The specific conductance of a $0.1 \ N \ KCl$ solution at $23 \ ^oC$ is $0.012 \ \Omega^{-1} \ cm^{-1}$. The resistance of a cell containing the solution at the same temperature was found to be $55 \ \Omega$. The cell constant will be .............. $cm^{-1}$.

Which of the following expressions represents the molar conductivity of an $AB_3$ type electrolyte?

An electrolyte of a polymer-salt complex of poly(ethylene oxide)-LiCF$_{3}$SO$_{3}$ is shaped into a free standing circular film of $20 \ mm$ diameter and a thickness of $20 \ \mu m$. When it is sandwiched between $2$ stainless steel circular electrodes of the same diameter, this cell exhibits a conductance of $\frac{314}{5} \ S$. What is the specific conductivity of the electrolyte?

At $298 \ K$,the limiting molar conductivity of a weak monobasic acid is $4 \times 10^2 \ S \ cm^2 \ mol^{-1}$. At $298 \ K$,for an aqueous solution of the acid,the degree of dissociation is $\alpha$ and the molar conductivity is $y \times 10^2 \ S \ cm^2 \ mol^{-1}$. At $298 \ K$,upon $20$ times dilution with water,the molar conductivity of the solution becomes $3y \times 10^2 \ S \ cm^2 \ mol^{-1}$. $(1)$ The value of $\alpha$ is. . . . . . $(2)$ The value of $y$ is. . . . . .

The conductivity of $0.20 \, M$ solution of $KCl$ at $298 \, K$ is $0.0248 \, S \, cm^{-1}$. Calculate its molar conductivity.

$\wedge _m^o$ for $NaCl$,$HCl$ and $NaA$ are $126.4$,$425.9$ and $100.5 \ S \ cm^2 \ mol^{-1}$,respectively. If the conductivity of $0.001 \ M \ HA$ is $5 \times 10^{-5} \ S \ cm^{-1}$,degree of dissociation of $HA$ is