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

If, for the higher concentration of KCl solution, the resistance of the conductivity cell is 100Omega$100\Omega$ then the resistance of the same cell with the dilute solution is mathrmxOmega$\mathrm{x}\Omega$ The value of mathbfx$\mathbf{x}$ is (Nearest integer)

### Related Formula Conductivity relationship with cell parameters: kappa = G cdot G^* = fracG^*R$$\kappa = G \cdot G^* = \frac{G^*}{R}$$ lambda_m = frackappa times 1000C$$\lambda_m = \frac{\kappa \times 1000}{C}$$ where G^*$G^*$ represents the static cell constant. ### Step 1: Setting Up Ratios Using concentration subscripts c$c$ (concentrated) and d$d$ (dilute): frackappa_ckappa_d = fracR_dR_c$$\frac{\kappa_c}{\kappa_d} = \frac{R_d}{R_c}$$ Expressing conductivity through molar conductivity values: kappa = fraclambda_m cdot C1000$$\kappa = \frac{\lambda_m \cdot C}{1000}$$ frac(lambda_m cdot C)_c(lambda_m cdot C)_d = fracR_dR_c$$\frac{(\lambda_m \cdot C)_c}{(\lambda_m \cdot C)_d} = \frac{R_d}{R_c}$$ Substituting the graphical read coordinates (C_c = 0.15^2, C_d = 0.1^2$C_c = 0.15^2, C_d = 0.1^2$ with scaled lambda_m$\lambda_m$ parameters): frac100 cdot (0.15)^2150 cdot (0.1)^2 = fracR_d100$$\frac{100 \cdot (0.15)^2}{150 \cdot (0.1)^2} = \frac{R_d}{100}$$ R_d = 150\,Omega$$R_d = 150\,\Omega$$ ### Pattern Recognition Sees: Resistance correlation across specific graph coordinates. Shortcut: Equate cell parameters through kappa propto frac1R$\kappa \propto \frac{1}{R}$ and solve for the target resistance directly. ### Evaluation Rubric / Model Answer null ### Chapter Mix Class 12 Chemistry: Electrochemistry