is directly proportional to the concentration. With \( \Lambda_m = 1.29 \times 10^{-4}\ \mathrm{S\,m^2\,mol^{-1}} \) and \( c \) in mol m−3 (1 M = 1000 mol m−3):
(D) 0.05 M: \( \kappa = 1.29 \times 10^{-4} \times 50 = 0.00645\ \mathrm{S\,m^{-1}} \)
(B) 0.075 M: \( \kappa = 1.29 \times 10^{-4} \times 75 = 0.00968\ \mathrm{S\,m^{-1}} \)
(A) 0.1 M: \( \kappa = 1.29 \times 10^{-4} \times 100 = 0.0129\ \mathrm{S\,m^{-1}} \)
(C) 0.15 M: \( \kappa = 1.29 \times 10^{-4} \times 150 = 0.0194\ \mathrm{S\,m^{-1}} \)
Shortcut: With \( \Lambda_m \) the same, no calculation is needed: increasing conductivity is the order of increasing concentration, 0.05 < 0.075 < 0.1 < 0.15.