JEE Main · 2025 · 28 Jan 2025 · Shift 1 · Redox Reactions and Electrochemistry

For a strong electrolyte like KCl, molar conductivity falls roughly linearly with $\sqrt{c}$: from the graph, ${\Lambda }_m=100$ S cm² mol⁻¹ at the higher concentration ($\sqrt{c}=0.15$) and ${\Lambda }_m=150$ S cm² mol⁻¹ at the lower, dilute concentration ($\sqrt{c}=0.1$). The cell constant $G^{\ast }=\kappa R$ is fixed for a given cell, and $\kappa =\frac{{\Lambda }_{m}c}{1000}$, so ${\Lambda }_{m}cR$ is the same for both solutions. With $c=(\sqrt{c}{)}^2$: $100\times (0.15{)}^2\times 100=150\times (0.1{)}^2\times R_{dil}$, giving $225=1.5R_{dil}$, so $R_{dil}=150\Omega$.