Given below is the plot of the molar conductivity vs $\sqrt{concentration}$ for KCl in aqueous solution.

If, for the higher concentration of KCl solution, the resistance of the conductivity cell is 100Ω, then the resistance of the same cell with the dilute solution is ‘x’Ω. The value of x is _________ (nearest integer)

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answer is 150.

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Detailed Solution

$\begin{aligned} R = ρ \frac{ℓ}{A} \\ κ = G \cdot G^{*} G = \frac{1}{R}; κ = \frac{1}{ρ} \\ G^{*} = \frac{ℓ}{A} \\ R = Resistance \\ ρ = Resistivity \\ \frac{ℓ}{A} = cellconstant (G^{*}) \end{aligned}$

$\begin{aligned} \frac{κ_{c}}{κ_{d}} = \frac{R_{d}}{R_{c}}; λ_{m} = \frac{κ \times 1000}{C} \\ \frac{κ_{c}}{κ_{d}} = \frac{(λ_{m} \cdot C)}{{(λ_{m} \cdot C)}_{d}} = \frac{R_{d}}{R_{c}} \\ \frac{c = concentrated sol.}{} d = diluted solution \\ \frac{100 \cdot (0.15)^{2}}{150 \cdot (0.1)^{2}} = \frac{R_{d}}{100} \\ R_{d} = 150 Ω \end{aligned}$