A $5.0 \mathrm{mmol} \mathrm{dm}^{-3}$ aqueous solution of KCl has a conductance of 0.55 mS when measured in a cell of cell constant $1.3 \mathrm{~cm}^{-1}$. The molar conductivity of this solution is _____ $\mathrm{mSm}^{2} \mathrm{~mol}^{-1}$. (Round off to the nearest integer).

JEE Main · 2021 · 16 Mar 2021 · Shift 2 · Redox Reactions and Electrochemistry

5.0 mmol dm^{- 3}

aqueous solution of KCl has a conductance of 0.55 mS when measured in a cell of cell constant

1.3 cm^{- 1}

. The molar conductivity of this solution is _____

mSm^{2} mol^{- 1}

. (Round off to the nearest integer).

Answer: 14

The conductivity follows from the measured conductance and the cell constant,

κ = G \times \frac{l}{A} = 0.55 \times 1.3 = 0.715

mS cm

^{- 1}

, and one siemens per centimetre is a hundred siemens per metre, so

κ = 71.5

mS m

^{- 1}

. The concentration

5.0

mmol dm

^{- 3}

5.0

mol m

^{- 3}

in the same system of units, so

Λ_{m} = \frac{κ}{c} = \frac{71.5}{5.0} = 14.3 mS m^{2} mo l^{- 1}

To the nearest integer the molar conductivity is 14 mS m

^{2}

mol

^{- 1}

JEE Main · 2021 · 16 Mar 2021 · Shift 2 · Integer answer