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

If, for the higher concentration of KCl solution, the resistance of the conductivity cell is $100 \Omega$, then the resistance of the same cell with the dilute solution is ' $x$ ' $\Omega$
The value of $x$ is __________ (Nearest integer)

Question

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

If, for the higher concentration of KCl solution, the resistance of the conductivity cell is $100 \Omega$, then the resistance of the same cell with the dilute solution is ' $x$ ' $\Omega$
The value of $x$ is __________ (Nearest integer)

Aicharya · Accepted Answer

$\begin{aligned} & \mathrm{R}=ho \frac{\ell}{\mathrm{A}} \ & \kappa=\mathrm{G} \cdot \mathrm{G}^* \quad \mathrm{G}=\frac{1}{\mathrm{R}} ; \kappa=\frac{1}{ho}\end{aligned}$ $\begin{aligned} \mathrm{G}^*= & \frac{\ell}{\mathrm{A}} \ \mathrm{R} & =	ext { Resistance } \ ho & =	ext { Resistivity } \ \frac{\ell}{\mathrm{A}} & =	ext { cell constant }\left(\mathrm{G}^*ight)\end{aligned}$ $\begin{aligned} & \frac{\kappa_{\mathrm{c}}}{\kappa_{\mathrm{d}}}=\frac{\mathrm{R}_{\mathrm{d}}}{\mathrm{R}_{\mathrm{c}}} ; \lambda_{\mathrm{m}}=\frac{\kappa 	imes 1000}{\mathrm{C}} \ & \frac{\kappa_{\mathrm{c}}}{\kappa_{\mathrm{d}}}=\frac{\left(\lambda_{\mathrm{m}} \cdot \mathrm{C}ight)}{\left(\lambda_{\mathrm{m}} \cdot Cight)_{\mathrm{d}}}=\frac{\mathrm{R}_{\mathrm{d}}}{R_{\mathrm{c}}} \quad \ & \mathrm{c}=	ext { concentrated sol. } \quad \mathrm{d} 	ext { = diluted solution } \ & \frac{100 \cdot(0.15)^2}{150.(0.1)^2}=\frac{R_{\mathrm{d}}}{100} \ & \mathrm{R}_{\mathrm{d}}=150 \Omega\end{aligned}$

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

Solution